Students undertake a project, involving original research in one of the School's research themes, which encompass a diverse range of "cutting-edge" topics, including: active galaxies, astrophysical fluid dynamics and magneto-hydrodynamics, galaxy evolution, first stars, the formation of stars, stellar evolution, stellar nucleosynthesis, nuclear astrophysics, chemical evolution, galactic archaeology, supernovae and supernovae remnants, neutron stars, stellar transients, supermassive black holes, high energy astrophysics, gravitational wave astronomy, stellar and planetary dynamics and exoplanets. A full list of projects will be made available to students prior to commencing their MSc program.

The research project may be observational, computational or theoretical in nature, or it may involve a combination of these research paradigms. Each student will be assigned an academic supervisor (or supervisors), who will oversee the research project and provide mentoring. Students will be required to undertake a comprehensive literature review and report their preliminary results via a seminar. The major outcomes of the project will be communicated in the form of a thesis. Students will also be required to defend their research outcomes via an oral examination. For most students their project will be continued into the second year of the MSc program; hence ASP4000 will lay the foundations for a substantial ongoing research project in the second year of the degree.

As part of their research training, students will be affiliated with one of the School's research groups (aligned with their research project) and will be required to attend weekly group meetings, seminars and colloquia. Opportunities will also be provided to students to receive training in specialist areas associated with their research project, e.g., technical computing, visualisation of data, specific observational techniques, etc.

On completion of this unit students will be able to:

1. Understand, use and explain the basic concepts and principles of the research literature which underpin the chosen area of astrophysics research.
2. Synthesise and interpret the knowledge gained in the study of the underpinning research literature. This leads to the ability to identify a niche topic or topics within this existing body of literature, which represents a gap in current knowledge. This problem should be suitable for original research.
3. Advance our understanding of an existing problem or problems in the chosen area for original research.
4. Present the results of the original research in written form as a thesis, and also present key thesis results in oral form as a final seminar.
5. Defend the results of the original research in an oral exam.

Literature review: 20%

Seminar: 10%

Thesis: 70%

48 hours per week which includes 36 hours of independent research; 7 hours of literature review, seminar and thesis preparation; 3 hours attendance at group meetings, seminars colloquia; 1 hour specialist training and 1 hour consultation with supervisor.

See also Unit timetable information

Master of Science in Astrophysics

Students undertake a project, involving original research in one of the School's research themes, which encompass a diverse range of "cutting-edge" topics, including: active galaxies, astrophysical fluid dynamics and magneto-hydrodynamics, galaxy evolution, first stars, the formation of stars, stellar evolution, stellar nucleosynthesis, nuclear astrophysics, chemical evolution, galactic archaeology, supernovae and supernovae remnants, neutron stars, stellar transients, supermassive black holes, high energy astrophysics, gravitational wave astronomy, stellar and planetary dynamics and exoplanets. A full list of projects will be made available to students prior to commencing their MSc program.

The research project may be observational, computational or theoretical in nature, or it may involve a combination of these research paradigms. Each student will be assigned an academic supervisor (or supervisors), who will oversee the research project and provide mentoring. Students will be required to undertake a comprehensive literature review and report their preliminary results via a seminar. The major outcomes of the project will be communicated in the form of a thesis. Students will also be required to defend their research outcomes via an oral examination. For most students their project will be continued into the second year of the MSc program; hence ASP4001 will lay the foundations for ASP4002Not offered in 2019 and a substantial ongoing research project in the second part of the degree.

As part of their research training, students will be affiliated with one of the School's research groups (aligned with their research project) and will be required to attend fortnightly weekly group meetings, seminars and colloquia. Opportunities will also be provided to students to receive training in specialist areas associated with their research project, e.g., technical computing, visualisation of data, specific observational techniques, etc.

On completion of this unit students will be able to:

1. Understand, use and explain the basic concepts and principles of the research literature which underpin the chosen area of astrophysics research.
2. Synthesise and interpret the knowledge gained in the study of the underpinning research literature. This leads to the ability to identify a niche topic or topics within this existing body of literature, which represents a gap in current knowledge. This problem should be suitable for original research.
3. Advance our understanding of an existing problem or problems in the chosen area for original research.
4. Present the results of the original research in written form of an interim report, and also present key results in oral form as an interim seminar.

Interim Literature review: 20%

Interim Seminar: 20%

Interim Report: 60%

24 hours per week which includes 18 hours of independent research; 4 hours of literature review, seminar and thesis

preparation (averaged over the semester); attendance at group meetings, seminars colloquia equivalent to 1 hour per week; specialist training and consultation with supervisor, 1 hour each per fortnight.

See also Unit timetable information

Master of Science in Astrophysics

Students undertake studies in three selected topics in Astrophysics and related fields, which provide the foundational basis for modern astrophysics and cosmology. These develop expertise in computational astrophysics, observational astronomy, data analysis and the skills required to effectively communicate their findings using contemporary communication tools. The three topics comprise:

Computational astrophysics (compulsory)

Advanced observational astronomy

Foundations of general relativity and cosmology.

NB: Subject to approval by the Chief Examiner, one of the topics in ASP4020 may be replaced by a topic from PHS4020.

On completion of this unit students will be able to:

1. Demonstrate an understanding of fundamental aspects of observational astronomy, computational astrophysics, cosmology, and related disciplines.
2. Develop skills in computation and astronomical observation that are fundamental to the study of astrophysics.
3. Synthesize and interpret astrophysical knowledge.
4. Make effective use of information and communication technology for the collection and analysis of data, the solution to problems in astrophysics and the written/oral presentation of work relevant to the area of study.

Examinations (2 hours): 50%

Tests: 20%

Assignments: 30%

A total of 24 hours per week

• 3-three hours lectures/workshops/tutorials
• Three hours of consultation and online discussions involving peers and staff
• 12 hours of independent study

See also Unit timetable information

Master of Science in Astrophysics

Students undertake studies in three selected topics in Astrophysics and related fields, which provide fundamental instruction in key aspects of modern astrophysics.

These develop expertise in computational modelling, data analysis and the skills required to effectively communicate their findings using contemporary communication tools. The three topics are chosen from:

Dynamics of Exoplanets

Stellar Astrophysics - Part 1

Magneto-Hydrodynamic Theory and Applications - Part 1

NB: Subject to approval by the Chief Examiner, one of the topics in ASP4021 may be replaced by a topic from PHS4021.

On completion of this unit students will be able to:

1. Demonstrate an understanding of fundamental aspects of computational modelling in astrophysics and related disciplines.
2. Develop skills in computational modelling that are fundamental to the study of astrophysics.
3. Synthesise and interpret astrophysical knowledge.
4. Make effective use of information and communication technology for the collection and analysis of data, the solution to problems in astrophysics and the written/oral presentation of work relevant to the area of study.

Examinations (2 hours): 50%

Tests: 20%

Assignments: 30%

24 hours per week

• 3 x Three hours lectures/workshops/tutorials per week
• Three hours of consultation and online discussions involving peers and staff
• 12 hours of independent study per week

See also Unit timetable information

Master of Science in Astrophysics

Students undertake an advanced research project involving original work on a topic chosen in consultation with an academic supervisor. The topic may be a continuation of research completed in ASP4000, enabling a deeper insight into a larger research problem. In this case, it is expected that the research outcomes will also be suitable for submission for publication in a peer-reviewed international journal.

Alternatively, the project may be a separate topic to ASP4000, but the student must display a more mature research methodology than was required for ASP4000.

On completion of this unit students will be able to:

1. Understand, use and explain the basic concepts and principles of the research literature which underpin the chosen area of astrophysics research.
2. Synthesise and interpret the knowledge gained in the study of the underpinning research literature. This leads to the ability to identify a niche topic or topics within this existing body of literature, which represents a gap in current knowledge. This problem should be suitable for original research.
3. Solve an outstanding problem or problems in the chosen area for original research.
4. Present the results of the original research in written form as a thesis, and also present key thesis results in oral form as a final seminar.
5. Defend the results of the original research in an oral exam.

Seminar 20%

Thesis 80%

48 hours per week which includes 36 hours of independent research; 7 hours of final seminar and thesis preparation; 3 hours attendance at group meetings, seminars colloquia; 1-hour specialist training and 1-hour consultation with a supervisor.

See also Unit timetable information

Master of Science in Astrophysics

Students undertake a research project involving original work on a topic chosen in consultation with an academic supervisor. The topic may be a continuation of research completed in ASP4002Not offered in 2019, enabling a deeper insight into a larger research problem. In this case, it is expected that the research outcomes will also be suitable for submission for publication in a peer-reviewed international journal.

Alternatively, the project may be a separate topic to ASP4002Not offered in 2019, but the student must display a more mature research methodology than was required for ASP4002Not offered in 2019.

On completion of this unit students will be able to:

1. Understand, use and explain the basic concepts and principles of the research literature which underpin the chosen area of astrophysics research.
2. Synthesise and interpret the knowledge gained in the study of the underpinning research literature. This leads to the ability to identify a niche topic or topics within this existing body of literature, which represents a gap in current knowledge. This problem should be suitable for original research.
3. Solve an outstanding problem or problems in the chosen area for original research.
4. Present the results of the original research in written form as an interim thesis, and also present key thesis results in oral form as an interim seminar.

Interim seminar 25%

Interim thesis 75%

24 hours per week which includes 18 hours of independent research; 4 hours of literature review, interim seminar and interim thesis preparation (averaged over the semester); attendance at group meetings, seminars colloquia equivalent to 1 hour per week; specialist training and consultation with a supervisor, 1 hour each per fortnight.

See also Unit timetable information

Master of Science in Astrophysics

Students undertake advanced studies in three selected topics in astrophysics and related fields. These extend the expertise in astronomical observation, analysis and the skills required to effectively communicate their findings using contemporary communication tools.

Topics comprise:

Advanced data analysis

Gravitational astrophysics

Magneto-hydrodynamic theory and applications - Part 2

NB: Subject to approval by the Chief Examiner, one of the topics in ASP5020 may be replaced by a topic from PHS5020Not offered in 2019.

On completion of this unit students will be able to:

1. Demonstrate an understanding of advanced astrophysics and related disciplines.
2. Demonstrated high-level skills in computation and/or astronomical observation that are essential for advanced astrophysics.
3. Synthesize and interpret advanced astrophysical knowledge.
4. Apply knowledge and critical thinking skills to the solution of complex problems.

Examinations (2 hours): 50%

Tests: 20%

Assignments: 30%

A total of 24 hours per week:

• 3 three-hours of lectures/workshops/tutorials per week
• Three hours of consultation and online discussions involving peers and staff
• 12 hours of independent study per week

See also Unit timetable information

Master of Science in Astrophysics

Students undertake advanced studies in three selected topics in physics and related fields.

These extend the expertise in theoretical and computational physics, data analysis and the skills required to effectively communicate their findings using contemporary communication tools.

The topics are:

Advanced statistical mechanics and critical phenomena

Advanced condensed matter physics - Part B

Advanced quantum information theory and quantum computation

Quantum fluids and many-body theory

X-ray optics and synchrotron science

NB: Subject to approval by the Chief Examiner, one of the topics in PHS5021Not offered in 2019 may be replaced by a topic from ASP5021.

On completion of this unit students will be able to:

1. Demonstrate an understanding of advanced theoretical and computational physics, and related disciplines.
2. Demonstrate high-level skills in theoretical/computation physics and/or experimental physics that are essential for advanced contemporary physics.
3. Synthesize and interpret advanced knowledge in theoretical, computational and/or experimental physics.
4. Apply knowledge and critical thinking skills to the solution of complex problems in contemporary physics.

Examinations (2 hours): 50%

Tests: 20%

Assignments: 30%

A total of 24 hours per week

• 3 three-hours of lectures/workshops/tutorials per week
• Three hours of consultation and online discussions involving peers and staff
• 12 hours of independent study per week

See also Unit timetable information

Master of Science in Astrophysics

Students will undertake a supervised research project. Candidates may commence the honours year at the beginning of either the first or second semester. Students will carry out a research project and present the results of their study in both written and oral form. Information about research projects will be available from the course coordinator towards the end of the preceding semester.

On completion of this unit students will be able to:

1. Critically review the scientific literature in their discipline;
2. Understand, discuss and actively participate in the design, development and implementation of a research project;
3. Execute, analyse and evaluate a set of laboratory-based exercises, showing an improved ability to work with minimal supervision and to implement their own ideas;
4. Demonstrate proficiency in computer-based literature searching word processing and other computer programs commonly used in their chosen chemistry discipline;
5. Experience then discuss the breadth and diversity of the chemical sciences, specifically through, but not limited to, attendance at seminars;
6. Demonstrate proficiency in safe work practices for a chemical laboratory, including the use of MSDS and the performance of risk assessments;
7. Synthesise and present in a format suitable for the discipline, experimental results and data analysis associated with the research project;
8. Present orally the scientific research findings to an appropriate expert audience;
9. Integrate the research findings from the project into the larger context of research in that particular field, primarily through completion of the required thesis;
10. Demonstrate the capability to learn new technical skills within the research project ambit and use these proficiently and safely.

Thesis: 93%

Final presentation: 7% (Hurdle)

Hurdle requirement: To pass this unit a student must complete the proposal presentation.

30 hours of self-guided and supervised study and research per week

See also Unit timetable information

Medicinal chemistry

This unit provides advanced instruction in quantitative methods, thesis writing and current topics to students enrolled in the honours program in medicinal chemistry. Students will gain an understanding of advanced experimental design, data analysis and scientific writing that will assist them in completing their honours thesis. Further classes and coursework relating to current topics in medicinal chemistry will assist students in critical analysis of journal articles, providing further support for their academic development in research science.

On completion of this unit students will be able to:

1. Develop a realistic experimental plan, including a timeline, for the research project undertaken in CHM4180;
2. Appreciate and outline the key principles in Intellectual Property as it relates to the discipline and the CHM4180 research project;
3. Efficiently and competently use appropriate bibliographic software (eg. EndNote);
4. Explain the operation of, and where relevant and appropriate, competently use, the equipment discussed in the workshops component of this course;
5. Demonstrate an appropriate high level of understanding of the material presented in the selected lecture modules - this understanding is demonstrated through the relevant assessment tasks.

Essay: 50%

Statistics coursework: 30%

Oral presentation: 20%

One to three hours of lectures and/or tutorials per week over 12 weeks

See also Unit timetable information

Medicinal chemistry

Student will do a research project in weather, climate or ocean science. The main relevant areas of research are: aerosols (including cloud seeding), boundary layers, climate change, clouds, convection, ENSO, general circulation, synoptic-dynamical meteorology, mesoscale meteorology, numerical modelling, tropical meteorology, and bushfires and fire weather. A full list of project will be made available to students before enrolling in the MSC program. The research project may be theoretical, computational or observation-based. Each student will work under the supervision of at least one of the academic members of staff. The project will involve a literature review, original research, a written thesis and an oral report on the work. In most cases, the project will continue into the second year of the MSc.

On completion of this unit, students will be able to:

1. Understand, synthesise and summarise the existing literature.
2. Identify gaps in our knowledge in their chosen area of research.
3. Develop a research plan
4. Commence original research in the chosen area.
5. Present their preliminary findings in a brief written thesis and oral presentation.

This is unit is the first half of a two-semester research project.

Progress will be assessed through a written progress report (50%) and an oral presentation (50%).

A total of 24 hours per week comprising:

• attendance at a 1-hour seminar
• a 1-hour consultation with the supervisor
• 10 hours per week of reading and summarising the literature (averaged over the semester)
• 1 hour per week developing the research plan (averaged over the semester)
• 10 hours per week of research (averaged over the semester)
• 1 hour per week writing the progress report (averaged over the semester)
• 1 hour per week preparing the oral report (averaged over the semester).

See also Unit timetable information

Master of Science in Atmospheric Science

Students will do a research project in weather, climate or ocean science. The main relevant areas of research are aerosols (including cloud seeding), boundary layers, climate change, clouds, convection, ENSO, general circulation, synoptic-dynamical meteorology, mesoscale meteorology, numerical modeling, tropical meteorology, and bushfires and fire weather. A full list of projects will be made available to students before enrolling in the MSC program. The research project may be theoretical, computational or observation-based. Each student will work under the supervision of at least one of the academic members of staff. The project will involve a literature review, original research, a written thesis and an oral report on the work. In most cases, the project will continue into the second year of the MSc.

On completion of this unit, students will be able to:

1. Understand, synthesise and summarise the existing literature.
2. Identify gaps in our knowledge in their chosen area of research.
3. Advance our knowledge in the chosen area through original research.
4. Present their findings in a written thesis and oral presentation.

This unit is the second half of a two-semester research project.

Literature review: 20%

Oral presentation: 10%

Thesis: 70%

A total of 24 hours per week comprising:

• Attendance at a 1-hour seminar
• A 1-hour consultation with the supervisor
• 17 hours per week of research (averaged over the semester)
• 4 hours per week writing the thesis (averaged over the semester)
• 1 hour per week preparing the oral report (averaged over the semester).

See also Unit timetable information

Master of Science in Atmospheric Science

Students undertake a project, involving original research in one of the School's research themes, which encompass a diverse range of modern Earth Science topics, including: geochemistry, geochronology, geophysics, remote sensing, Geographic Information Systems, spatial data science, soil science, petrology, palaeontology, geodynamics, structural geology, tectonics, biogeography, physical geography, climate science, paleoclimate, hydrogeology, hydrology, ore deposits geology. A full list of projects will be made available to students prior to commencing their MSc program.

The research project may be experimental, computational, theoretical or field based in nature, or it may involve a combination of these research paradigms. Each student will be assigned an academic supervisor (or supervisors), who will oversee the research project and provide mentoring. Students will be required to undertake a comprehensive literature review and report their preliminary results via a seminar. The major outcomes of the project will be communicated in the form of a thesis. Students will also be required to defend their research outcomes via an oral examination. For most students their project will be continued into the second year of the MSc program; hence EAE4000 will lay the foundations for a substantial ongoing research project in the second year of the degree.

As part of their research training, students will be affiliated with one of the School's research groups (aligned with their research project) and will be required to attend weekly group meetings, seminars and colloquia. Opportunities will also be provided to students to receive training in specialist areas associated with their research project, e.g., analytical methods, technical computing, visualisation of data, specific experimental techniques, field techniques, etc.

On completion of this unit students will be able to:

1. Understand, use and explain the basic concepts and principles of the research literature which underpin the chosen area of research in Earth Science.
2. Synthesise and interpret the knowledge gained in the study of the underpinning research literature. This leads to the ability to identify a niche topic or topics within this existing body of literature, which represents a gap in current knowledge. This problem should be suitable for original research.
3. Advance our understanding of an existing problem or problems in the chosen area for original research.
4. Present the preliminary findings in a written report also present key results in oral form as a preliminary seminar.

