mathematics-and-statistics/index

aos

18 September 2017 23 January 2021

Students who commenced study in 2015 should refer to this area of study entry for direction on the requirements; to check which units are currently available for enrolment, refer to the unit indexes in the the current edition of the Handbook. If you have any queries contact the managing faculty for your area of study.

This area of study entry applies to students commencing this course in 2015 and should be read in conjunction with the relevant course entry in the Handbook. Any units listed for this area of study relate only to the 'Requirements' outlined in the Faculty of Science component of any bachelors double degrees.

Managing faculty | Faculty of Science |
---|---|

Offered by | School of Mathematical Sciences |

Campus(es) | Clayton |

Coordinator | Dr Leo Brewin (Levels one and two mathematics); Dr Simon Clarke (Level three mathematics); Dr Simon Clarke (applied mathematics); Associate Professor Burkard Polster (pure mathematics); Associate Professor Kais Hamza (mathematical statistics); Dr Jerome Droniou (Honours) |

**Notes**

- Unit codes that are not linked to their entry in the Handbook are not available for study in the current year.

Mathematics and statistics encompass the formal study of numerical, algebraic and analytical structures, the development of quantitative methods essential for the practice and development of science, engineering, economics and other fields, and the development and utilisation of mathematical and numerical models in various contexts.

Applied mathematics deal with the application of techniques and models to the solutions of problems from many branches of modern science, engineering, information technology and commerce.

Pure mathematics deals with the abstract, the rigour and the beauty of perfection. Although pure mathematics constructions are motivated by reasons other than applications, such constructions often become the basis for applied mathematics to solve the most concrete problems.

Statistics is the branch of mathematics that captures the interplay of data and theory. Applied and mathematical statistics combine to extract useful knowledge from data. Mathematical statistics develops the methodology, while applied statistics exploits the theory to learn from real-life information. The use of statistics is constantly expanding, and a sound knowledge of the discipline is important even for those who do not complete a major in the area.

There are cross links between statistics and pure and applied mathematics, and this is reflected in the mix of units students can choose from to complete a major or extended major.

Graduates will be able to:

- understand specific basic knowledge and display key technical skills in single- and multi-variable calculus and linear algebra, and their applications
- demonstrate high-level knowledge and skills of the important techniques, terminology and processes of mathematics, as appropriate to the sub-discipline of specialisation
- develop, apply, integrate and generate knowledge through abstraction and by using high-level critical thinking skills to analyse and solve mathematical problems
- apply knowledge of mathematics and sound mathematical modelling to a range of applications across science, medicine, economics or engineering
- collect, organise, analyse and interpret quantitative information meaningfully, using mathematical and/or statistical tools as appropriate to the sub-discipline of specialisation
- demonstrate skills in the written presentation of a mathematical argument that enable mathematical concepts, processes and results to be communicated effectively to diverse audiences
- work both individually and collectively with staff and colleagues on the synthesis of mathematical knowledge and the application of mathematical skills to problem solving.

- MAT1830 Discrete mathematics for computer science
- MTH1000 Special topics in mathematics level one (not offered in 2015)
- MTH1010 Functions and their applications
- MTH1020 Analysis of change
- MTH1030 Techniques for modelling
- MTH1035 Techniques for modelling (advanced)
- MTH2010 Multivariable calculus
- STA1010 Statistical methods for science

- ASP2062 Introduction to astrophysics
- ATM2020 Climate dynamics of the atmosphere and oceans
- ATM2030 Clouds, weather and forecasting
- MTH2000 Mathematics research project level 2
- MTH2010 Multivariable calculus
- MTH2015 Multivariable calculus (advanced)
- MTH2021 Linear algebra with applications
- MTH2025 Linear algebra (advanced)
- MTH2032 Differential equations with modelling
- MTH2121 Algebra and number theory
- MTH2132 The nature and beauty of mathematics
- MTH2140 Real analysis
- MTH2222 Mathematics of uncertainty
- MTH2232 Mathematical statistics

- ASP3012 Stars and galaxies
- ASP3051 Relativity and cosmology
- ATM3040 Physical meteorology
- ATM3050 Dynamical meteorology
- MTH3000 Mathematics research project level 3
- MTH3011 Partial differential equations
- MTH3020 Complex analysis and integral transforms
- MTH3051 Introduction to computational mathematics
- MTH3060 Advanced ordinary differential equations
- MTH3110 Differential geometry
- MTH3121 Algebra and number theory
- MTH3140 Real analysis
- MTH3150 Algebra and number theory II
- MTH3160 Functional analysis
- MTH3230 Time series and random processes in linear systems
- MTH3241 Random processes in the sciences and engineering
- MTH3251 Financial mathematics
- MTH3310 Applied mathematical modelling
- MTH3360 Fluid dynamics

The units MTH1035, MTH2015 and MTH2025 are advanced versions of MTH1030, MTH2010 and MTH2021, respectively. For the purpose of sequence requirements listed below, MTH1030, MTH2010 and MTH2025 can be replaced by their corresponding advanced version.