This is unit is the first half of a two-semester research project.

Progress will be assessed through a written progress report which includes a literature review (50%) and an oral presentation (50%).

24 hours per week

Attendance at weekly group meetings (.5 hours per week)

Attendance at seminars and colloquia (.5 hours per week)

At least .5 hours per week of consultation with the supervisor

Specialist training (approximately .5 hours per week)

Preparation of literature review (approximately 1 hour per week averaged over the semester)

Preparation for the seminar (approximately .5 hours per week averaged over the semester)

Preparation of Progress report (approximately 1.5 hours per week averaged over the semester)

19 hours of independent research per week

See also Unit timetable information

Master of Science in Earth Science

Students undertake a project, involving original research in one of the School's research themes, which encompass a diverse range of modern Earth Science topics, including: geochemistry, geochronology, geophysics, remote sensing, Geographic Information Systems, spatial data science, soil science, petrology, palaeontology, geodynamics, structural geology, tectonics, biogeography, physical geography, climate science, paleoclimate, hydrogeology, hydrology, ore deposits geology. A full list of projects will be made available to students prior to commencing their MSc program.

The research project may be experimental, computational, theoretical or field based in nature, or it may involve a combination of these research paradigms. Each student will be assigned an academic supervisor (or supervisors), who will oversee the research project and provide mentoring. Students will be required to undertake a comprehensive literature review and report their preliminary results via a seminar. The major outcomes of the project will be communicated in the form of a thesis. Students will also be required to defend their research outcomes via an oral examination. For most students their project will be continued into the second year of the MSc program; hence EAE4000 will lay the foundations for a substantial ongoing research project in the second year of the degree.

As part of their research training, students will be affiliated with one of the School's research groups (aligned with their research project) and will be required to attend weekly group meetings, seminars and colloquia. Opportunities will also be provided to students to receive training in specialist areas associated with their research project, e.g., analytical methods, technical computing, visualisation of data, specific experimental techniques, field techniques, etc.

On completion of this unit students will be able to:

1. Understand, use and explain the basic concepts and principles of the research literature which underpin the chosen area of research in Earth Science.
2. Synthesise and interpret the knowledge gained in the study of the underpinning research literature. This leads to the ability to identify a niche topic or topics within this existing body of literature, which represents a gap in current knowledge. This problem should be suitable for original research.
3. Advance our understanding of an existing problem or problems in the chosen area for original research.
4. Present the results of the original research in written form as a thesis, and also present key thesis results in oral form as a preliminary seminar.
5. Defend the results of the original research in an oral exam.

This unit is the second half of a two-semester research project.

Literature review: 20%

Oral presentation: 10%

Thesis: 70%

24 hours per week

• Attendance at weekly group meetings (half hour per week)
• Attendance at seminars and colloquia (half hour per week)
• At least half hour per week of consultation with the supervisor
• Specialist training (approximately half hour per week)
• Preparation of literature review (approximately 1 hour per week averaged over the semester)
• Preparation for the seminar (approximately half hour per week averaged over the semester)
• Preparation of Progress report (approximately 1.5 hours per week averaged over the semester)
• 19 hours of independent research per week

See also Unit timetable information

Master of Science in Earth Science

Dynamical meteorology concerns itself with the causes of atmospheric motion. The unit begins with a scale analysis of the equations of motion for mid latitude weather systems, which leads to the most important theoretical development modern meteorology - the quasi-geostrophic theory. This theory and its generalisation are used to explain Rossby waves and their interaction with the mean state, the development of extratropical cyclones, the causes of vertical motion, and the structure and evolution of cold fronts. The theory for gravity waves is developed also.

On completion of this unit students will be able to:

1. Understand the dynamical principles governing the fluid flow in a rotating frame of reference;
2. Apply these principles to explain the dynamics of many common mid latitude weather systems;
3. Demonstrate a high level of knowledge of the important mathematical techniques used to solve problems in mid latitude dynamics;
4. Read, understand and critically analyse the scientific literature on mid latitude dynamics.

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 2 hours and 10 minutes.

Assignments: 30%

Research paper review: 30%

Examination (2 hours): 40%

A total of 12 hours per week comprising:

• three 1-hour lectures;
• three hours per week on assignments, reports and preparation of a talk;
• six hours of independent study.

See also Unit timetable information

Master of Science in Atmospheric Science

The unit aims to teach the skills of geological mapping in two classic field locations of Australian geology, in Broken Hill (poly-deformed and high-grade metamorphic terrane) and Bermagui (poly-deformed, highly complex terrane). In both field camp, the emphasis will be on observing, recording, and interpreting geologic phenomena in a natural environment. Students will draw on a theoretical background of lectures and laboratory studies in first, second and third-year geology to analyse real rocks in the real world. Students will use their observations and interpretations to construct geological maps and cross-sections and determine the geological history of complex poly-deformed terrane. The concept of key locality for observation and critical thinking for correlation between key locality will be introduced and applied to produce map and cross sections of highly complexly deformed terranes.

On completion of this unit, students will be able to:

1. produce structural geological maps;
2. observe and interpret the distribution of lithologies and structures in the field;
3. correlate observations and interpretations at the outcrop scale to produce consistent map and cross-sections;
4. determine the relationship between structure and metamorphic assemblages;
5. visualise complex three dimensional geometries;
6. unravel the geological history of complexly deformed terranes;
7. determine overprinting relationships from field geology;
8. communicate results in a written report;
9. work in a team environment and communicate of results with peers;
10. equip students with discipline-specific knowledge and expertise appropriate for post-graduate research in the field; equip students with discipline-specific knowledge and expertise enabling them to take their place as professional geologists in industry or government organisations; develop their field mapping techniques.

Fieldwork exercises Broken Hill: 45%

Fieldwork exercises Bermagui: 35%

Presentation: 10%

Report: 10%

• Total of 80 hours for Broken Hill
• Total of 40 hours for Bermagui
• 24 hours independent study

See also Unit timetable information

Master of Science in Earth Science

This is an intensive 12-day field trip to New Zealand, one of the best natural laboratories in which to learn about geology. Apart from being dramatically different to Australia in terms of modern day geological activity, it is a ribbon continent with a complex assembly of allochthonous terranes, part of which was formerly part of Australia. It has hyperactive back arc volcanism, spectacular geothermal activity, very active seismicity and is one of the few countries in the world with glaciers at sea level. Some of the main concepts to be covered will be:

Arcs and back-arc architecture, seismicity and volcanism

Transpressional fault systems

Geothermal springs and geothermal power

The relationship of these to ore deposits

Glaciers as a record of Holocene climate change

Seismic hazards and engineering responses

On successful completion of this unit students will be able to:

1. Explain the relationships between the ancient geological processes preserved in Australia and the young processes occurring in New Zealand.
2. Use new skills in interpreting evidence of deformation and origin of a fault structure.
3. Understand and interpret field evidence of the different mechanisms driving different types of metamorphism.
4. Prepare a stratigraphic log.
5. Understand and interpret field characteristics of geochemical processes.
6. Present an overview of a complex geological topic to a educated geoscience audience.

Presentation: 50%

Essays: 50%

• 12 days fieldwork
• 56 hours of independent study

See also Unit timetable information

Master of Science

The analysis of geomaterials (e.g., rocks, minerals, soils, water) presents unique challenging related to their complexity. This hands-on unit will introduce the basic analytical tools used by geochemists and environmental scientists for measuring the mineralogical, chemical, and isotopic compositions of geomaterials. We will also cover some advanced topics, in particular the use of synchrotron light in geosciences.

The unit is suitable for any geoscientist working with geochemical data.

Specific topics covered include:

1. Laboratory inductions, basics of analytical chemistry (e.g., precision, accuracy, blanks)
2. Working in the wet lab.
3. Mass spectroscopy - trace elements
4. Mass spectroscopy - isotope ratios
5. Mass spectroscopy - geochronology
6. Sample prep. Budget. Plan a project.
7. Water chemistry
8. X-ray Diffraction
9. Synchrotron-based spectroscopy, diffraction and microscopy
10. Electron microscopy and microprobe techniques

On completion of this unit students will be able to:

1. Understand the different analytical tools that can be used to study geochemical systems and the information they deliver.
2. Prepare samples, acquire data, and interpret the results.
3. Use a range of analytical techniques.
4. Design and conduct an analytical campaign - including budgeting, selecting adequate samples and analytical tools, quality control, and reporting the results

Practical work: 20%

Assignment: 30%

Presentation: 50%

• Two weeks of lecture and laboratory activities, totalling 70 hours
• Two weeks for working on projects, including three hours supervised study
• Two half day field trips

See also Unit timetable information

Master of Science

The unit aims to provide post-graduate students with a work-integrated learning experience that simulates an exploration program for mineral commodities. The unit will be taught as a group project, with students working in teams of 3 to 4 within their own level. The project will require identification of a target commodity based geological and geophysical information, justification of the target selection including a literature review, acquisition and synthesis of the appropriate geological, geochemical, and geophysical data, interpretation of the data, developing of an exploration targeting strategy, and an economic analysis of the program. Projects will be designed to prepare students for comparable experiences in the workplace. Students will develop skills in data synthesis and analysis, geological interpretation, critical and lateral thinking using diverse geoscientific data.

On completion of this unit students will be able to:

1. Students will develop the ability to work in a team environment to achieve project objectives;
2. Students will develop their oral presentation skills that enable them to express the concepts they develop, the data required to test the concept, and the outcomes and interpretations of the simulated exploration program;
3. Students will construct a geoscientific report outlining the objectives, methodology, data required and the outcomes and interpretations of the simulated exploration program;
4. Students will gain an ability to integrate multiple large datasets to synthesise and interpret geological information.

Presentation: 10%

Geochemical and geophysical data collection design: 20%

Drilling program design: 20%

Final group report and group presentation: 50%

The project requires a workload commitment of 144 hours over the semester

See also Unit timetable information

Masters of Science (Earth Science)

This unit will enable students to develop the skills required to conceive and deliver an applied research project in environmental earth science. Students will develop and carry out a research project in collaboration with other students on a key topic that is of relevance to industry, government or non-government organisations. The topic will be chosen by the students from a list provided by the unit coordinator. This unit will allow students to develop their research skills in earth sciences while working in team in developing a research project, formulating hypotheses and aims, collecting and analysing data, and interpreting and describing the implications of the results. The presentation of the final results will develop presentation and written skills.

On completion of this unit students will be able to:

1. Develop a project proposal with appropriate research questions, aims, hypotheses and methodological approaches
2. Critically review the literature relevant to the project.
3. Generate, analyse and interpret data using appropriate data analysis methods
4. Communicate the findings, implications and limitations of the project in the broader scientific and social context in a clear and professional manner, in written and oral forms.
5. Collaborate effectively with their peers.

Project proposal: 20%

Poster presentation: 20%

Final report: 60%

A total of 144 hrs for the semester consisting of a combination of structured workshops, group meetings, presentations, and individual study.

Short (one-day) site visits or field trips may also be required.

See also Unit timetable information

Master of Science in Earth Sciences

This unit will provide post-graduate students with an overview of how drones (unmanned aerial vehicles, UAVs), photogrammetry and digital mapping tools are being applied in the Earth Sciences. The unit will be taught as a series of hands-on workshops and projects. Workshops and associated projects will cover UAV operations, survey design, sensor technology, 3D photogrammetric model calculations using structure from motion software, data extraction from point clouds and ortho-images, and digital mapping. Student projects will be designed to prepare students for use of UAVs for applications in geology, geophysics and environmental Earth Science. Students will develop skills in data acquisition, synthesis, and analysis, geological and environmental interpretation, critical and lateral thinking using diverse digital image data.

On completion of this unit students will be able to:

1. Ability to work in a team environment
2. Oral presentation skills.
3. Geoscience and environmental reporting skills.
4. Ability to integrate multiple large datasets to synthesise and interpret geological and environmental information.

Acquisition of UAV survey and digital mapping data, generation of a geometrically and geographically referenced photogrammetric model: 25%

Photogrammetric modelling, analysis of 3D point cloud and orthoimagery, and digital mapping: 35%

Final report and presentation: 40%

• One 3-hour workshop per week consisting of lectures and presentations
• Nine hours of independent study per week

See also Unit timetable information

Masters of Science (Earth Science)

This course will introduce the concept of a GIS as a problem solving technology within the geosciences and is designed to provide practical experience in the processing of regional geophysical datasets for the purpose of undertaking geological interpretation.

Specific topics will include map projections and georeferencing, distortions in image data, raster and vector data models, incorporating digital terrain models and geophysical data, introduction to boolean logic and functions, data accuracy and access issues and limitations of GIS. The course is designed to allow the student to go through step-by-step methodologies of processing data, interpretation techniques, and modelling of geophysical data.

On completion of this unit students will be able to:

1. An ability to identify the kind of digital information and software most appropriate to solving different geological problems.
2. An opportunity to demonstrate their ability to work with state-of-the-art geological data sets in digital form.
3. Confidence and competence to interrogate geological problems employing modern digital techniques.
4. Equip students with discipline-specific knowledge and expertise appropriate for post-graduate research in the field; equip students with discipline-specific knowledge and expertise enabling them to take their place as professional geologists in industry or government organisations;
5. Develop skills to process regional geophysical datasets, develop strategies to interpret geology from regional aeromagnetic and gravity data, integrate geological data into the geophysical interpretation, practical experience in geophysical interpretation and best practices in modeling geophysical data.

8 x GIS based practical assignments, due during the teaching week (each worth 5%).

A GIS based assignment (10%) as a 500 word report which will include a series of map to communicate their findings is due by the last day of class.

A 2000-word equivalent interpretation of geophysical images including lithologies, structures and overprinting relationship, due by last day of classes (30%).

An accompanying report (3000-words) on the rationale for interpretation and a short tectonic history of the area consistent with the interpretation due by the last day of classes (20%).

• 28 hours of lectures,
• 42 hours of practicals,
• 16 hours of independent study

See also Unit timetable information

Master of Science (Honours)

Remote sensing has become one of the important and widely applied methods for environmental and earth resource monitoring and evaluation. The information extracted from remotely sensed images may be used in many ways, e.g. as a basis for mapping land use/cover, for understanding environmental processes and for estimating biophysical variables. This unit will introduce the basic concepts and principles of remote sensing, and prepare students with image interpretation and digital image processing skills with an emphasis on the use of remote sensing imagery for vegetation, atmosphere, geology, water, soils and landform analysis.

On completion of this unit, students will be able to:

1. To explain and apply the major concepts and principles of remote sensing and digital image processing for earth science applications.
2. To identify the types of information that can be extracted from remotely sensed data on the environment and earth resources.
3. To explain and apply the fundamental image interpretation elements (e.g., tone, texture, size, shape, pattern, site and association)
4. To visually interpret aerial photos and satellite images.
5. To conduct digital image processing and analysis using a digital image processing system to extract information.

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 2 hours and 10 minutes.

Examination (2 hours): 50%

Practical work: 50%

• One 2-hour lecture and one 3-hour practical per week
• Seven hours of independent study per week

See also Unit timetable information

Master of Earth Science

This unit aims to teach the knowledge and skills for exploring the spatial patterns that result from social and physical processes on or near the Earth's surface. It examines the theories and methods of quantitative geography, including spatial data exploration, hypothesis testing and spatial predictive modelling, provides practical training in fundamental tools of spatial analysis in GIS, and develops skills in finding, understanding and applying appropriate spatial analysis tools, and correctly interpreting and presenting the results.

On completion of this unit students will be able to:

1. Explain the concepts and nature of spatial data analysis.
2. Explain the geographical concepts of distance, adjacency and interaction and how fundamental they are in performing spatial data analysis.
3. Explain and apply different approaches to spatial data exploration.
4. Explain spatial statistics, assumptions and how they are used to characterise spatial patterns and processes.
5. Demonstrate competency in the use of spatial data analysis tools.
6. Interpret and communicate effectively the results of spatial data analysis.
7. Demonstrate the ability to plan, design and implement a spatial data analysis project.

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 2 hours and 10 minutes.

Examination (2 hours): 50%

Practical work: 35%

Group project: 15%

• One 2-hour lecture and one 3-hour practical per week
• Seven hours of independent study per week

See also Unit timetable information

Master of Earth Science

The unit aims to teach the skills required to visualise and analyse (multivariate statistics) geological, geochemical and geophysical data in 3D, build 3D geological models, build property models (similar to resource estimation) and visualise and extract information from digital outcrop models. The units will expose the students to industry-standard software packages such as R, Orange, Gocad, Leapfrog Geo, Geomodeller, Geoscience analyst.

On completion of this unit, students will be able to:

1. Import and visualise exploration data in industry-standard 3D modelling packages (LeapFrog Geo, Gocad, Geomodeller, Geoscience analyst)
2. Analyse assays and geochemical data using deep learning methods (multivariate statistics) in R and/or Orange
3. Understand the concept of implicit modelling
4. Build 3D geological models
5. Perform geologically constrained interpolation of data and indicator data (derived from classification through deep learning).

Practical work: 60%

Report: 40%

• 1.5-hours of lectures and 3-hours of practicals per week
• 1.5-hours of independent study per week

See also Unit timetable information

Master of Science (Honours)

Students will do a research project in weather, climate or ocean science. The main relevant areas of research are aerosols (including cloud seeding), boundary layers, climate change, clouds, convection, ENSO, general circulation, synoptic-dynamical meteorology, mesoscale meteorology, numerical modelling, tropical meteorology, and bushfires and fire weather.

In most cases, the project will be a continuation of that completed in EAE4001 but expanded and deepened. The intention is that the completed project should be suitable for submission for publication in a research journal.

Alternatively, the student may choose a different research project, with the aim of developing a greater breadth of understanding of atmospheric science. Nonetheless, the student must demonstrate greater research maturity and command of the subject matter than that required for EAE4001.

The research project may be theoretical, computational or observation-based. Each student will work under the supervision of at least one of the academic members of staff. The project will involve a literature review, original research, a written thesis and an oral report on the work.

On completion of this unit, students will be able to:

1. Understand, synthesise and summarise the existing literature.
2. Identify gaps in our knowledge in their chosen area of research.
3. Advance our knowledge in the chosen area through original research.
4. Present their findings in a written thesis and oral presentation.

Progress will be assessed through a written progress report: 50% and an oral presentation: 50%

A total of 24 hours per week.

If the student starts a new project:

• attendance at a 1-hour seminar
• 1-hour consultation with the supervisor
• 10 hours per week of reading and summarising the literature (averaged over the semester)
• 1 hour per week developing the research plan (averaged over the semester)
• 10 hours per week of research (averaged over the semester)
• 1 hour per week writing the progress report (averaged over the semester)
• 1 hour per week preparing the oral report (averaged over the semester)

If the student continues and existing project:

attendance at a 1-hour seminar

• 1-hour consultation with the supervisor
• 17 hours per week of research (averaged over the semester)
• 4 hours per week writing the thesis (averaged over the semester)
• 1 hour per week preparing the oral report (averaged over the semester)

See also Unit timetable information

Master of Science in Atmospheric Science

Students will do a research project in weather, climate or ocean science. The main relevant areas of research are aerosols (including cloud seeding), boundary layers, climate change, clouds, convection, ENSO, general circulation, synoptic-dynamical meteorology, mesoscale meteorology, numerical modelling, tropical meteorology, and bushfires and fire weather.

In most cases, the project will be a continuation of that completed in EAE5000Not offered in 2019 but expanded and deepened. The intention is that the completed project should be suitable for submission for publication in a research journal.

Alternatively, the student may choose a different research project, with the aim of developing a greater breadth of understanding of atmospheric science. Nonetheless, the student must demonstrate greater research maturity and command of the subject matter than that required for EAE5000Not offered in 2019.

The research project may be theoretical, computational or observation-based. Each student will work under the supervision of at least one of the academic members of staff. The project will involve a literature review, original research, a written thesis and an oral report on the work.

On completion of this unit, students will be able to:

1. Understand, synthesise and summarise the existing literature.
2. Identify gaps in our knowledge in their chosen area of research.
3. Advance our knowledge in the chosen area through original research.
4. Present their findings in a written thesis and oral presentation.

This unit is the second half of a two-semester research project

Literature review: 20%

Oral presentation: 10%

Thesis: 70%

A total of 24 hours per week comprising:

• Attendance at a 1-hour seminar
• 1-hour consultation with the supervisor
• 17 hours per week of research (averaged over the semester)
• 4 hours per week writing the thesis (averaged over the semester)
• 1 hour per week preparing the oral report (averaged over the semester)

See also Unit timetable information

Master of Science in Atmospheric Science

Students undertake an advanced research project involving original work on a topic chosen in consultation with an academic supervisor. The topic may be a continuation of research completed in EAE4000, enabling a deeper insight into a larger research problem. In this case, it is expected that the research outcomes will also be suitable for submission for publication in a peer-reviewed international journal.

Alternatively, the project may be a separate topic to EAE4000, but the student must display a more mature research methodology than was required for EAE4000.

On completion of this unit students will be able to:

1. Understand, use and explain the basic concepts and principles of the research literature which underpin the chosen area of research in Earth Science.
2. Synthesise and interpret the knowledge gained in the study of the underpinning research literature. This leads to the ability to identify a niche topic or topics within this existing body of literature, which represents a gap in current knowledge. This problem should be suitable for original research.
3. Advance our understanding of an existing problem or problems in the chosen area for original research.
4. Present the results of the original research in written form as a thesis, and also present key thesis results in oral form as a preliminary seminar.
5. Defend the results of the original research in an oral exam.

Progress will be assessed through a written progress report: 50% and an oral presentation: 50%

A total of 24 hours per week:

• Attendance at weekly group meetings (half hour per week)
• Attendance at seminars and colloquia (half hour per week)
• At least half hour per week of consultation with the supervisor
• Specialist training (approximately half hour per week)
• Preparation for the seminar and or literature review (if starting a new project) (approximately 1.5 hours per week averaged over the semester)
• Preparation of a progress report (approximately 1.5 hours per week averaged over the semester)
• 19 hours of independent research per week

See also Unit timetable information

Master of Science in Earth Science

Students undertake an advanced research project involving original work on a topic chosen in consultation with an academic supervisor. The topic may be a continuation of research completed in EAE4000, enabling a deeper insight into a larger research problem. In this case, it is expected that the research outcomes will also be suitable for submission for publication in a peer-reviewed international journal.

Alternatively, the project may be a separate topic to EAE4000, but the student must display a more mature research methodology than was required for EAE4000.

On completion of this unit students will be able to:

1. Understand, use and explain the basic concepts and principles of the research literature which underpin the chosen area of research in Earth Science.
2. Synthesise and interpret the knowledge gained in the study of the underpinning research literature. This leads to the ability to identify a niche topic or topics within this existing body of literature, which represents a gap in current knowledge. This problem should be suitable for original research.
3. Advance our understanding of an existing problem or problems in the chosen area for original research.
4. Present the results of the original research in written form as a thesis, and also present key thesis results in oral form as a seminar.
5. Defend the results of the original research in an oral exam.

Seminar: 20%

Thesis: 80%

A total of 24 hours per week:

• Attendance at weekly group meetings (half hour per week)
• Attendance at seminars and colloquia (half hour per week)
• At least half hour per week of consultation with the supervisor
• Specialist training (approximately half hour per week)
• Preparation for the seminar (approximately 1.5 hours per week averaged over the semester)
• Preparation of thesis (approximately 2.5 hours per week averaged over the semester)
• 18 hours of independent research per week

See also Unit timetable information

Master of Science in Earth Science

The unit will discuss some basic statistical methods for analysing climate dynamics with the aim of understanding the physical mechanisms driving the observed structures (statistics). The unit will start with a discussion on the basics of probability theory, time series analysis, stochastic models and multi-variate data (pattern) analysis. It will then focus on the principles of decision making in statistical analysis (significance tests), which is followed by a discussion of the pitfalls and general strategies in statistical analysis. The unit will not focus on deriving statistical parameters, but rather will emphasise how these methods can be applied and will discuss the potential pitfalls in interpreting statistical results.

On completion of this unit students will be able to:

1. Complete a statistical analysis on probability distributions, time series, and multi-variate data.
2. Apply standard statistical methods in climate dynamics data analysis.
3. Interpret the outcomes of the statistical analysis in the context of climate dynamics.
4. Read, understand and critically analyse the scientific literature on data analysis in climate dynamics.

Examination (2 hours): 50%

Assignments: 50%

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in EAE5020 will be expected to demonstrate a higher level of learning in this subject than those enrolled in EAE4020. The assignments and exam in this unit will use some common items from the EAE4020 assessment tasks, in combination with several higher level questions and tasks.

A total of 12 hours per week comprising:

• Two 1-hour lectures per week
• One 1-hour laboratory per week
• 3 hours working on assignments
• 6 hours of independent study

See also Unit timetable information

Master of Science in Atmospheric Science

Dynamical meteorology concerns itself with the causes of atmospheric motion. The unit begins with a scale analysis of the equations of motion for mid latitude weather systems, which leads to the most important theoretical development modern meteorology - the quasi-geostrophic theory. This theory and its generalisation, is used to explain Rossby waves and their interaction with the mean state, the development of extratropical cyclones, the causes of vertical motion, and the structure and evolution of cold fronts. The theory for gravity waves is developed also.

On completion of this unit students will be able to:

1. Understand the dynamical principles governing the fluid flow in a rotating frame of reference;
2. Apply these principles to explain the dynamics of many common mid latitude weather systems;
3. Demonstrate a high level of knowledge of the important mathematical techniques used to solve problems in mid latitude dynamics;
4. Read, understand and critically analyse the scientific literature on mid latitude dynamics.

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 2 hours and 10 minutes.

Assignments: 30%

Research paper review: 30%

Examination (2 hours): 40%

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in EAE5021 will be expected to demonstrate a higher level of learning in this subject than those enrolled in EAE4021. The assignments and exam in this unit will use some common items from the EAE4021 assessment tasks, in combination with several higher level questions and tasks.

A total of 12 hours per week comprising:

• Three 1-hour lectures
• Three hours per week on assignments, reports and preparation of a talk
• Six hours of independent study

See also Unit timetable information

Master of Science in Atmospheric Science

This unit provides an introduction to the large-scale circulation features of the atmosphere and the processes that maintain them. Students will be introduced to a set of mathematical tools that will be used to analyse the transport of energy, momentum and moisture through the atmosphere and to build a conceptual picture for how these transports are achieved by the atmospheric circulation. The unit will also touch on how the large-scale atmospheric circulation may respond to climate change, and students will be given the opportunity to engage with the scientific literature on this topic.

On completion of this unit students will be able to:

1. Apply the various analysis techniques used to estimate the atmospheric thermodynamic state and large-scale circulation and evaluate their strengths and weaknesses.
2. Appraise the main features of the atmospheric circulation and the processes that contribute to their maintenance.
3. Apply mathematical tools to analyse the transports of energy, momentum and water through the atmosphere.
4. Critically engage with the scientific literature regarding the large-scale atmospheric circulation and its possible changes under climate change.

Assignments: 30%

Research paper review: 20%

Examination (2 hours): 50%

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in EAE5022 will be expected to demonstrate a higher level of learning in this subject than those enrolled in EAE4022. The assignments and exam in this unit will use some common items from the EAE4022 assessment tasks, in combination with several higher level questions and tasks.

A total of 12 hours per week comprising:

• Two 1.5-hour lectures
• Three hours per week on assignments, reports and preparation of a talk
• Six hours of independent study

See also Unit timetable information

Master of Science in Atmospheric Science

Boundary layer meteorology pertains to 'the part of the troposphere that is directly influenced by the presence of the earth's surface, and responds to surface forcings with a timescale of about an hour or less.' This unit details: aspects of turbulence unique to the boundary layer, the surface layer including Monin-Obukhov similarity theory, surface fluxes and boundary layer entrainment processes, a hierarchy of numerical models of the boundary layer. Finally, this unit discusses air pollution meteorology within the boundary layer.

On completion of this unit students will be able to:

1. Apply a conceptual definition of the atmospheric boundary layer and various quantitative definitions.
2. Appraise the dynamical and physical processes that affect that atmospheric boundary layer.
3. Appraise the diurnal cycle of the terrestrial boundary layer and the evolution of the maritime boundary layer during warm and cold air advection.
4. Appraise a hierarchy of models of the atmospheric boundary layer and construct a 'mixed layer model'.
5. Critically analyse scientific literature on the atmospheric boundary layer.

Examination (2 hours): 50%

Assignments: 30%

Oral presentation: 10%

Report: 10%

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in EAE5024 will be expected to demonstrate a higher level of learning in this subject than those enrolled in EAE4024. The assignments and exam in this unit will use some common items from the EAE4024 assessment tasks, in combination with several higher level questions and tasks.

A total of 12 hours per week comprising:

• Three 1-hour lectures
• Three hours on assignments, reports and preparation of a talk
• 6 hours of independent study

See also Unit timetable information

Master of Science in Atmospheric Science

Physical oceanography is the study of the ocean, its motion and the underlying physical processes. This unit will begin with a brief foray into descriptive physical oceanography, where details of the mean circulation and physical structure of the ocean will be presented along with the oceanographic past and present instruments and observing platforms. The unit will then cover aspects of dynamical physical oceanography particularly relevant for tropical and subtropical oceans, including the introduction of the equations of motion, Ekman layer theory and wind-driven circulation, geostrophic circulation, western boundary currents and internal waves. The unit will then finish by introducing interactions at the air-sea interface and how the related coupled ocean-atmosphere dynamics can lead to climatically relevant modes of climate variability, like the El Nino-Southern Oscillation.

On completion of this unit students will be able to:

1. Identify the mean circulation of the tropical to subtropical ocean and detail the underlying dynamical principles responsible for this circulation.
2. Appraise how the ocean adjusts to perturbations, and utilise these dynamical principles to explain observed variations;
3. Demonstrate a high level of knowledge of the important numerical techniques used to solve problems in physical oceanography;
4. Critically analyse the scientific literature on ocean dynamics.

Assignments: 30%

Research paper review: 30%

Examination (3 hours): 40%

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in EAE5025 will be expected to demonstrate a higher level of learning in this subject than those enrolled in EAE4025Not offered in 2019. The assignments and exam in this unit will use some common items from the EAE4025Not offered in 2019 assessment tasks, in combination with several higher level questions and tasks.

A total of 12 hours per week comprising:

• Two 1-hour lectures
• One 1-hour lectorial
• Three hours on assignments, reports and preparation of a talk
• 6 hours of independent study

See also Unit timetable information

Master of Science in Atmospheric Science

The unit aims to teach the skills of geological mapping in two classic field locations of Australian geology, in Broken Hill (poly-deformed and high-grade metamorphic terrane) and Bermagui (poly-deformed, highly complex terrane). In both field camp, the emphasis will be on observing, recording, and interpreting geologic phenomena in a natural environment.. Students will draw on a theoretical background of lectures and laboratory studies in first, second and third-year geology to analyse real rocks in the real world. Students will use their observations and interpretations to construct geological maps and cross-sections and determine the geological history of complex poly-deformed terrane. The concept of key locality for observation and critical thinking for correlation between key locality will be introduced and applied to produce map and cross sections of highly complexly deformed terranes. At 5th year level, mapping will be completed using digital mapping technologies (e.g. mapping tablets and software) and students will be expected to integrate additional geophysical and remote sensing datasets to better constrain their geological maps and sections.

On completion of this unit, students will be able to:

1. Produce structural geological maps;
2. Observe and interpret the distribution of lithologies and structures in the field;
3. Correlate observations and interpretations at the outcrop scale to produce consistent map and cross-sections;
4. Determine the relationship between structure and metamorphic assemblages;
5. Visualise complex three dimensional geometries;
6. Unravel the geological history of complexly deformed terranes;
7. Determine overprinting relationships from field geology;
8. Communicate results in a written report;
9. Work in a team environment and communicate of results with peers;
10. Equip students with discipline-specific knowledge and expertise appropriate for post-graduate research in the field; equip students with discipline-specific knowledge and expertise enabling them to take their place as professional geologists in industry or government organisations; develop their field mapping techniques;
11. Develop digital geology skills including in the field.

Fieldwork exercises Broken Hill: 45%

Fieldwork exercises Bermagui: 35%

Presentation: 10%

Report: 10%

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in EAE5060 will be expected to demonstrate a higher level of learning in this subject than those enrolled in EAE4060. The assignments in this unit will use some common items from the EAE4060 assessment tasks, in combination with several higher level questions and tasks.

• Total of 40 hours for Bermagui
• Total of 80 hours for Broken Hill
• 24 hours independent study

See also Unit timetable information

Master of Science in Earth Science

This is an intensive 12-day field trip to New Zealand, one of the best natural laboratories in which to learn about geology. Apart from being dramatically different to Australia in terms of modern day geological activity, it is a ribbon continent with a complex assembly of allochthonous terranes, part of which was formerly part of Australia. It has hyperactive back arc volcanism, spectacular geothermal activity, very active seismicity and is one of the few countries in the world with glaciers at sea level. Some of the main concepts to be covered will be:

• Arcs and back-arc architecture, seismicity and volcanism
• Transpressional fault systems
• Geothermal springs and geothermal power
• The relationship of these to ore deposits
• Glaciers as a record of Holocene climate change
• Seismic hazards and engineering responses

On successful completion of this unit students will be able to:

1. Explain the relationships between the ancient geological processes preserved in Australia and the young processes occurring in New Zealand.
2. Use new skills in interpreting evidence of deformation and origin of a fault structure.
3. Understand and interpret field evidence of the different mechanisms driving different types of metamorphism.
4. Prepare a stratigraphic log.
5. Understand and interpret field characteristics of geochemical processes.
6. Present an overview of a complex geological topic to a educated geoscience audience.

Presentation: 50%

Essays: 50%

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in EAE5061 will be expected to demonstrate a higher level of learning in this subject than those enrolled in EAE4061. The assignments in this unit will use some common items from the EAE4061 assessment tasks, in combination with several higher level questions and tasks.

• 12 days fieldwork
• 56 hours of independent study

See also Unit timetable information

Master of Science

The analysis of geomaterials (e.g., rocks, minerals, soils, water) presents unique challenging related to their complexity. This hands-on unit will introduce the basic analytical tools used by geochemists and environmental scientists for measuring the mineralogical, chemical, and isotopic compositions of geomaterials. We will also cover some advanced topics, in particular the use of synchrotron light in geosciences.

The unit is suitable for any geoscientist working with geochemical data.

Specific topics covered include:

1. Laboratory inductions, basics of analytical chemistry (e.g., precision, accuracy, blanks)
2. Working in the wet lab.
3. Mass spectroscopy - trace elements
4. Mass spectroscopy - isotope ratios
5. Mass spectroscopy - geochronology
6. Sample prep. Budget. Plan a project.
7. Water chemistry
8. X-ray Diffraction
9. Synchrotron-based spectroscopy, diffraction and microscopy
10. Electron microscopy and microprobe techniques

On completion of this unit students will be able to:

1. Understand the different analytical tools that can be used to study geochemical systems and the information they deliver.
2. Prepare samples, acquire data, and interpret the results.
3. Use a range of analytical techniques.
4. Design and conduct an analytical campaign - including budgeting, selecting adequate samples and analytical tools, quality control, and reporting the results.

Practical work: 30%

Assignment: 40%

Presentation: 30%

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in EAE5062 will be expected to demonstrate a higher level of learning in this subject than those enrolled in EAE4062. The assignments in this unit will use some common items from the EAE4062 assessment tasks, in combination with several higher level questions and tasks.

• Two weeks of lecture and laboratory activities, totalling 70 hours
• Two weeks for working on projects, including three hours supervised study
• Two half day field trips

See also Unit timetable information

Master of Science

The unit aims to provide post-graduate students with a work-integrated learning experience that simulates an exploration program for mineral commodities. The unit will be taught as a group project, with students working in teams of 3 to 4 within their own level. The project will require identification of a target commodity based geological and geophysical information, justification of the target selection including a literature review, acquisition and synthesis of the appropriate geological, geochemical, and geophysical data, interpretation of the data, developing of an exploration targeting strategy, and an economic analysis of the program. Projects will be designed to prepare students for comparable experiences in the workplace. Students will develop skills in data synthesis and analysis, geological interpretation, critical and lateral thinking using diverse geoscientific data.

On completion of this unit students will be able to:

1. Students will develop the ability to work in a team environment to achieve project objectives.
2. Students will develop their oral presentation skills that enable them to express the concepts they develop, the data required to test the concept, and the outcomes and interpretations of the simulated exploration program.
3. Students will construct a geoscientific report outlining the objectives, methodology and data required, and the outcomes and interpretations of the simulated exploration program.
4. Students will gain an ability to integrate multiple large datasets to synthesise and interpret geological information.
5. Students will gain an ability to use geoscientific data to undertake an economic assessment of a mineral exploration program including the cost of the program and the size of the target required to economically develop a mine.