- MTH1020 and MTH1030, or MTH1030 and MTH2010, or MTH1030 and one of MAT1830, MTH1000 or STA1010
- MTH2010 (if not already completed at level one)
- the remaining 6 or 12 points from MTH2021, MTH2032, MTH2121, MTH2140 and MTH2222

- a minor in mathematics
- MTH2021 (if not already completed)
- at least one of MTH3011, MTH3051, MTH3110, MTH3140
- the remaining 12 or 18 points from the MTH units at level two and three listed above
- a total of at least 18 points at level three

- a major in mathematics
- the remaining 24 points from the MTH, ATM and ASP units at level two and three listed above
- a total of at least 36 points at level three

- completion of a minor in mathematics that includes MTH2032
- MTH2021 (if not already completed)
- at least three units from MTH3011, MTH3020, MTH3051, MTH3060, MTH3310, MTH3360, ASP3012, ASP3051 or ATM3050 including at least two of MTH3011, MTH3051, MTH3060 and MTH3310
- any remaining points from the MTH, ATM and ASP units at level two and three listed above

- a minor in mathematics that includes MTH2032
- MTH2021 (if not already completed)
- at least six units (36pts) from MTH3011, MTH3020, MTH3051, MTH3060, MTH3310, MTH3360, ASP3012, ASP3051, ATM3040, ATM3050 or MTH3251 including at least three (18pts) of MTH3011, MTH3020, MTH3051, MTH3060 and MTH3310
- any remaining points from the MTH, ATM and ASP units at level two and three listed above

- MTH1020 and MTH1030, or MTH1030 and MTH2010, or MTH1030 and one of MAT1830 or MTH1000
- MTH2010 (if not already completed at level one) and MTH2021
- MTH2140 or MTH3140, and MTH2121 or MTH3121
- the remaining 12 or 18 points from MTH2222, MTH3110, MTH3150, MTH3160, MTH3011, MTH3020 and MTH3230
- a total of at least 18 points at level three

- MTH1020 and MTH1030, or MTH1030 and MTH2010, or MTH1030 and one of MAT1830 or MTH1000
- MTH2010 (if not already completed at level one) and MTH2021
- MTH2140 or MTH3140, and MTH2121 or MTH3121
- the remaining points from MTH2222, MTH3000, MTH3110, MTH3150, MTH3160, MTH3011, MTH3020 and MTH3230
- a total of at least 36 points at level three

- either STA1010 and MTH1030, or MTH1030 and MTH2010, or MTH1030 and MTH1000
- MTH2222, MTH2232, and one of MTH2010, MTH2021 or MTH2140 (MTH2010 must be included if not already completed in level one)
- three units from ETC3400, ETC3420, MTH3230, MTH3241 and MTH3251, including at least two of MTH3230, MTH3241 and MTH3251

- either STA1010 and MTH1030, or MTH1030 and MTH2010, or MTH1030 and MTH1000
- MTH2010 (if not already completed in level one), MTH2222, MTH2232
- at least three units from ETC3400, ETC3420, MTH3230, MTH3241 and MTH3251, including at least two of MTH3230, MTH3241 and MTH3251
- the remaining points from the MTH, ATM and ASP units at level two and three listed above
- a total of at least 36 points at level three

- either STA1010 and MTH1030, or MTH1030 and MTH2010, or MTH1030 and MTH1000
- MTH2010 (if not already completed in level one), MTH2222, MTH2232
- ETC3400, ETC3460, MTH3230, MTH3241, MTH3251 and at least one of ETC3420 or ETC3530
- the remaining points from level two and level three units ETC2410, MTH2021, MTH2140, ETC3420, ETC3530, MTH3011, MTH3051 and MTH3060

- 24 points of relevant level three mathematics and statistics units, of which normally 18 points are relevant to the project

There are many possible combinations of mathematics units and strong prerequisite requirements on mathematics sequences. Students considering completing a sequence in mathematics or statistics are advised to determine the prerequisites for any higher-level units in their area of interest before finalising their choice of units and may seek the assistance of the relevant coordinator. As a general rule, it is advisable to choose a set of units at any level that leave several options open at higher levels.

Level one mathematics units are provided for students from a wide variety of backgrounds, from those who have not studied mathematics at VCE level to those who have completed VCE Specialist Mathematics units 3 and 4. It is recommended that all science students should include some level-one mathematics units in their course, particularly those who have not completed VCE Mathematical Methods units 3 and 4.

The units MTH1010, MTH1020 and MTH1030 are provided in support of other science disciplines, as well as preparation for further studies in mathematics. They should be taken sequentially commencing from a point that depends on a student's previous studies in mathematics, for example by their level of preparation from VCE level. MTH2010 is available to students at both first and second level who have completed MTH1030, including first-year students who have taken MTH1030 in their first semester. Further details of recommended mathematics sequences are provided below.