Presentation: 10%

Geochemical and geophysical data collection design: 20%

Drilling program design: 20%

Final report and presentation (with an additional component that includes an assessment of the size of the target required to economically develop a mine and the cost of the exploration program): 50%

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in EAE5063 will be expected to demonstrate a higher level of learning in this subject than those enrolled in EAE4063. The assignments in this unit will use some common items from the EAE4063 assessment tasks, in combination with several higher level questions and tasks.

The project requires a workload commitment of 144 hours over the semester

See also Unit timetable information

Masters of Science (Earth Science)

This unit will enable students to develop the skills required to conceive and deliver an applied research project in environmental earth science. Students will develop and carry out a research project in collaboration with other students on a key topic that is of relevance to industry, government or non-government organisations. The topic will be chosen by the students from a list provided by the unit coordinator. This unit will allow students to develop their research skills in earth sciences while working in team in developing a research project, formulating hypotheses and aims, collecting and analysing data, and interpreting and describing the implications of the results. The presentation of the final results will develop presentation and written skills.

On completion of this unit students will be able to:

1. Develop a project proposal with appropriate research questions, aims, hypotheses and methodological approaches
2. Critically review the literature relevant to the project.
3. Generate, analyse and interpret data using appropriate data analysis methods
4. Communicate the findings, implications and limitations of the project in the broader scientific and social context in a clear and professional manner, in written and oral forms.
5. Collaborate effectively with their peers.

Project proposal: 20%

Literature Review: 10%

Poster presentation: 10%

Final report: 50%

Oral presentation: 10%

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in EAE5064 will be expected to demonstrate a higher level of learning in this subject than those enrolled in EAE4064. The assignments in this unit will use some common items from the EAE4064 assessment tasks, in combination with several higher level questions and tasks.

A total of 144 hrs for the semester consisting of a combination of structured workshops, group meetings, presentations, and individual study. Short (one-day) site visits or field trips may also be required.

See also Unit timetable information

Master of Science in Earth Science

This unit will provide post-graduate students with an overview of how drones (unmanned aerial vehicles, UAVs), photogrammetry and digital mapping tools are being applied in the Earth Sciences. The unit will be taught as a series of hands on workshops and projects. Workshops and associated projects will cover UAV operations, survey design, sensor technology, 3D photogrammetric model calculations using structure from motion software, data extraction from point clouds and ortho-images, and digital mapping. Student projects will be designed to prepare students for use of UAVs for applications in geology, geophysics and environmental Earth Science. Students will develop skills in data acquisition, synthesis and analysis, geological and environmental interpretation, critical and lateral thinking using diverse digital image data.

On completion of this unit students will be able to:

1. Ability to work in a team environment
2. Oral presentation skills.
3. Geoscience and environmental reporting skills
4. Ability to integrate multiple large datasets to synthesise and interpret geological and environmental information.

Acquisition of UAV survey and digital mapping data, generation of a geometrically and geographically referenced photogrammetric model: 25%

Photogrammetric modelling, analysis of 3D point cloud and orthoimagery, and digital mapping: 30%

Independent project: 15%

Final report and presentation: 30%

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in EAE5065 will be expected to demonstrate a higher level of learning in this subject than those enrolled in EAE4065. The assignments in this unit will use some common items from the EAE4065 assessment tasks, in combination with several higher level questions and tasks.

• One 3-hour workshop per week consisting of lectures and student presentations
• Nine hours of independent study per week

See also Unit timetable information

Masters of Science (Earth Science)

This course will introduce the concept of a GIS as a problem solving technology within the geosciences and is designed to provide practical experience in the processing of regional geophysical datasets for the purpose of undertaking geological interpretation.

Specific topics will include map projections and georeferencing, distortions in image data, raster and vector data models, incorporating digital terrain models and geophysical data, introduction to boolean logic and functions, data accuracy and access issues and limitations of GIS. The course is designed to allow the student to go through step-by-step methodologies of processing data, interpretation techniques, and modelling of geophysical data.

On completion of this unit students will be able to:

1. An ability to identify the kind of digital information and software most appropriate to solving different geological problems.
2. An opportunity to demonstrate their ability to work with state-of-the-art geological data sets in digital form.
3. Confidence and competence to interrogate geological problems employing modern digital techniques.
4. Equip students with discipline-specific knowledge and expertise appropriate for post-graduate research in the field; equip students with discipline-specific knowledge and expertise enabling them to take their place as professional geologists in industry or government organisations;
5. Develop skills to process regional geophysical datasets, develop strategies to interpret geology from regional aeromagnetic and gravity data, integrate geological data into the geophysical interpretation, practical experience in geophysical interpretation and best practices in modeling geophysical data.

28 hours of lectures,

42 hours of practical's,

16 hours of independent study

• 28 hours of lectures,
• 42 hours of practicals,
• 16 hours of independent study

See also Unit timetable information

Master of Science

Honours

Remote sensing has become one of the important and widely applied methods for environmental and earth resource monitoring and evaluation. The information extracted from remotely sensed images may be used in many ways, e.g. as a basis for mapping land use/cover, for understanding environmental processes and for estimating biophysical variables. This unit will introduce the basic concepts and principles of remote sensing, and prepare students with image interpretation and digital image processing skills with an emphasis on the use of remote sensing imagery for vegetation, atmosphere, geology, water, soils and landform analysis.

On completion of this unit, students will be able to:

1. To understand the major concepts and principles of remote sensing and digital image processing for earth science applications.
2. To identify the types of information that can be extracted from remotely sensed data on the environment and earth resources.
3. To understand, explain and apply the fundamental image interpretation elements (e.g., tone, texture, size, shape, pattern, site and association)
4. To visually interpret aerial photos and satellite images.
5. To conduct digital image processing and analysis using a digital image processing system to extract information.

Master of Earth Science

This unit aims to teach the knowledge and skills for exploring the spatial patterns that result from social and physical processes on or near the Earth's surface. It examines the theories and methods of quantitative geography, including spatial data exploration, hypothetic testing and spatial predictive modelling, provides practical training in fundamental tools of spatial analysis in GIS, and develops skills in finding, understanding and applying appropriate spatial analysis tools, and correctly interpreting and presenting the results.

On completion of this unit students will be able to:

1. To understand the concepts and nature of spatial data analysis.
2. To understand the geographical concepts of distance, adjacency and interaction and how fundamental they are in performing spatial data analysis.
3. To understand and apply different approaches to spatial data exploration.
4. To understand spatial statistics, assumptions and how they are used to explain spatial patterns and processes.
5. To demonstrate competency in the use of spatial data analysis tools.
6. To be able to interpret and communicate effectively the results of spatial data analysis.
7. To demonstrate the ability to plan, design and implement a spatial data analysis project.

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 2 hours and 10 minutes.

Examination (2 hours): 50%

Practical work: 25%

Project: 25%

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in EAE5068 will be expected to demonstrate a higher level of learning in this subject than those enrolled in EAE4068. The assignments and exam in this unit will use some common items from the EAE4068 assessment tasks, in combination with several higher level questions and tasks.

• One 2-hour lecture and one 3-hour practical per week
• Seven hours of independent study per week

See also Unit timetable information

Master of Earth Science

The unit aims to teach the skills required to visualise and analyse (multivariate statistics) geological, geochemical and geophysical data in 3D, build 3D geological models, build property models (similar to resource estimation) and visualise and extract information from digital outcrop models. The units will expose the students to industry-standard software packages such as R, Orange, Gocad, Leapfrog Geo, Geomodeller, Geoscience Analyst.

On completion of this unit, students will be able to:

1. Import and visualise exploration data in industry-standard 3D modelling packages (LeapFrog Geo, Gocad, Geomodeller, Geoscience Analyst)
2. Analyse assays and geochemical data using deep learning methods (multivariate statistics) in R and/or Orange
3. Understand the concept of implicit modelling
4. Build 3D geological models
5. Perform geologically constrained interpolation of data and indicator data (derived from classification through deep learning).

Practical work: 60%

Report: 40%

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in EAE5069 will be expected to demonstrate a higher level of learning in this subject than those enrolled in EAE4069. The assignments in this unit will use some common items from the EAE4069 assessment tasks, in combination with several higher level questions and tasks.

• 1.5-hours of lectures
• 3-hours of practical's and
• 1.5-hours of independent study per week

See also Unit timetable information

Master of Science

Honours

The unit provides a practical introduction to the principles, techniques and applications in GIS for environmental problem solving and decision making. It covers a wide range of topics including general nature of spatial data, spatial data quality, georeferencing, raster and vector approaches, spatial data management, spatial analysis, spatial modelling, spatial visualisation, terrain analysis, and GIS applications in land use analysis, hydrology, ecology, geoscience, environmental policy and decision analysis.

On completion of this unit student will be able to:

1. Understand the fundamental principles of GIS.
2. Comprehend the nature of spatial data and their importance in environmental science.
3. Identify environmental problems that can be solved with GIS.
4. Grasp basic GIS skills.
5. Demonstrate a high level of skills in the use of GIS software (ArcGIS).
6. Design GIS-based solutions to environmental problems.

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 2 hours and 10 minutes.

Within semester assessment: 75%

Examination (2 hours): 25%

Minimum total expected workload to achieve the learning outcomes for this unit is 144 hours per semester typically comprising a mixture of scheduled learning activities and independent study. A unit requires on average three/four hours of scheduled activities per week. Scheduled activities may include a combination of teacher directed learning, peer directed learning and online engagement.

See also Unit timetable information

Environmental security

This field-based unit is taught in the National Park/World Heritage Area of Cinque Terre on the Italian Riviera. Identified by UNESCO as an environment and cultural landscape worth preserving, the region is under immense pressure due to climate change, rural depopulation, abandoning of agricultural lands, landscape instability, and burgeoning tourism. The unit provides unique opportunities for interaction with staff of the National Park and various local and national authorities through guest lectures. During the time spent on the Cinque Terre students will explore the environment through numerous field trips. Whilst on site, students will complete an independent research project investigating the challenges of sustainably integrating tourism and agricultural objectives, while minimising negative environmental and cultural impacts.

On completion of this unit students will be able to:

1. Evaluate the range of complex environmental, social and economic interrelationships that shape the Cinque Terre and be able to differentiate a cultural landscape from a natural landscape;
2. Propose and justify a solutions-based research project demonstrating an understanding of sustainability in the context of a region of truly global significance;
3. Design a research proposal demonstrating an understanding of field-based techniques of survey, analysis and presentation of results;
4. Reflect upon and critically analyse personal and professional development with reference to addressing problems of sustainability in a region of global significance.
5. Execute a collaborative research project that shows a critical understanding of the real-world challenges associated with addressing sustainable development;
6. Communicate a solutions-based approach in a clear and coherent way that is effective for the purpose and the intended audience.

Pre-departure project proposal 15%

In-field project presentation: 10%

Field studies journal: 20%

Research report: 55%

• 3 2-hour pre-briefing workshops prior to departure
• 7.5 days intensive located in the Cinque Terre, Italy involving lectures, tutorials and fieldwork
• 3 days lectures, discussion, workshops (mornings)
• 4 days directed project work
• Presentations on final morning
• Post-trip independent work on journal and research project

See also Unit timetable information

S6002 Master of Environment and Sustainability

This unit, together with ENS5020, sets the context for considering the interactions and interdependence between nature and society and the basic principles of sustainability (social, economic and environmental), reflected in the Sustainable Development Goals.

This unit (Global challenges and sustainability) provides the scientific basis for understanding contemporary global environmental change and its implications for society.

Using the current global policy context in this area, it introduces the science of sustainability and the environment and its relevance to human well-being. It explores the key threats to sustainability, such as climate change, human migration, resource scarcity and emerging diseases. Core concepts covered in the unit include those of scale, systems and complexity.

The unit teaches problem structuring methods, evidence-based approaches and methods of interpreting risk and uncertainty. Particular emphasis is placed on developing skills to integrate evidence into sustainability actions across multiple sectors, systems and scales. Theory will be complemented with group learning exercises, professional development activities and engagement with practitioners.

On completion of this unit students will be able to:

1. Evaluate and integrate the multidisciplinary scientific evidence for contemporary global change and ecosystem services.
2. Forecast challenges associated with global change and sustainability through analysing evidence and applying scientific knowledge, concepts and methods.
3. Appraise, classify and prioritise complex systems, problems and solutions relevant to sustainability.
4. Devise evidence-based approaches to sustainability through integrating data with multidisciplinary tools, frameworks and principles.
5. Plan evidence-based sustainability actions across multiple sectors, systems and scales.
6. Effectively communicate scientific knowledge across disciplines and communities of practice in environment and sustainability.

Within semester assessment: 100%

Contact hours equivalent to minimum 4 hours per week.

Additional requirements of at least twenty hours of independent work.

See also Unit timetable information

International development practice

International sustainable tourism management

This unit, together with ENS5010, sets the context for considering the interactions and interdependence between nature and society and the basic principles of sustainability (social, economic and environmental), as reflected in the Sustainable Development Goals.

This unit explores the values and perspectives of stakeholders alongside existing social structures that inform and affect how global challenges (as taught in unit ENS5010) are perceived and acted upon.

Within society there are varied understandings of the relationships between the social, environmental and economic dimensions of sustainability. How sustainability is viewed and addressed is shaped by a diversity of multi-stakeholder perspectives and value systems along with their capacity to influence economic, regulatory, and policy regimes.

This unit develops student's capacity to map and critically analyse:

1. multi-stakeholders and social structures affecting sustainability; ii) different ideological, cultural, philosophical, psychological and disciplinary perspectives on sustainability; and,

   iii) their implications for policymaking, development of business cases, disciplinary research, and action.

On completion of this unit students will be able to:

1. Evaluate and critique the historical roots, conceptual notions, frameworks and current debates on sustainability and sustainable development.
2. Examine environmental, social and economic dimensions of sustainability, and their interactions, through analysing different philosophical and ideological values and perspectives on sustainability and sustainable development.
3. Recognise the complex economic, regulatory and policy regimes that stakeholders influence and are shaped by.
4. Integrate the perspectives of different disciplines within an interdisciplinary context.
5. Plan practical courses of action, policy-making and business cases by considering and analysing the implications of differing stakeholder perspectives and social structures.
6. Construct, articulate and effectively communicate critical and analytical arguments, in oral and written form, relevant to discussions of sustainability worldviews and philosophies.

Within semester assessment: 100%

• Contact hours equivalent to minimum 4 hours per week.
• Additional requirements for at least 20 hours of independent work.

See also Unit timetable information

International sustainable tourism management

This unit examines the ways in which multiple forms of global change interact to drive the loss of biodiversity and ecosystem services. Solutions for securing biodiversity and ecosystem services and ensuring the protection and sustainable use of renewable resources are discussed.

The unit uses relevant policies and management approaches by which biodiversity and ecosystems are governed, to evaluate the scientific evidence base underpinning these, and to identify gaps and future solutions. Example topics covered include integrated land-use planning, area- and species-based conservation strategies, biosecurity, and the development of sustainable harvest systems.

Students will develop their understanding of the concepts and the skills needed for translating and integrating scientific evidence into decision-making for the protection of biodiversity and ecosystems. To enhance this understanding students will collaborate with peers and experts to develop their capacity to use biological knowledge and evidence in professional planning, management and conservation.

On completion of this unit students will be able to:

1. Articulate fundamental scientific knowledge of biodiversity and ecosystem services to a multidisciplinary audience.
2. Critically analyse contemporary topics and debates in biodiversity and ecosystem science and demonstrate a practical understanding of the state of biodiversity and ecosystem services.
3. Identify and use appropriate strategies and tools for planning, management and conservation.
4. Interpret and assess the validity and implications of biodiversity and ecosystem assessment and reporting.
5. Apply effective communication skills to collaborate across academia, government and non-governmental and corporate organisations and negotiate diverse perspectives on biodiversity and ecosystems.

Within semester assessment: 100%

Contact hours equivalent to 4-hours per week and additional requirements include at least 8-hours of independent pre and post class work per week.

See also Unit timetable information

Environmental security

This unit provides a fundamental understanding of the science, policy and regulatory frameworks relating to the nexus between climate change, renewable and non-renewable energy resources. The physical science, climate models, projections and impacts are discussed along with national and international climate change policy and regulatory aspects.

The unit will develop skills and understandings to translate the best contemporary climate change science into appropriate decision-making to preserve the physical, biological and economic systems upon which human security depends. Students will also gain understanding of climate change scenario development, vulnerability assessment and mitigation and adaptation responses at organisational, community and national levels.

The unit will involve site visits to both renewable (solar arrays and wind farms) and non-renewable energy generation facilities. To facilitate these understandings visits will also be made, for example, to local government authorities in Victoria dealing with climate change vulnerabilities and assessments. The critical links between climate change, climate change impacts and human security are emphasised throughout the unit.

On completion of this unit students will be able to:

1. Articulate the fundamental scientific principles and issues related to climate change, including the differences between mitigation and adaptation policies, to a multidisciplinary audience.
2. Critically analyse contemporary issues and debates in climate change science and demonstrate a practical understanding of the outputs, assumptions and limitations of climate change modelling, especially as it relates to scenario development.
3. Demonstrate the ability to research, construct and deliver professional scientific evidence-based proposals, technical reports, articles and policy documents.
4. Identify appropriate strategies and tools for climate change planning, management and impact assessment.
5. Apply effective communication skills to collaborate across academia, government and non-governmental and corporate organisations and negotiate diverse perspectives on relevant topics.

Within semester assessment: 100%

Contact hours equivalent to 4-hours per week including 16 hours of experiential activity (field trips/site visits).

Additional requirements include at least 8-hours of independent pre and post class work.

See also Unit timetable information

Environmental security

This unit will give students the knowledge and perspectives to manage water resources for human consumption, recreation and ecological values. The unit will commence by covering the basics of the hydrological cycle necessary to understand the factors controlling groundwater and surface water availability.

Fundamentals of water quality and pollutants and their behaviour including, metals, organic contaminants, nutrients and algal blooms, pathogens and acidification (within the context of acid sulfate soils, mine drainage and ocean acidification) will also be addressed. Application of this knowledge will then be undertaken with case studies of contaminated systems, their assessment and remediation approaches.

Finally the unit will cover the policy approaches used to manage water resources around the world including local and international examples of the development of water quality guidelines and frameworks. Current approaches used to balance the needs of ecological values and human water needs, will also be discussed with global and local examples.

On completion of this unit students will be able to:

1. Articulate the key aspects of the hydrological cycle that control surface and groundwater availability and evaluate approaches used to quantify and predict this.
2. Describe and understand the key physical, chemical and biological threats to water quality, including the key classes and behaviour of pollutants such as metals, organic contaminants, nutrients and acidity.
3. Understand, apply and design water quality guidelines to protect different water uses and purposes.
4. Design management strategies to maintain, improve and remediate water availability and quality in surface groundwater and marine systems.
5. Effectively communicate the key issues associated with water quantity and quality to the public and policy makers.

Within semester assessment: 100%

• Contact hours, within the seminar component, equate to 4 hours per week + Additional requirements include at least 8-hours of independent pre and post class work.

See also Unit timetable information

Environmental security

Leadership for sustainable development requires the ability to influence societal change in a range of complex contexts at varying scales. Critical appreciation is needed of processes and mechanisms that affect and guide such change.

The unit breaks down the complexity of change processes, examining the various components of societal change (rules, norms, values, knowledge), and the different dimensions of our social world (institutional, political, organisational, community), that either help or hinder sustainable development. The unit also explores a range of formal and informal processes of influence.

Blending theoretical and practical insights, the unit will equip students with a suite of tools and mechanisms for influencing, supporting and facilitating change towards sustainable development at a variety of scales, drawing on science-policy partnerships, strategic planning, social and organisational learning and advocacy networks.

On completion of this unit students will be able to:

1. Investigate, interpret and assess selected societal change theories, evaluating key conceptual frameworks, methods and current debates.
2. Explore the complexity of societal change processes and identify the dimensions of societal change.
3. Critically analyse and select processes and strategies for facilitating societal change at different scales (i.e. community, organisational, institutional, political).
4. Evaluate how organisations and communities can influence their social and political context and how this context can in turn encourage or require them to act in a sustainable way.
5. Design, develop and effectively communicate a change management intervention for a real-world sustainability challenge, grounded in theory, evidence and practice.

Within semester assessment: 100%

Contact hours equivalent to minimum 2 hours per week.

Additional requirements for at least 10 hours of independent work.

This unit is taught in intensive mode and will require attendance at up to four full days of face-to-face teaching, including two weekend days at Clayton, and three allocated weekday workshops within the semester period. Attendance at these sessions is compulsory. Independent online work will take place within semester in addition to the face to face teaching.

See also Unit timetable information

Leadership for sustainable development

International development practice

Behavioural change approaches are an important, and often very cost effective, part of the mix of solutions to many sustainability and other public policy issues, such as water conservation, energy efficiency and immunisation. Considerable opportunities exist in this space, as comparatively little time and effort is usually invested in understanding the drivers of individual behaviour and designing solutions that target these drivers.

With a mix of theoretical and practical work, this unit will enable students to understand individual behaviour in a way that identifies opportunities for change. It will take students through a process of unpacking public policy challenges and identifying real-life behavioural solutions. This involves prioritising behaviours and target audiences and understanding drivers of behaviour and potential solutions. Students will also learn to work collaboratively to design, test and evaluate behaviour change interventions.

On completion of this unit students will be able to:

1. Understand and evaluate selected theories of behaviour, including their historical roots, key conceptual notions, frameworks and current debates.
2. Diagnose the motives and drivers of individual behaviour.
3. Diagnose behavioural problems and develop prioritisation criteria and apply these to real-world scenarios.
4. Critically evaluate and apply a range of behavioural interventions to target priority behaviours.
5. Integrate principles for behavioural field trial interventions and analyse the effectiveness of these trials.
6. Collaboratively design and effectively communicate potential behaviour change programs.

Within semester assessment: 100%

Contact hours equivalent to minimum 2 hours per week plus additional requirements for at least 10 hours of independent work.

See also Unit timetable information

Leadership for sustainable development

International development practice

Building the capacity for effective leadership for sustainable development, at an individual, team and organisational scale, is one critical factor in addressing contemporary sustainability challenges.

This unit frames 'leadership' as a process of influence that delivers a shared vision, aligns resources towards that vision and generates commitment to collective success. It recognises the importance of individual and group-based leadership to successful sustainable development outcomes, and focuses on those aspects of leadership that can be consciously developed, such as critical leadership skills and choosing appropriate strategies to match the context. The unit differs from traditional MBA-style leadership training in that it selects the theoretical frameworks/models, leadership roles, case studies and skill sets from the vast leadership literature that are most relevant to practitioners who seek to advance sustainable development.

Starting with the concept of self-leadership, students will learn strategies and skills to develop their own leadership abilities as well as understand principles and practices for exerting influence and effecting change to support sustainable development.

Students will also develop an individual leadership development plan, drawing on the concept of 'self-leadership', the principles and methods of leadership development and the types of knowledge, skills and networks typically needed for sustainable development leadership. This plan will set out developmental objectives and specific actions to improve leadership performance and capacity.

On completion of this unit students will be able to:

1. Assess contexts in which sustainable development practitioners typically operate and examine the leadership implications.
2. Identify the characteristics of typical leadership roles in promoting sustainable development and analyse how leaders collaborate to achieve common goals.
3. Identify and assess the types of knowledge, skills and networks typically needed to perform in common leadership roles in sustainable development.
4. Examine the principles and methods of leaders and leadership development.
5. Critically analyse and evaluate case studies of leadership using relevant leadership theories, models and frameworks.
6. Create an individual leadership development plan.

Within semester assessment: 100%

Contact hours equivalent to minimum two hours per week.

Additional requirements for at least 10 hours of independent work.

See also Unit timetable information

Leadership for sustainable development

International development practice

ENS5900 (24 credit points) provides an opportunity for students to pursue a major academically-oriented piece of research in their chosen discipline during the advanced practice component of the course. A research thesis enables students to consolidate the theoretical knowledge and analytical skills acquired during the Master course in a research context. It requires independent learning and research by the student on a chosen topic related to the core and elective units offered in the specialisation. The unit primarily comprises independent research but includes some scheduled activities to enhance and develop transferable skills for success in research. Students are assessed primarily on the thesis. Students also undertake a reflective task to help develop and present novel perspectives on their research within the broader field of environment and sustainability. This authentic research experience represents a pathway to a PhD.

On completion of this unit students will be able to:

1. Critically analyse, evaluate and integrate academic literature.
2. Formulate effective research questions.
3. Conceptualise, design and manage an academic research project.
4. Conduct independent and ethical research, applying sound principles of study design and appropriate data analysis methods.
5. Develop an academically sound and logical argument through correctly analysing, interpreting and presenting evidence.
6. Demonstrate advanced academic writing skills by producing a thesis appropriate for publication in the chosen field.
7. Articulate the implications and applications of research.

Within semester assessment: 100%

The minimum expected workload for independent research combined with scheduled activities is 576 hours over the course of one semester.

See also Unit timetable information

ENS5901 (12 credit points), in combination with ENS5902, enables students to undertake research over two semesters during the advanced practice component of the course. ENS5901 provides an opportunity for students to pursue a major academically-oriented piece of research in their chosen discipline. This advanced and authentic experience will develop transferable research skills for professional practice across sectors and provides a pathway to a PhD. Over the course of ENS5901 and ENS5902, students are assessed based on a research thesis (90%) and a conceptual development/reflection task (10%). The format and requirements of the research thesis will vary according to the requirements of the specialisation. In addition to independent research, the unit includes some scheduled activities to enhance and develop transferable research skills in study design, analysis and academic writing. Students from any specialisation can undertake the unit if they fulfil the academic requirements and gain approval from an appropriate supervisor. ENS5901 with ENS5902 provide the same experience as ENS5900, but enable students to undertake research over two semesters.

On completion of this unit students will be able to:

1. Critically analyse, evaluate and integrate academic literature.
2. Formulate effective research questions.
3. Conceptualise, design and manage an academic research project.
4. Conduct independent and ethical research, applying sound principles of study design and appropriate data analysis methods.
5. Develop an academically sound and logical argument through correctly analysing, interpreting and presenting evidence.
6. Demonstrate advanced academic writing skills by producing a thesis appropriate for publication in the chosen field.
7. Articulate the implications and applications of research.

Within semester assessment: 100%

The minimum expected workload for independent research combined with scheduled activities is 288 hours over the course of one semester.

See also Unit timetable information

ENS5902 (12 credit points) is a continuation of ENS5901. ENS5902, in combination with ENS5901, enables students to undertake research over two semesters during the advanced practice component of the course. ENS5902 provides an opportunity for students to pursue a major academically-oriented piece of research in their chosen discipline. This advanced and authentic experience will develop transferable research skills for professional practice across sectors and provides a pathway to a PhD. Over the course of ENS5901 and ENS5902, students are assessed based on a research thesis (90%) and a conceptual development/reflection task (10%). The format and requirements of the research thesis will vary according to the requirements of the specialisation. In addition to independent research, the unit includes some scheduled activities to enhance and develop transferable research skills in study design, analysis and academic writing. Students from any specialisation can undertake the unit if they fulfil the academic requirements and gain approval from an appropriate supervisor. ENS5901 with ENS5902 provide the same experience as ENS5900, but enable students to undertake research over two semester

On completion of this unit students will be able to:

1. Critically analyse, evaluate and integrate academic literature
2. Formulate effective research questions
3. Conceptualise, design and manage an academic research project
4. Conduct independent and ethical research, applying sound principles of study design and appropriate data analysis methods
5. Develop an academically sound and logical argument through correctly analysing, interpreting and presenting evidence
6. Demonstrate advanced academic writing skills by producing a thesis appropriate for publication in the chosen field
7. Articulate the implications and applications of research

Within semester assessment: 100%

The minimum expected workload for independent research combined with scheduled activities is 288 hours over the course of one semester.

See also Unit timetable information

ENS5910 (12 points) is the unit for students who wish to develop their professional competencies for working effectively in an applied interdisciplinary context. In this unit, teams composed of 3-5 students from different disciplines will work in association with a partner organisation from government, private industry or not-for-profit to identify, analyse and address 'real-world' complex, sustainability challenges.

In their mixed-disciplinary teams, students will focus on a sustainability governance, policy or management topic that has been identified as a 'wicked problem' by a partner organisation associated with Monash Sustainable Development Institute (MSDI).

With guidance from an MSDI supervisor and the partner organisation, the team will diagnose and analyse different perspectives, values at stake and politics of the project and will present a well-argued, plainly communicated and easily accessible analysis of the wicked problem. Within the team the students will negotiate and integrate their knowledge to develop a context specific and relevant solution to the identified sustainability challenge. The team will deliver a proposed solution implementation strategy to the partner organisation that includes mechanisms to create and enable the desired change.

Students will communicate the project findings in the format specified by the academic supervisor and/or partner organisation. Part of the teams' interdisciplinary project outcomes will be a project report that is to be shared with the partner organisation. The unit includes some scheduled activities alongside the project work to enhance and develop professional skills. Students from any specialisation can undertake this unit if they fulfil the academic requirements and gain approval from their specialisation and unit coordinator.

On completion of this unit students will be able to:

1. Plan and execute a collaborative team project in cooperation with a partner organisation.
2. Negotiate complexity, uncertainty and risk while practicing multi-disciplinary decision making.
3. Translate, evaluate and integrate varied disciplinary knowledge to find solutions to complex sustainability challenges.
4. Identify and critically appraise social, environmental and economic considerations when designing solutions for sustainable development.
5. Propose and justify a solution-based approach to a sustainable development challenge, alongside an implementation - change strategy.
6. Demonstrate critical understanding of the real-world challenges associated with addressing sustainable development.
7. Communicate in a clear and coherent way that is effective for the purpose and the intended audience.

Within semester assessment: 100%

The minimum expected workload for project work combined with any scheduled activities is 288 hours over the course of one semester.

See also Unit timetable information

ENS5920 (12 credit points) enables students to undertake an applied project in environment and sustainability during the advanced practice year of the course. It provides an opportunity to pursue a contained research topic, in an applied manner, in collaboration with other students. This involves developing the capacity to integrate and apply knowledge and skills from different specialisations. The topic, chosen by students from a list of research topics provided by the unit coordinator, will draw upon the subject matter covered in the course and address an applied challenge in the field of environment and sustainability. It will allow students to build upon the research skills and experiences developed within their specialisation. This unit culminates in an oral presentation and written research report. The unit includes some scheduled activities and a reflection task alongside the project work to enhance and develop professional skills.

On completion of this unit students will be able to:

1. Critically analyse, reflect upon and synthesise the literature relevant to the project.
2. Design and select sound research questions and methodological approaches and frameworks.
3. Develop a project proposal, including a clear model or conceptualisation of the project.
4. Investigate and apply established professional practice relevant to the project.
5. Critically analyse outcomes, using appropriate data analysis and established theory and practice.
6. Communicate the findings, implications and limitations of the project in a clear and professional manner, in written and verbal forms.
7. Collaborate effectively to deliver a major project.

Within semester assessment: 100%

The minimum expected workload for project work combined with any scheduled activities is 288 hours over the course of one semester.

See also Unit timetable information

ENS5930 (12 points) is the unit for students who wish to undertake a professional internship during a semester of the advanced practice year of the Master of Environment and Sustainability. Students undertake a project defined by a host organisation domestically or internationally with the approval of the unit and specialisation coordinator. The placement may be an affiliated arrangement where a consultancy or research project is carried out in association with the organisation and physical location at the organisation is not required. Host organisations may be from a diverse range of industries and sectors, including government departments, private industry and not-for-profit organisations. Students communicate the project findings to the host organisation in the format specified by the host organisation, such as a consultation paper, report, commentary, manual, submission or speech. The host organisation provides field supervision, and the Faculty of Arts provides academic supervision. The unit includes some scheduled activities alongside the project work to enhance and develop professional skills. Students from any specialisation can undertake this unit if they fulfil the academic requirements and gain approval from the appropriate coordinators.

On completion of this unit students will be able to:

1. Apply broad discipline knowledge to find solutions to complex problems.
2. Exercise critical thinking and professional judgment in developing new understandings.
3. Show technical skill in designing, conducting and reporting on a research project.
4. Plan, execute and reflect upon a professional project with a degree of independence and accountability.
5. Communicate in a clear and coherent way that is effective for the purpose and the intended audience.
6. Collaborate with others on a project in a workplace setting.

Within semester assessment: 100%

The minimum expected workload for project work combined with any scheduled activities is 288 hours over the course of one semester.

See also Unit timetable information

This unit will explore the latest approaches and techniques for the genetic manipulation of organisms and their applications in contemporary biotechnology. Students will gain hands on experience in advanced molecular genetic techniques used to study and manipulate gene function and for generating a range of different transgenic organisms, including microbes, plants and animals. The application of these techniques in biotechnology will be demonstrated using a range of examples such as: bioremediation, bioprospecting, crop modification, disease modelling, gene drives, phage therapy, nanotechnology and assisted reproduction. Students will also gain appreciation of relevant ethical and regulatory considerations and of impacts of genetic biotechnology on society.

Upon successful completion of this unit, students will be able to:

1. Demonstrate and apply knowledge of contemporary areas of molecular genetics and biotechnology, and the challenges faced;
2. Illustrate and explain how transgenic organisms are produced via genome manipulation across a range of species;
3. Source, synthesise and critically analyse literature to form the basis of a project;
4. Independently design and implement experimental approaches to solve a research problem in genetics and biotechnology;
5. Demonstrate proficiency in molecular genetics laboratory techniques, in problem-solving and experimental design, and in data collection, analysis, interpretation and presentation;

6. Convey to a non-specialist audience the relevance and value of genetics and biotechnology to human society.

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 2 hours and 10 minutes.

Project proposal (3,000 words): (30%)

Journal club presentation: (10%)

Practical reports: (30%)

End of semester written exam (2 hour open book): (30%) (Hurdle)

• 5 contact hours (2 hours lectures/seminars and 3 hours practical/ workshop
• 7 hours of private study (assignments/projects and designated pre-class and post-class online learning activities to prepare for classes and consolidate knowledge)

See also Unit timetable information

Biotechnology

Genetics

Computational statistical inference merges statistics with computational mathematics stochastic computation, computational linear algebra, and optimization to fully exploit the power of ever-increasing data sets, sophisticated mathematical models, and cutting-edge computer architectures. Driven by applied problems in finance, biology, geophysics, and data analytics, this unit aims to provide an integrated view of computational statistical inference and introduce advanced computational methods used in this emerging field.

This unit covers both practical algorithms and theoretical foundations of statistical inference, with cases studies on a selection of application problems. The main topics are parameter estimation and Bayesian inference, missing data problems and expectation maximisation, advanced Monte Carlo methods including importance sampling and Markov chain Monte Carlo, approximate Bayesian computation, linear and nonlinear filtering methods, classification, Gaussian processes, and kernel methods.

On completion of this unit students will be able to:

1. Apply sophisticated computational statistical inference in a wide range of application problems that require the integration of mathematical modelling with observed data to provide credible interpretation of the underlying system.
2. Explain the roles of likelihood models, missing data, and Bayesian inference and formalise parameter estimation problems in complex applications using these concepts.
3. Develop and apply advanced expectation-maximization methods to missing data problems.
4. Use the principle of Bayesian inference and apply expert computational methods to estimate parameters of statistical models and mathematical models.
5. Implement advanced computational methods used in statistical inference, including importance sampling, filtering, and Markov chain Monte Carlo, and understand the asymptotic behaviour of these methods.
6. Apply machine learning tools such as classification, Gaussian processes, and kernel methods to analyse and interpret complicate data sets and understand the computational aspects of these tools.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

• 3 hours of lectures and 1h of tutorial per week
• 8 hours independent study per week

See also Unit timetable information

Master of Mathematics

Measure theory is one of the few theories which permeates all core mathematical domains (pure, applied and statistics). We develop Lebesgue integration and probability theory from the core elements of measure theory. The initial background will be kept to a minimum. In particular, it is only required knowledge of real analysis and elementary probability theory (prior knowledge of functional analysis is not required, but it is definitely encouraged). On the other hand, the topics covered in this course will be fundamental for the understanding of advanced courses (differential geometry, advanced analysis, partial differential equations), as described above.

The unit will cover such pure topics as: semi-rings, algebras, and sigma-algebras of sets, measures, outer measures, the Lebesgue and Borel measures, construction of Vitali sets, measurable and integrable functions, the Lebesgue integral and the fundamental theorems, the Lebesgue spaces, iterated measures and the Fubini theorem, modes of convergence, signed measures, decomposition of measures and the Radon-Nikodym theorem, approximation results for the Lebesgue measure.

The unit will also cover topics which are essential for probability theory: such as Borel-Cantelli Lemma, independence, Kolmogorov 0-1 law, exponential bounds, conditional expectation, martingales.