The units STA1010 and MAT1830 in combination with MTH1030 can form part of a mathematics sequence at level one, but any student who is considering completing a minor or major sequence in mathematics may limit their options at higher years if MTH1030 is not taken in their first year. STA1010 is designed specifically as a service unit in data analysis and statistics for students intending to major in other disciplines, particularly in psychology and the life sciences, as well as forming part of the normal statistics sequence. MAT1830 is a specialist mathematics unit but it also has a service role, being recommended for students of computer science.

For students who have completed VCE Mathematical Methods units 3 and 4 with a study score of at least 25, the recommended mathematics level one sequence is MTH1020 and MTH1030.

For students who have completed VCE Specialist Mathematics units 3 and 4 with a study score of at least 30, the recommended level one mathematics sequence is MTH1030 and MTH2010. These students may also choose to take MAT1830 or STA1010 instead of MTH2010 in their first year.

For other students, the recommended level-one mathematics units are MTH1010 and MTH1020.

Students not intending to take any level-two mathematics units may choose any one of the above recommended sequences or replace the second unit in any of the sequences by STA1010.

It is recommended that Bachelor of Science students complete SCI1020 prior to STA1010 if they have not completed VCE Mathematical Methods units 3 and 4.

The units MTH1035 and MTH2015 are advanced versions of MTH1030 and MTH2010 and are intended to provide challenge to high achieving students. These units replace MTH1030 and MTH2010 in the minors and majors listed above.

It is strongly recommended that students enrolling in any level-two mathematics units read the requirements of their desired major or extended major carefully to ensure that those units can be counted towards that major, and that any prerequisite requirements at level three will have been satisfied. Further advice and assistance on this matter can be obtained from either the relevant coordinator (listed above) or Science Student ServicesScience Student Services (http://monash.edu/science/current/undergraduate/help/).

MTH2025 is an advanced version of MTH2021 and is intended to provide challenges to high achieving students. This unit replaces MTH2021 in the minors and majors listed above.

Students intending to undertake a major in applied mathematics are recommended to complete MTH2032 in their second year of enrolment, along with either MTH2010 (if not already completed) or one of MTH2021 or MTH2025.

The unit MTH2222 covers the theoretical material needed to complete a major in mathematical statistics. It is only offered in second semester, so students who wish to complete MTH2222 and who have not completed MTH2010 or one of MTH2021 or MTH2025 by the end of the first semester must take MTH2010 concurrently with MTH2222.

It is strongly recommended that students enrolling in any level-three mathematics units read the requirements of their desired major or extended major carefully to ensure that those units can be counted towards that major or extended major, and that all other requirements will have been satisfied. Further advice and assistance on this matter can be obtained from either the relevant coordinator (listed above) or Science Student ServicesScience Student Services (http://monash.edu/science/current/undergraduate/help/).

The School of Mathematical Sciences offers a broad range of mathematics units at level three. Many of these units are intended for non-specialist third-level studies in mathematics. Specialist unit areas include algebra, analysis and geometry, applied and computational mathematics, mathematical statistics and probability, astrophysics and fluid dynamics.

Students intending to undertake a major in applied mathematics who have not already completed either MTH2021 or MTH2025 should normally take one of these units in their third year of enrolment.

The unit MTH3000 (Mathematics research project level 3) is only available to students who have completed at least two MTH3 units with a sufficient level of achievement. Students seeking to enrol in this unit should contact the coordinator in the first instance.

In addition to the requirements listed above, students must meet the entry requirements for the science honours program relevant to their course of enrolment. See the entries for:

- S3002 Bachelor of Science Advanced - Research (Honours)
- 0051 Bachelor of Science (Honours)
- 2188 Bachelor of Science (Science Scholar Program) (Honours)

Full details regarding the course structure for honours in this area of study are outlined in course 0051 Bachelor of Science (Honours).

- S2000 Bachelor of Science
- S3001 Bachelor of Science Advanced - Global Challenges (Honours)
- S3002 Bachelor of Science Advanced - Research (Honours)

- 4642 Bachelor of Aerospace Engineering (Honours) and Bachelor of Science
- 0530 Bachelor of Arts and Bachelor of Science
- 3528 Bachelor of Biomedical Science and Bachelor of Science
- 1469 Bachelor of Commerce and Bachelor of Science
- D3005 Bachelor of Education (Honours) and Bachelor of Science
- 4646 Bachelor of Environmental Engineering (Honours) and Bachelor of Science
- 4069 Bachelor of Journalism and Bachelor of Science
- L3007 Bachelor of Laws (Honours) and Bachelor of Science
- 3517 Bachelor of Science and Bachelor of Computer Science
- 4638 Bachelor of Science and Bachelor of Engineering (Honours)
- S2003 Bachelor of Science and Bachelor of Global Studies