On successful completion of this unit, students will be able to:

1. Formulate complex problems using appropriate measure theory terminology.
2. Use sophisticated tools from measure theory in various areas of Mathematics (e.g. partial differential equations, geometric analysis, dynamical systems, general relativity, probability theory).
3. Identify specific situations to which the fundamental results of measure theory apply, and demonstrate advanced expertise in applying these results to said situations.
4. Communicate complex results and specialised information using the language of measure theory.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

3 hours of lectures and 1h of tutorial per week.

8 hours independent study per week.

See also Unit timetable information

Master of Mathematics

Manifolds are topological spaces that are locally homeomorphic to Euclidean space. A differentiable structure on a manifold makes it possible to generalize many concepts from calculus in Euclidean spaces to manifolds. This is an introductory course on differentiable manifolds and related basic concepts, which are the common ground for differential geometry, differential topology, global analysis, i.e. calculus on manifolds including geometric theory of integration, and modern mathematical physics. Topics covered in the unit include: Smooth manifolds and coordinate systems, tangent and cotangent bundles, tensor bundles, tensor fields and differential forms, Lie derivatives, exterior differentiation, connections, covariant derivatives, curvature, and Stokes's Theorem.

On completion of this unit students will be able to:

1. Apply expert differential geometric techniques to solve problems that arise in pure and applied mathematics.
2. Construct coherent and precise logical arguments.
3. Develop and extend current techniques in differential geometry so that they can be applied to new situations in novel ways.
4. Communicate complex ideas effectively.

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 3 hours and 10 minutes.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

• 3 hours of lectures and 1 hour of tutorial per week
• 8 hours of independent study per week

See also Unit timetable information

Master of Mathematics

The study of low-dimensional topology is the study of spaces of dimensions 2, 3, and 4, including the study of surfaces and their symmetries, knots and links, and structures on 3 and 4-manifolds. It has applications to mathematical fields such as geometry and dynamics; it also has modern applications to fields such as microbiology, physics, and computing. The unit will cover core concepts in low-dimensional topology such as surfaces and the mapping class group, descriptions of 3-manifolds by Heegaard splittings and Dehn fillings, cobordism in 4-dimensions. Additional topics may include prime and torus decompositions of 3-manifolds, knot and link invariants, contact and symplectic structures on manifolds, foliations, 3-manifold geometries, and applications to mathematical physics.

On completion of this unit students will be able to:

1. Formulate complex mathematical arguments using ideas from low-dimensional topology.
2. Apply sophisticated tools of low-dimensional topology to tackle novel problems, for example, to distinguish or classify new spaces, etc.
3. Communicate mathematical concepts and arguments.
4. Apply critical thinking to judge the validity of mathematical reasoning.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

• 3 hours of lectures
• 1-hour tutorial and
• 8 hours of independent study per week

See also Unit timetable information

Master of Mathematics

This unit develops the main tools from algebra that are used to study and distinguish spaces. These tools are used in a variety of fields, from mathematics to theoretical physics to computer science. Algebraic topology relates to concrete problems, and sophisticated tools will be presented to tackle such problems. The core topics covered in the unit include the fundamental group and covering spaces, and homology. Cohomology and/or homotopy theory will also be studied.

On completion of this unit students will be able to:

1. Demonstrate a profound understanding of the core concepts in algebraic topology.
2. Formulate complex mathematical arguments in algebraic topology.
3. Apply sophisticated tools of algebraic topology to tackle new problems.
4. Communicate difficult mathematical concepts and arguments with clarity.
5. Apply critical thinking to judge the validity of mathematical reasoning.

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 3 hours and 10 minutes.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

• 3 hours of lectures and 1 hour tutorial per week
• 8 hours of independent study per week

See also Unit timetable information

Master of Mathematics

In this course, you will investigate manifolds using the tools of analysis. In this setting, curvature and topology become crucial. The topics covered may include Riemann surfaces, Lie derivatives, Hodge theory, spectral theory on manifolds, comparison theorems, topics in mathematical physics, and geometric differential equations such as the minimal surface equation, geometric evolution equations, and harmonic maps. You will also examine some foundational theorems in the field, such as the uniformisation theorem, the resolution of the Yamabe problem, or the positive mass theorem.

On completion of this unit students will be able to:

1. Apply sophisticated tools of mathematical analysis to understand manifolds in a variety of settings
2. Demonstrate a profound understanding of connections between the geometry of a manifold, and the analytic properties of the manifold.
3. Communicate complex information and results with clarity.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

• 3 hours of lectures
• 1-hour tutorial and
• 8 hours of independent study per week

See also Unit timetable information

Master of Mathematics

Partial Differential Equations are ubiquitous in the modelling of physical phenomena. This topic will introduce the modern theory of partial differential equations of different types, in particular, the existence of solutions in an appropriate space. Fourier analysis, one of the most powerful tools of modern analysis, will also be covered. The following topics are covered in the unit: Sobolev spaces theory (weak derivatives, continuous and compact embeddings, trace theorem); elliptic equations (weak solutions, Lax-Milgram theorem); Parabolic equation (existence, maximal principle); Hyperbolic and dispersive equations (well-posedness).

On completion of this unit students will be able to:

1. Synthetise advanced mathematical knowledge in the basic theory of fundamental PDEs.
2. Interpret the construction of generalised functions (distribution) and how it relates to modern notions of derivative and function spaces.
3. Synthetise techniques and properties of Fourier Analysis.
4. Apply sophisticated Fourier analysis methods to problems in PDEs and related fields.
5. Apply recent developments in research on PDEs

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 3 hours and 10 minutes.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam

• 3 hours of lectures and 1 hour tutorial per week
• 8 hours of independent study per week

See also Unit timetable information

Master of Mathematics

Groups are abstract mathematical objects capturing the concept of symmetry, and therefore are ubiquitous in many mathematical disciplines and other fields of science, such as physics, chemistry, and computer science. This unit is an introductory course on group theory and computational methods, using the computer algebra system GAP (www.gap-system.org). This unit will cover a selection of topics from the following list. Abstract Groups: knowing the basic definitions and standard results; Group Actions: orbits, stabilisers, and the orbit-stabiliser theorem; Group Presentations: free groups, abelian invariants, Todd-Coxeter algorithm; Permutation Groups: stabiliser chains, bases and strong generating sets, membership test; Nilpotency and Solvability: knowing the basic definitions and properties. Polycyclic Groups: polycyclic series and generating sets, polycyclic presentations; GAP: learn how to use the computer algebra system GAP to compute with groups.

On completion of this unit students will be able to:

1. Formulate complex problems using appropriate terminology in algebra;
2. Demonstrate a profound understanding of abstract concepts in group theory;
3. Appreciate the nature of algebraic proofs, be able to use a variety of proof-techniques unique to working with groups;
4. Apply a variety of expert algorithms for different algebraic objects, in particular, groups;
5. Use the computer algebra system GAP to compute with groups and related structures.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

3 hours of lectures and 1h of tutorial per week.

8 hours independent study per week.

See also Unit timetable information

Master of Mathematics

Networks are ubiquitous and fundamental in the modern world, whether they are computer networks, transport networks, food webs, polymer chains, social networks and so on. Graph theory is the mathematics of networks. Familiarity with the basic notions and terminology will be assumed and built on to give an advanced understanding of a number of topics chosen from the following list: random graph theory, probabilistic method, extremal graph theory, Ramsey theory, advanced algorithms, combinatorial optimisation, geometric graph theory, topological graph theory, structural graph theory, algebraic graph theory, graph colouring, matroid theory.

On completion of this unit students will be able to:

1. Formulate complex problems using appropriate graph-theoretic terminology.
2. Appreciate the role of graph theory in other areas of mathematics.
3. Apply sophisticated mathematical methods in the setting of graph theory.
4. Apply sophisticated graph-theoretic arguments in a variety of settings.
5. Communicate complex information about graphs.
6. Apply critical thinking in the field of graph theory.
7. Read, understand and verify expert mathematical proofs about graphs.
8. Develop and write mathematical proofs about graphs.
9. Understand several real-world applications of graph theory.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

3 hours of lectures and 1h of tutorial per week.

8 hours independent study per week.

See also Unit timetable information

Master of Mathematics

Combinatorics is the study of arrangements and combinations of discrete objects. Combinatorial problems arise in many areas of pure mathematics, (e.g. algebra, probability, topology, and geometry), and in many applied areas as well (e.g. communications, operations research, experiment design, genetics, statistical physics etc). This unit will cover a selection of topics from the following list: combinatorial enumeration, ordinary and exponential generating functions, asymptotic enumeration, counting via matrix functions or group actions, the principle of inclusion-exclusion, Mobius inversion, permutations, partitions, compositions, combinatorial designs, Latin squares, Steiner triple systems, block designs, Hadamard matrices, finite geometries, algebraic combinatorics, strongly regular graphs, symmetric functions, Young tableaux, additive combinatorics and combinatorial geometry.

On completion of this unit students will be able to:

1. Formulate complex problems using appropriate combinatorial terminology.
2. Demonstrate a profound understanding of the benefits and challenges unique to working with discrete mathematical objects.
3. Recognise certain features of combinatorial problems which indicate their level of difficulty.
4. Apply sophisticated combinatorial arguments in a variety of settings.
5. Appreciate the role of combinatorics in other areas of mathematics.
6. Understand several real-world applications of combinatorics.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

• 3 hours of lectures
• 1-hour tutorial and
• 8 hours of independent study per week

See also Unit timetable information

Master of Mathematics

This unit covers the key principles to approximate and understand solutions of linear, weakly nonlinear, and strongly nonlinear equations by asymptotic analysis and dynamical systems theory. The main topics are: local analysis of linear ODEs, including irregular singular points and asymptotic series; asymptotic expansion of integrals, including stationary phase and steepest descent; introduction to regular/singular perturbation series; matched asymptotic expansion; multiple scale analysis, WKB theory; dynamical systems theory, including bifurcation, stability, and an introduction to chaos.

On completion of this unit students will be able to:

1. Appreciate the need for advanced approximate methods in applied mathematics when exact solutions are not available and for when numerical solution requires asymptotic boundary conditions
2. Formally explain the meanings of asymptotic relations and be able to apply them in comparing particular functions
3. Use sophisticated asymptotic methods to obtain local and global approximate solutions to a variety of problems arising in applied mathematics
4. Employ regular and singular perturbation methods to obtain approximate solutions of problems containing small parameters
5. Recognize and apply the mathematical concepts and tools underlying the evolution of nonlinear dynamical systems and the transition to chaos.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

3 hours of lectures and 1h of tutorial per week.

8 hours independent study per week.

See also Unit timetable information

Master of Mathematics

Computational methods are of paramount importance for solving real-world problems in applied mathematics.This unit teaches widely used numerical methods for problems from science, engineering, biology and finance that are modeled by partial differential equations (PDEs). The unit covers numerical methods for PDEs of elliptic, parabolic and hyperbolic type, as well as advanced solution methods for the linear and nonlinear systems of equations that may arise from the discretisation of the PDEs. Topics covered may include finite difference methods, finite element methods, and finite volume methods; iterative and multigrid solvers for linear and nonlinear systems; nonlinear hyperbolic conservation laws; and other topics in numerical PDEs.The concepts of numerical accuracy, stability and efficiency play a central role in the unit. Students will receive an introduction to the theory of the numerical methods (with derivations of the methods and some proofs), and will learn to implement the computational methods efficiently. Applications will be covered from various domains such as heat transfer, option pricing, biology, and fluid mechanics.

On completion of this unit students will be able to:

1. Explain the mathematical theory behind a selection of important numerical methods for PDEs, including the derivation of the methods and the analysis of their properties.
2. Explain and apply notions of accuracy, stability and computational cost when solving PDE problems numerically.
3. Demonstrate proficiency in numerical methods for PDEs and linear system solving, and apply them to problems in science, engineering, biology and finance.
4. Implement advanced numerical PDE methods, and demonstrate the correctness and efficiency of the implementations in systematic computational tests.
5. Apply critical thinking and demonstrate written and oral communication skills in the field of computational mathematics.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

3 hours of lectures and 1 hour of tutorial per week

See also Unit timetable information

Master of Mathematics

This unit gives an introduction to the numerical approximation and control of differential equations, with a focus on both the mathematical foundations and the practical usages of these notions. Topics covered include computational dynamics; optimisation and set-valued analysis; implicit and explicit time steppings; weak formulations of partial differential equations; finite element methods; finite volume methods; implementation and convergence analysis.

On completion of this unit students will be able to:

1. Describe and rigorously analyse sophisticated numerical methods for DEs;
2. Implement numerical methods for standard models;
3. Understand the mathematical properties of advanced numerical methods, and use this understanding to select appropriate method for each specific problem;
4. Describe the nature and usage of optimal control problems;
5. Cast a real-world problem into an optimal control problem;
6. Communicate and critically discuss the outcome of numerical methods for DEs.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

• 3 hours of lectures and a 1 hour tutorial per week
• 8 hours of independent study per week

See also Unit timetable information

Master of Mathematics

This unit covers the theory, techniques and applications of optimisation, with a focus on applications in data analytics. The emphasis is on advanced methods for nonlinear continuous optimisation. In addition to its theoretical description of optimisation algorithms, the unit also has a strong practical focus with students required to solve problems computationally through programming. Topics covered include a selection from quasi-Newton methods, augmented Lagrangian methods, and stochastic gradient descent methods, with applications to machine learning and neural networks. Furthermore, the unit will cover constrained optimisation methods that may include quadratic programming, interior point methods, as well as stochastic meta-heuristics for nonlinear optimisation. Applications of these methods may include support vector machines and other classification methods.

On completion of this unit students will be able to:

1. Develop specialised mathematical knowledge in nonlinear optimisation algorithms and their efficient computer implementation
2. Understand the connection between optimisation and the training of data science models.
3. Determine an appropriate choice of optimisation approach based on problem characteristics.
4. Apply sophisticated optimisation methods to large problems arising from data analytics
5. Translate the result of optimisation into the application domain
6. Apply critical thinking in the field of computational optimisation

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 3 hours and 10 minutes.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

• 3 hours of lectures and 1 hour tutorial per week
• 8 hours of independent study per week

See also Unit timetable information

Master of Mathematics

This unit briefly discusses plasma physics, covering single particle motion and kinetic plasma theory, and then introduces the fluid description to derive the equations of magnetohydrodynamics (MHD). It then explores basic MHD, including ideal and dissipative MHD, magnetic hydrostatics, and MHD waves. A detailed spectral theory of MHD waves is developed. Applications will be made to solar structures and observations.

Stability and dynamics of solar features from the photosphere to corona will be analysed/simulated. These studies will be accompanied by the state-of-art visualisation techniques such as Python VTK, Mayavi and Paraview. Algorithms and ODE/PDE solvers to allow for Interactive MHD Visualisation will be an essential part of our tasks.

On completion of this unit students will be able to:

1. Develop advanced knowledge of the terms in the governing equations of kinetic and fluid theories.
2. Identify the MHD equations and derive the associated mass and momentum conservation equations
3. Identify the terms in the MHD version of Ohm's Law and use the equation to explain convection electric fields and frozen-in magnetic fields
4. Demonstrate expert knowledge on magnetic pressure and tension forces
5. Derive the dispersion equation for the basic MHD wave modes and describe their properties, such as propagation of magnetohydrodynamic waves
6. Show using simple examples of how this system of equations can be applied to different astrophysical and laboratory phenomena.
7. Reach a high level of achievement in writing and presenting sophisticated visualisation methods of computational visualisation
8. Communicate complex information on waves and MHD theory with the use of visualisation methods.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam

3 hours of lectures and 1 hour of tutorial per week

8 hours independent study per week

See also Unit timetable information

Master of Mathematics

This unit is an introduction to some of the most important mathematical concepts in theoretical biology. The coursework for this unit will be entirely mathematical and assumes no prior expertise in biology. The course also includes a significant project whereby students will be paired with students enrolled in M6030 (Master of Biotechnology) to investigate a real biological question in an interdisciplinary setting.

The aim of the course is to introduce both mathematical methods and biological applications and to generate a realisation of the potential of mathematics in biological research. The lectures will be organised by application (population, chemical, physiological, etc) but will focus on mathematical analysis and the insights that they generate.

Whilst 'mathematical biology' has the potential to cover a wide range of activities, we will focus on phenomenological models of continuous, discrete or stochastic natures as opposed to data-driven areas of mathematics such as computational mathematics, statistics, data science, machine learning, etc.

On completion of this unit students will be able to:

1. Apply and extend classical models in mathematical biology.
2. Use sophisticated mathematical techniques in the analysis of mathematical models in biology.
3. Construct mathematical models for biological systems.
4. Apply critical thinking to address problems in an interdisciplinary group setting.
5. Communicate effectively across interdisciplinary borders.

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 3 hours and 10 minutes.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

• 3 hours of lectures and 1 hour tutorial per week
• 8 hours of independent study per week

See also Unit timetable information

Master of Mathematics

The master project, which can be academic or industrial, is the capstone unit of the degree. It involves individual work, under supervisor's guidance, on an open topic. To conduct this project, the student has to draw on the knowledge assimilated in other units, and possibly to develop additional skills in a few relevant areas. A substantial report has to be produced, and the main outcomes are presented in the form of a seminar.

On completion of this unit students will be able to:

1. Conduct a rigorous scientific literature review covering a broad field.
2. Develop expert skills in independent assimilation of forefront mathematical material.
3. Develop and apply sophisticated mathematical methods to tackle open challenging problems.
4. Communicate specialised information, in both oral and written form, in a professional format.
5. Apply critical thinking in the field of advanced mathematics and/or its applications to other sciences.

For students taking the unit over one semester:

Oral presentation: 30%

Written report: 70%

For students taking the unit over two semesters:

Intermediate report: 20%

Oral presentation: 30%

Final written report: 50%

1h meeting with supervisor per week

13h personal work per week

1-hour meeting with supervisor per week

13-hours personal work per week

See also Unit timetable information

Master of Mathematics

This unit enables students to work in small groups on a focused topic in mathematics, not covered in other units. Each group is supervised by an academic staff. The work consists in individual reading, group sessions to facilitate understanding and develop communication skills, and seminar-like presentations. The overall purpose of this unit is for students to learn how to self-develop knowledge on a specific mathematical subject, by gathering information from written sources (textbooks, mathematical research papers, etc.) and by communicating with peers.

On completion of this unit students will be able to:

1. Assimilate sophisticated concepts from mathematical literature.
2. Develop expert strategies to efficiently work in groups and/or one-to-one with their supervisor.
3. Communicate complex and specialised content both orally and in writing.
4. Apply critical thinking in the field of advanced mathematics and its applications.

Progress report: 10%

Oral presentation: 30%

Written report: 60%

1-hour meeting with the supervisor per week

13 hours of personal or group work

See also Unit timetable information

Master of Mathematics

This unit enables students to work in small groups on a focused topic in mathematics, not covered in other units. Each group is supervised by an academic staff. The work consists of individual reading, group sessions to facilitate understanding and develop communication skills, and seminar-like presentations. The overall purpose of this unit is for students to learn how to self-develop knowledge on a specific mathematical subject, by gathering information from written sources (textbooks, mathematical research papers, etc.) and by communicating with peers.

On completion of this unit students will be able to:

1. Assimilate sophisticated concepts from mathematical literature.
2. Develop expert strategies to efficiently work in groups and/or one-to-one with their supervisor.
3. Communicate complex and specialised content both orally and in writing.
4. Apply critical thinking in the field of advanced mathematics and its applications.

Progress report: 10%

Oral presentation: 30%

Written report: 60%

1-hour meeting with the supervisor per week

13 hours of personal or group work

See also Unit timetable information

Master of Mathematics

Computational statistical inference merges statistics with computational mathematics stochastic computation, computational linear algebra, and optimization to fully exploit the power of ever-increasing data sets, sophisticated mathematical models, and cutting-edge computer architectures. Driven by applied problems in finance, biology, geophysics, and data analytics, this unit aims to provide an integrated view of computational statistical inference and introduce advanced computational methods used in this emerging field.

This unit covers both practical algorithms and theoretical foundations of statistical inference, with cases studies on a selection of application problems. The main topics are parameter estimation and Bayesian inference, missing data problems and expectation maximisation, advanced Monte Carlo methods including importance sampling and Markov chain Monte Carlo, approximate Bayesian computation, linear and nonlinear filtering methods, classification, Gaussian processes, and kernel methods.

On completion of this unit students will be able to:

1. Apply sophisticated computational statistical inference in a wide range of application problems that require the integration of mathematical modelling with observed data to provide credible interpretation of the underlying system.
2. Explain the roles of likelihood models, missing data, and Bayesian inference and formalise parameter estimation problems in complex applications using these concepts.
3. Develop and apply advanced expectation maximization methods to missing data problems.
4. Use the principle of Bayesian inference and apply expert computational methods to estimate parameters of statistical models and mathematical models.
5. Implement advanced computational methods used in statistical inference, including importance sampling, filtering, and Markov chain Monte Carlo, and understand the asymptotic behaviour of these methods.
6. Apply machine learning tools such as classification, Gaussian processes, and kernel methods to analyse and interpret complicate data sets and understand the computational aspects of these tools.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in MTH5089 will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4089. The assignments and exam in this unit will use some common items from the MTH4089 assessment tasks, in combination with several higher level questions and tasks.

3 hours of lectures and 1 hour of tutorial per week

10 hours of independent study per week

See also Unit timetable information

Enrolment in the Master of Mathematics

Measure theory is one of the few theories which permeates all core mathematical domains (pure, applied and statistics). We develop Lebesgue integration and probability theory from the core elements of measure theory. The initial background will be kept to a minimum. In particular, it is only required knowledge of real analysis and elementary probability theory (prior knowledge of functional analysis is not required, but it is definitely encouraged). On the other hand, the topics covered in this course will be fundamental for the understanding of advanced courses (differential geometry, advanced analysis, partial differential equations), as described above.

The unit will cover such pure topics as: semi-rings, algebras, and sigma-algebras of sets, measures, outer measures, the Lebesgue and Borel measures, construction of Vitali sets, construction of non-Borel Lebesgue measurable sets, measurable and integrable functions, the Lebesgue integral and the fundamental theorems, change of variables formula in Euclidean space, the Lebesgue spaces, iterated measures and the Fubini theorem, modes of convergence, signed measures, decomposition of measures and the Radon-Nikodym theorem, approximation results for the Lebesgue measure, Hausdorff measure and dimension, Haar measures, ergodic measures.

The unit will also cover topics which are essential for probability theory: such as Borel-Cantelli Lemma, independence, Kolmogorov 0-1 law, exponential bounds, conditional expectation, martingales.

On successful completion of this unit, students will be able to:

1. Formulate complex problems using appropriate measure theory terminology.
2. Use sophisticated tools from measure theory in various areas of Mathematics (e.g. partial differential equations, geometric analysis, dynamical systems, general relativity, probability theory).
3. Identify specific situations to which the fundamental results of measure theory apply, and demonstrate advanced expertise in applying these results to said situations.
4. Communicate complex results and specialised information using the language of measure theory.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in MTH5099 will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4099. The assignments and exam in this unit will use some common items from the MTH4099 assessment tasks, in combination with several higher level questions and tasks.

3 hours of lectures and 1 hour of tutorial per week

10 hours of independent study per week

See also Unit timetable information

Master of Mathematics

Manifolds are topological spaces that are locally homeomorphic to Euclidean space. A differentiable structure on a manifold makes it possible to generalize many concepts from calculus in Euclidean spaces to manifolds. This is an course on differentiable manifolds and related basic concepts, which are the common ground for differential geometry, differential topology, global analysis, i.e. calculus on manifolds including geometric theory of integration, and modern mathematical physics.

Foundational topics covered in the unit include: Smooth manifolds and coordinate systems, tangent and cotangent bundles, tensor bundles, tensor fields and differential forms, Lie derivatives, exterior differentiation, connections, covariant derivatives, curvature, and Stokes's Theorem.

This unit will also cover advanced topics and applications such as: Degree Theory, de Rham cohomology, symplectic geometry, classical mechanics, the Hopf-Rinow theorem, Lie Groups and homogeneous spaces.

On completion of this unit students will be able to:

1. Apply expert differential geometric techniques to solve problems that arise in pure and applied mathematics.
2. Construct coherent and precise logical arguments.
3. Develop and extend current techniques in differential geometry so that they can be applied to new situations in novel ways.
4. Communicate complex ideas effectively.
5. Independently learn and assimilate new mathematical ideas and techniques.

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 3 hours and 10 minutes.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in MTH5111 will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4111. The assignments and exam in this unit will use some common items from the MTH4111 assessment tasks, in combination with several higher level questions and tasks.

• 3 hours of lectures and 1 hour tutorial per week
• 10 hours of independent study per week

See also Unit timetable information

Master of Mathematics

Elliptic and Parabolic partial differential equations. Sobolev Spaces. Weak and strong solutions. Maximum principle. Comparison principle. Viscosity solutions. Stochastic control theory. The dynamic programing principle. Feynman-Kac representation formulas.

On completion of this unit students will be able to:

1. Develop specialised mathematical knowledge and skills within the field of partial differential equations.
2. Understand the complex connections between stochastic analysis and partial differential equations.
3. Apply critical thinking to problems in partial differential equations that relate to financial models.
4. Apply problem solving skills within the finance context.
5. Formulate expert solutions to practical financial problems using specialised cognitive and technical skills within the field of partial differential equations.
6. Communicate complex information in an accessible format to a non-mathematical audience.

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 3 hours and 10 minutes.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

Four contact hours per week

See also Unit timetable information

The study of low-dimensional topology is the study of spaces of dimensions 2, 3, and 4, including the study of surfaces and their symmetries, knots and links, and structures on 3 and 4-manifolds. It has applications to mathematical fields such as geometry and dynamics; it also has modern applications to fields such as microbiology, physics, and computing. The unit will cover core concepts in low-dimensional topology such as surfaces and the mapping class group, descriptions of 3-manifolds by Heegaard splittings and Dehn fillings, cobordism in 4-dimensions. Additional topics may include prime and torus decompositions of 3-manifolds, knot and link invariants, contact and symplectic structures on manifolds, foliations, 3-manifold geometries, and applications to mathematical physics.

On completion of this unit students will be able to:

1. Formulate complex mathematical arguments using ideas from low-dimensional topology.
2. Apply sophisticated tools of low-dimensional topology to tackle novel problems, for example, to distinguish or classify new spaces, etc.
3. Communicate mathematical concepts and arguments.
4. Apply critical thinking to judge the validity of mathematical reasoning.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in MTH5113 will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4113Not offered in 2019. The assignments and exam in this unit will use some common items from the MTH4113Not offered in 2019 assessment tasks, in combination with several higher level questions and tasks.

• 3 hours of lectures
• 1-hour tutorial and
• 10 hours of independent study per week

See also Unit timetable information

Master of Mathematics

This unit develops the main tools from algebra that are used to study and distinguish spaces. These tools are used in a variety of fields, from mathematics to theoretical physics to computer science. Algebraic topology relates to concrete problems, and sophisticated tools will be presented to tackle such problems. The core topics covered in the unit include the fundamental group and covering spaces, and homology. Cohomology and/or homotopy theory will also be studied.

On completion of this unit students will be able to:

1. Demonstrate profound understanding of the core concepts in algebraic topology.
2. Formulate complex mathematical arguments in algebraic topology.
3. Apply sophisticated tools of algebraic topology to tackle new problems.
4. Communicate difficult mathematical concepts and arguments with clarity.
5. Apply critical thinking to judge the validity of mathematical reasoning.

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 3 hours and 10 minutes.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in MTH5115 will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4115. The assignments and exam in this unit will use some common items from the MTH4115 assessment tasks, in combination with several higher level questions and tasks.

• 3 hours of lectures and 1 hour tutorial per week
• 10 hours of independent study per week

See also Unit timetable information

Master of Mathematics

In this course, you will investigate manifolds using the tools of analysis. In this setting, curvature and topology become crucial. The topics covered may include Riemann surfaces, Lie derivatives, Hodge theory, spectral theory on manifolds, comparison theorems, topics in mathematical physics, and geometric differential equations such as the minimal surface equation, geometric evolution equations, and harmonic maps. You will also examine some foundational theorems in the field, such as the uniformisation theorem, the resolution of the Yamabe problem, or the positive mass theorem.

You will also learn, through guided self-reading, additional topics based on their specific background (what other analysis units - Partial differential equations, Measure theory, etc. - they have already taken).

On completion of this unit students will be able to:

1. Apply sophisticated tools of mathematical analysis to understand manifolds in a variety of settings.
2. Demonstrate a profound understanding of connections between the geometry of a manifold, and the analytic properties of the manifold.
3. Communicate complex information and results with clarity.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in MTH5121 will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4121Not offered in 2019. The assignments and exam in this unit will use some common items from the MTH4121Not offered in 2019 assessment tasks, in combination with several higher level questions and tasks.

3 hours of lectures

1-hour tutorial and

10 hours of independent study per week

See also Unit timetable information

Master of Mathematics

Partial Differential Equations are ubiquitous in the modelling of physical phenomena. This topic will introduce the modern theory of partial differential equations of different types, in particular the existence of solutions in an appropriate space. Fourier analysis, one of the most powerful tools of modern analysis, will also be covered. The following topics are covered in the unit: Sobolev spaces theory (weak derivatives, continuous and compact embeddings, trace theorem); elliptic equations (weak solutions, Lax-Milgram theorem); Parabolic equation (existence, maximal principle); Hyperbolic and dispersive equations (well-posedness).

On completion of this unit students will be able to:

1. Synthetise advanced mathematical knowledge in the basic theory of fundamental PDEs.
2. Interpret the construction of `generalised functions' (distribution) and how it relates to modern notions of derivative and function spaces.
3. Synthetise techniques and properties of Fourier Analysis.
4. Apply sophisticated Fourier analysis methods to problems in PDEs and related fields.
5. Apply recent developments in research on PDEs

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 3 hours and 10 minutes.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in MTH5123 will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4123. The assignments and exam in this unit will use some common items from the MTH4123 assessment tasks, in combination with several higher level questions and tasks.

• 3 hours of lectures and 1 hour tutorial per week
• 10 hours of independent study per week

See also Unit timetable information

Master of Mathematics

Groups are abstract mathematical objects capturing the concept of symmetry, and therefore are ubiquitous in many mathematical disciplines and other fields of science, such as physics, chemistry, and computer science. This unit is an introductory course on group theory and computational methods, using the computer algebra system GAP (www.gap-system.org). This unit will cover a selection of topics from the following list. Abstract Groups: knowing the basic definitions and standard results; Group Actions: orbits, stabilisers, and the orbit-stabiliser theorem; Group Presentations: free groups, abelian invariants, Todd-Coxeter algorithm; Permutation Groups: stabiliser chains, bases and strong generating sets, membership test; Nilpotency and Solvability: knowing the basic definitions and properties. Polycyclic Groups: polycyclic series and generating sets, polycyclic presentations; GAP: learn how to use the computer algebra system GAP to compute with groups. Some of the material will be self-taught through guided reading.

On completion of this unit students will be able to:

1. Formulate complex problems using appropriate terminology in algebra
2. Demonstrate a profound understanding of abstract concepts in group theory
3. Appreciate the nature of algebraic proofs, be able to use a variety of proof-techniques unique to working with groups;
4. Apply a variety of expert algorithms for different algebraic objects, in particular, groups
5. Use the computer algebra system GAP to compute with groups and related structures.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in MTH5141 will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4141. The assignments and exam in this unit will use some common items from the MTH4141 assessment tasks, in combination with several higher level questions and tasks.

Master of Mathematics

Networks are ubiquitous and fundamental in the modern world, whether they are computer networks, transport networks, food webs, polymer chains, social networks and so on. Graph theory is the mathematics of networks. Familiarity with the basic notions and terminology will be assumed and built on to give an advanced understanding of a number of topics chosen from the following list: random graph theory, probabilistic method, extremal graph theory, Ramsey theory, advanced algorithms, combinatorial optimisation, geometric graph theory, topological graph theory, structural graph theory, algebraic graph theory, graph colouring, matroid theory.

On completion of this unit students will be able to:

1. Formulate complex problems using appropriate graph-theoretic terminology.
2. Appreciate the role of graph theory in other areas of mathematics.
3. Apply sophisticated mathematical methods in the setting of graph theory.
4. Apply sophisticated graph-theoretic arguments in a variety of settings.
5. Communicate complex information about graphs.
6. Apply critical thinking in the field of graph theory.
7. Read, understand and verify expert mathematical proofs about graphs.
8. Develop and write mathematical proofs about graphs.
9. Understand several real-world applications of graph theory.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

3 hours of lectures and 1 hour of tutorial per week

10 hours of independent study per week

See also Unit timetable information

Master of Mathematics

Combinatorics is the study of arrangements and combinations of

discrete objects. Combinatorial problems arise in many areas of pure mathematics, (e.g. algebra, probability, topology, and geometry), and in many applied areas as well (e.g. communications, operations research, experiment design, genetics, statistical physics etc). This unit will cover a selection of topics from the following list: combinatorial enumeration, ordinary and exponential generating functions, asymptotic enumeration, counting via matrix functions or group actions, the principle of inclusion-exclusion, Mobius inversion, permutations, partitions, compositions, combinatorial designs, Latin squares, Steiner triple systems, block designs, Hadamard matrices, finite geometries, algebraic combinatorics, strongly regular graphs, symmetric functions, Young tableaux, additive combinatorics and combinatorial geometry.

On completion of this unit students will be able to:

1. Formulate complex problems using appropriate combinatorial terminology.
2. Demonstrate a profound understanding of the benefits and challenges unique to working with discrete mathematical objects.
3. Recognise certain features of combinatorial problems which indicate their level of difficulty.
4. Apply sophisticated combinatorial arguments in a variety of settings.
5. Appreciate the role of combinatorics in other areas of mathematics.
6. Understand several real-world applications of combinatorics.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in MTH5153 will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4153Not offered in 2019. The assignments and exam in this unit will use some common items from the MTH4153Not offered in 2019 assessment tasks, in combination with several higher level questions and tasks.

3 hours of lectures

1-hour tutorial and

10 hours of independent study per week

See also Unit timetable information

Master of Mathematics

Variations and quadratic variation of functions. Review of integration and probability. Brownian motion. Ito integrals and Ito's formula. Stochastic differential equations and diffusions. Calculation of expectations and PDE's, Feynman-Kac formula. Martingales and semimartingales. Change of probability measure and Girsanov theorem. Fundamental theorems of asset pricing. Change of numeraire. Application to options.

On completion of this unit students will be able to:

1. Develop specialised mathematical knowledge and skills within the field of stochastic calculus.
2. Understand the complex connections between financial and probabilistic concepts.
3. Apply sophisticated stochastic modelling skills within the context of financial markets.
4. Apply critical thinking to problems in stochastic calculus and financial mathematics.
5. Apply problem solving skills within the finance context.
6. Formulate expert solutions to practical financial problems using specialised cognitive and technical skills within the field of stochastic calculus.
7. Communicate complex information in an accessible format to a non-mathematical audience.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

Two 1.5-hour lectures and one 1-hour applied class per week

See also Unit timetable information

Doob's convergence theorem. Optional sampling theorem. Discrete Stochastic integral. Martingale inequalities such as Doob and Burkholder-Davis-Gundy inequalities. Bucy-Kalman filter. Applications to finance. Option pricing - discrete Black-Scholes formula. Control theory.

On completion of this unit students will be able to:

1. Develop specialised mathematical knowledge and skills within the theory of martingales.
2. Apply sophisticated stochastic modelling skills within a variety of contexts, from population biology to finance to management science, and more.
3. Apply critical thinking to problems in discrete-time stochastic processes in general, and in the theory of discrete-time martingales in particular.
4. Formulate expert solutions to practical financial, engineering or scientific problems using specialised cognitive and technical skills within the theory of discrete-time martingales.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

Two 1.5 -hour lectures and one 1-hour applied class per week

See also Unit timetable information

Homogeneous Markov chains in finite and countable state space. Foster-Lyapunov criterion for recurrence and transience. Random walks in one and more dimensions. Polya theorem. Limit theorems: law of iterated logarithms, functional central limit theorem. Connections with the Brownian motion and the heat equation. Applications of random walks to finance and insurance.

On completion of this unit students will be able to:

1. Develop specialised mathematical knowledge and skills within the theories of markov chains and random walks.
2. Apply sophisticated stochastic modelling skills within a variety of contexts, from a wide range of scientific areas of knowledge.
3. Apply critical thinking to problems in Markov chains in general, and in the theory of random walks in particular.
4. Formulate expert solutions to practical financial, engineering or scientific problems using specialised cognitive and technical skills within the theories of markov chains and random walks.

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 3 hours and 10 minutes.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

Two 2-hour lectures per week

See also Unit timetable information

This unit covers the key principles to approximate and understand solutions of linear, weakly nonlinear, and strongly nonlinear equations by asymptotic analysis and dynamical systems theory. The main topics are: local analysis of linear ODEs, including irregular singular points and asymptotic series; asymptotic expansion of integrals, including stationary phase and steepest descent; introduction to regular/singular perturbation series; matched asymptotic expansion; multiple scale analysis, WKB theory; dynamical systems theory, including bifurcation, stability, and an introduction to chaos.

On completion of this unit students will be able to:

1. Appreciate the need for advanced approximate methods in applied mathematics when exact solutions are not available and for when numerical solution requires asymptotic boundary conditions
2. Formally explain the meanings of asymptotic relations and be able to apply them in comparing particular functions
3. Use sophisticated asymptotic methods to obtain local and global approximate solutions to a variety of problems arising in applied mathematics
4. Employ regular and singular perturbation methods to obtain approximate solutions of problems containing small parameters
5. Recognize and apply the mathematical concepts and tools underlying the evolution of nonlinear dynamical systems and the transition to chaos.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in MTH5311 will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4311. The assignments and exam in this unit will use some common items from the MTH4311 assessment tasks, in combination with several higher level questions and tasks.

3 hours of lectures and 1 hour of tutorial per week

10 hours of independent study per week

See also Unit timetable information

Master of Mathematics

Computational methods are of paramount importance for solving real-world problems in applied mathematics.This unit teaches widely used numerical methods for problems from science, engineering, biology and finance that are modeled by partial differential equations (PDEs). The unit covers numerical methods for PDEs of elliptic, parabolic and hyperbolic type, as well as advanced solution methods for the linear and nonlinear systems of equations that may arise from the discretisation of the PDEs. Topics covered may include finite difference methods, finite element methods, and finite volume methods; iterative and multigrid solvers for linear and nonlinear systems; nonlinear hyperbolic conservation laws; and other topics in numerical PDEs.The concepts of numerical accuracy, stability and efficiency play a central role in the unit. Students will receive an introduction to the theory of the numerical methods (with derivations of the methods and some proofs), and will learn to implement the computational methods efficiently. Applications will be covered from various domains such as heat transfer, option pricing, biology, and fluid mechanics.

On completion of this unit students will be able to:

1. Explain the mathematical theory behind a selection of important numerical methods for PDEs, including the derivation of the methods and the analysis of their properties.
2. Explain and apply notions of accuracy, stability and computational cost when solving PDE problems numerically.
3. Demonstrate proficiency in numerical methods for PDEs and linear system solving, and apply them to problems in science, engineering, biology and finance.
4. Implement advanced numerical PDE methods, and demonstrate the correctness and efficiency of the implementations in systematic computational tests.
5. Apply critical thinking and demonstrate written and oral communication skills in the field of computational mathematics.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in MTH5321 will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4321. The assignments and exam in this unit will use some common items from the MTH4321 assessment tasks, in combination with several higher level questions and tasks.

3 hours of lectures and 1 hour of tutorial per week

10 hours of independent study per week

See also Unit timetable information

Master of Mathematics

his unit gives an introduction to the numerical approximation and control of differential equations, with a focus on both the mathematical foundations and the practical usages of these notions. Topics covered include: computational dynamics; optimisation and set-valued analysis; implicit and explicit time steppings; weak formulations of partial differential equations; finite element methods; finite volume methods; implementation and convergence analysis.

On completion of this unit students will be able to:

1. Describe and rigorously analyse sophisticated numerical methods for DEs
2. Implement numerical methods for standard models
3. Understand the mathematical properties of advanced numerical methods, and use this understanding to select appropriate method for appropriate
4. Describe the nature and usage of optimal control problems
5. Cast a real-world problem into an optimal control problem
6. Communicate and critically discuss the outcome of numerical methods for DEs.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in MTH5323 will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4323Not offered in 2019. The assignments and exam in this unit will use some common items from the MTH4323Not offered in 2019 assessment tasks, in combination with several higher level questions and tasks.

• 3 hours of lectures and 1 hour tutorial per week
• 10 hours of independent study per week

See also Unit timetable information

Master of Mathematics

his unit covers the theory, techniques and applications of optimisation, with a focus on applications in data analytics. The emphasis is on advanced methods for nonlinear continuous optimisation. In addition to its theoretical description of optimisation algorithms, the unit also has a strong practical focus with students required to solve problems computationally through programming. Topics covered include a selection from quasi-Newton methods, augmented Lagrangian methods, and stochastic gradient descent methods, with applications to machine learning and neural networks. Furthermore, the unit will cover constrained optimisation methods that may include quadratic programming, interior point methods, as well as stochastic meta-heuristics for nonlinear optimisation. Applications of these methods may include support vector machines and other classification methods.

On completion of this unit students will be able to:

1. Develop specialised mathematical knowledge in nonlinear optimisation algorithms and their efficient computer implementation
2. Understand the connection between optimisation and the training of data science models.
3. Determine an appropriate choice of optimisation approach based on problem characteristics.
4. Apply sophisticated optimisation methods to large problems arising from data analytics
5. Translate the result of optimisation into the application domain
6. Apply critical thinking in the field of computational optimisation

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 3 hours and 10 minutes.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in MTH5331 will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4331. The assignments and exam in this unit will use some common items from the MTH4331 assessment tasks, in combination with several higher level questions and tasks.

• 3 hours of lectures and 1 hour tutorial per week
• 10 hours of independent study per week

See also Unit timetable information

Master of Mathematics

This unit provides an introduction to optimisation over discrete domains using integer programming and combinatorial methods. Discrete optimisation is frequently used to model decision problems in business and industry. This unit covers some of the mathematical tools required to solve these types of problems in practice. Building on linear programming, the unit will cover dynamic programming, branch-and-bound, polyhedral analysis, decomposition methods and an introduction to heuristic search for combinatorial optimisation problems.

On completion of this unit students will be able to:

1. Develop specialised mathematical knowledge in discrete optimisation.
2. Understand the profound connections between discrete optimisation, continuous optimisation and combinatorics.
3. Apply sophisticated combinatorial optimisation and integer programming methods to a variety of practical optimisation problems.
4. Translate practical problem descriptions into mathematical formulations as discrete optimisation problems and communicate the results to non-technical audiences.
5. Apply critical thinking in the field of operations research.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in MTH5333 will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4333Not offered in 2019. The assignments and exam in this unit will use some common items from the MTH4333Not offered in 2019 assessment tasks, in combination with several higher level questions and tasks.

• 3 hours of lectures
• 1-hour tutorial and
• 10 hours of independent study per week

See also Unit timetable information

Master of Mathematics

This unit is an introduction to hydrodynamic stability theory that concerns the stability and instability of fluid flows. Students will be introduced to the theoretical methods required to understand how instabilities develop and how the flow transitions from a laminar to a turbulent state. Instability concepts will be applied to a range of flow systems with applications in biology, geophysics and aerodynamics.

Topics covered include: concepts of linear stability theory; temporal/spatial instabilities; Kelvin-Helmholtz instabilities; capillary instabilities; Rayleigh-Benard instabilities; centrifugal instabilities; inviscid and viscous shear flow instabilities in channels, pipes, cylinders and boundary layers; stability of parallel flows including Rayleigh's equation and inflexion point criteria, Fjortoft's theorem, Squire's theorem and the Orr-Sommerfeld equations; weakly nonlinear theory; coherent turbulent structures.

On completion of this unit students will be able to:

1. Illustrate a deep understanding of hydrodynamic stability theory.
2. Describe and identify the types of instability that form in many physical flows.
3. Derive and explain the significance of Rayleigh's inflexion point criterion, Fjortoft's theorem and Squire's theorem.
4. Summarise the derivation of the Orr-Sommerfeld equation for a given basic state, and undertake a stability analysis.
5. Understand and articulate the physical mechanisms leading to instability and the paths for laminar-turbulent transition.
6. Communicate complex ideas on mathematical treatment of fluid dynamics.

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 3 hours and 10 minutes.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in MTH5341 will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4341. The assignments and exam in this unit will use some common items from the MTH4341 assessment tasks, in combination with several higher level questions and tasks.

• 3 hours of lectures
• 1 hour of tutorial and
• 10 hours of independent study per week

See also Unit timetable information

This unit briefly discusses plasma physics, covering single particle motion and kinetic plasma theory, and then introduces the fluid description to derive the equations of magnetohydrodynamics (MHD). It then explores basic MHD, including ideal and dissipative MHD, magnetohydrostatic, and MHD waves. A detailed spectral theory of MHD waves is developed. Students are required to understand the dynamics of general plasma flows, wave modes in plasmas, instabilities, particle acceleration, and shocks.

Applications will be made to solar structures and observations.

Stability and dynamics of solar features from the photosphere to corona will be analysed/simulated. These studies will be accompanied by the state-of-art visualisation techniques such as Python VTK, Mayavi and Paraview. Algorithms and ODE/PDE solvers to allow for Interactive Visualisation will be an essential part of our tasks.

On completion of this unit students will be able to:

1. Develop advanced knowledge of the terms in the governing equations of kinetic and fluid theories.
2. Identify the MHD equations and derive the associated mass and momentum conservation equations
3. Identify the terms in the MHD version of Ohm's Law and use the equation to explain convection electric fields and frozen-in magnetic fields
4. Demonstrate expert knowledge on magnetic pressure and tension forces
5. Derive the dispersion equation for the basic MHD wave modes and describe their properties, such as propagation of magnetohydrodynamic waves
6. Show using simple examples how this system of equations can be applied to different astrophysical and laboratory phenomena.
7. Reach a high level of achievement in writing and presenting sophisticated visualisation methods of computational visualisation
8. Communicate complex information on waves and MHD theory with the use of visualisation methods
9. Develop MHD computer model data visualisation and analysis

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in MTH5343 will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4343Not offered in 2019. The assignments and exam in this unit will use some common items from the MTH4343Not offered in 2019 assessment tasks, in combination with several higher level questions and tasks.

3 hours of lectures and 1 hour of tutorial per week

10 hours of independent study per week

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Master of Mathematics

This unit is an introduction to some of the most important mathematical concepts in theoretical biology and a more in depth investigation into an elective area of interest. The coursework for this unit will be entirely mathematical and assumes no prior expertise in biology. The course also includes a significant project whereby students will be paired with students enrolled in M6030 (Master of Biotechnology) to investigate a real biological question in an interdisciplinary setting.

The aim of the course is to introduce both mathematical methods and biological applications and to generate a realisation of the potential of mathematics in biological research. The lectures will be organised by application (population, chemical, physiological, etc) but will focus on mathematical analysis and the insights that they generate.

We will focus on phenomenological models of continuous, discrete or stochastic natures as opposed to data-driven areas of mathematics such as computational mathematics, statistics, data science, machine learning, etc. One of the core components of the unit will be elected by each student enrolled in MTH5351 and an extension reading course will be organised in this area.

On completion of this unit students will be able to:

1. Apply and extend classical models in mathematical biology.
2. Use sophisticated mathematical techniques in the analysis of mathematical models in biology.
3. Construct mathematical models for biological systems.
4. Apply critical thinking to address problems in an interdisciplinary group setting.
5. Communicate effectively across interdisciplinary borders.
6. Individually manage student-directed learning and research concentrating on a particular area of mathematical biology at a level above that of the lecture material.

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 3 hours and 10 minutes.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in MTH5351 will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4351. The assignments and exam in this unit will use some common items from the MTH4331 assessment tasks, in combination with several higher level questions and tasks.

• 3 hours of lectures and 1 hour tutorial per week
• 10 hours of independent study per week

See also Unit timetable information

Master of Mathematics

Basic concepts of risk management and risk measures. Multivariate models. Copulas and dependence. Financial time series. Volatility models such as ARCH and GARCH processes. Aggregate risk. Extreme value theory. Market, credit, and operational risk models. Regulation and practice.

On completion of this unit students will be able to:

1. Apply different aspects of the theory and practice of risk modelling for financial institutions.
2. Understand different types of financial risks such as market, credit, and operational.
3. Estimate various risk measures such as Value-at-Risk and Expected Shortfall for different type of risks of a financial institution.
4. Construct and estimate various volatility processes such as ARCH and GARCH.
5. Construct a multivariate model and calibrate its parameters to real financial data either by a multivariate distribution (top-down approach) or copula (bottom-up approach)
6. Understand tail risk concept and quantify it based on either heavy tail distributions approach or extreme value theory.

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 3 hours and 10 minutes.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

Two 2-hour lectures per week

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Interest rate curves. Zero-coupon bonds, spot and forward interest rates. Interest rate derivatives. Stochastic differential equations. Change of measures. No arbitrage pricing and change of numeraire. One-factor short rate models, including Vasicek, Hull and White, CIR and affine models. Two-factor short rate models. The HJM framework and models for forward rates. LIBOR models. Pricing of interest rate derivatives: swaps, caps and swaptions.

On completion of this unit students will be able to:

1. Develop specialised mathematical knowledge and skills within the field of stochastic calculus.
2. Understand the complex connections between financial and probabilistic concepts.
3. Apply sophisticated stochastic modelling skills within the context of interest rate modelling.
4. Apply critical thinking to problems in interest rate modelling.
5. Formulate expert solutions to practical financial problems using specialised cognitive and technical skills within the field of stochastic calculus.
6. Communicate complex information in an accessible format to a non-mathematical audience.

NOTE: From 1 July 2019, the duration of all exams is changing to combine reading and writing time. The new exam duration for this unit is 3 hours and 10 minutes.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

Two 2-hour lectures per week

See also Unit timetable information

Introduction to computational methods in finance. Partial differential equations. Numerical solutions of partial differential equations using finite-difference techniques, and the pricing of European options. Implicit, explicit and Crank-Nicolson schemes. Convergence and stability. Numerical solutions of free-boundary value problems and the pricing of American options. The Black-Scholes and Heston stochastic volatility models. Risk-neutral valuation. Tree methods. Introduction to Monte Carlo methods. Euler and Milstein discretization schemes. Variance reduction techniques. Monte Carlo methods for multi-dimensional problems.

On completion of this unit students will be able to:

1. Develop specialised mathematical knowledge and computational skills within the fields of partial differential equations and probability theory.
2. Understand the complex connections between specialised financial and mathematical concepts.
3. Apply critical thinking to problems in partial differential equations that relate to financial derivatives.
4. Apply computational problem solving skills within the finance context.
5. Formulate expert solutions to practical financial problems using specialised cognitive and technical skills within the fields of partial differential equations and probability theory.
6. Communicate complex information in an accessible format to a non-mathematical audience.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

Two 1.5-hour lectures and one 1-hour applied class per week

See also Unit timetable information

Bayesian inference. Linear Gaussian models. Kalman filter. Maximum likelihood. Fischer information. Cramer-Rao bound. Supervised classification. Tree based methods. Support vector machines. Introduction to R.

On completion of this unit students will be able to:

1. Develop specialised statistical knowledge and skills within the field of statistical learning.
2. Understand the complex connections between specialised financial and mathematical concepts.
3. Apply critical thinking to problems in statistical learning that relate to financial models.
4. Apply estimation and calibration solving skills within the finance context.
5. Formulate expert solutions to practical financial problems using specialised cognitive and technical skills within the fields of statistical learning.
6. Communicate complex information in an accessible format to a non-mathematical audience.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

Two 1.5-hour lectures and one 1-hour applied class per week

See also Unit timetable information

Mathematical formulation of trading strategies; order book modelling; market Impact and optimal execution; efficient market hypothesis; the CAPM model; portfolio optimisation; optimal trading; correlation and covariance estimators; multivariate analysis; co-integration; micro-economy of derivatives pricing.

On completion of this unit students will be able to:

1. Develop specialised financial skills within the fields of statistics and probability theory.
2. Understand the complex connections between specialised financial and mathematical concepts.
3. Apply critical thinking to problems in statistics and probability that relate to financial markets.
4. Apply problem solving skills within the finance context.
5. Formulate expert solutions to practical financial problems using specialised cognitive and technical skills within the fields of statistics and probability.
6. Communicate complex information in an accessible format to a non-mathematical audience.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

Two 1.5-hour lectures and one 1-hour applied class per week

See also Unit timetable information

This unit is designed to provide students with industry research experience and project-based learning. Through the research project, students will be able to apply financial thinking, modelling techniques and mathematical and statistical skills acquired throughout the Masters programme to solve real-life problems in finance and related areas. In the process they will acquire invaluable experience and knowledge working either independently or collaboratively on an applicable industry project.

Students must complete a 12 week industry research project at the Masters level.

On completion of this unit students will be able to:

1. Put into practice financial thinking, modelling techniques and mathematical and statistical skills acquired throughout the programme;
2. Analyse financial and/or insurance data using tools developed throughout the programme;
3. Construct models and solutions in specific settings relating to financial and/or insurance problems;
4. Recommend solutions to real-life problems in finance and related areas;
5. Design solutions to real-life problems in finance and related areas based on financial thinking, modelling techniques and mathematical and statistical skills acquired throughout the programme;
6. Exhibit effective reporting and writing skills at an industry standard.

   At the end of this capstone unit, students are expected to gain graduate placements in relevant industries.

Three minor reports (10% each): 30%

Oral presentation: 20%

Final report: 50%

This unit is designed to provide students with industry research experience and project-based learning. Through the research project, students will be able to apply financial thinking, modelling techniques and mathematical and statistical skills acquired throughout the Masters programme to solve real-life problems in finance and related areas. In the process they will acquire invaluable experience and knowledge working either independently or collaboratively on an applicable industry project.

Students must complete a six week industry research project (or 12 weeks if part time) at the Masters level.

On completion of this unit students will be able to:

1. Put into practice financial thinking, modelling techniques and mathematical and statistical skills acquired throughout the programme.
2. Analyse financial and/or in.
3. Construct models and solutions in specific settings relating to financial and/or insurance problems;
4. Recommend solutions to real-life problems in finance and related areas.
5. Design solutions to real-life problems in finance and related areas based on financial thinking, modelling techniques and mathematical and statistical skills acquired throughout the programme.
6. Exhibit effective reporting and writing skills at an industry standard.

   At the end of this capstone unit, students are expected to gain graduate placements in relevant industries.

Minor reports (3 x 10%): 30%

Final report: 50%

Oral presentation: 20%

The workload in this unit is made up of two components:

• Research: On average 44 hours per week for 6 weeks (or 22 hours per week for 12 weeks), including meeting and discussion with the supervision team, background research, problem solving, numerical implementation and private study.
• Reporting and report writing: On average 4 hours per week for 6 weeks (or 2 hours per week for 12 weeks), including minor reports, final thesis and preparation of oral presentation.

See also Unit timetable information