Applied mathematics is concerned with using mathematical techniques and models to obtain practical solutions to concrete problems. This may help explain observations, or predict what may happen in the future. Applications of mathematics span most branches of modern science, engineering, information technology and commerce. In particular, biology and medicine are important emerging areas where a mathematical approach can reveal new knowledge. Applied mathematicians do not just rely on existing mathematical theories and techniques - often they need to develop new theories or adapt existing approaches to the specific application. They try to view problems in an abstract form, so they can identify links with other applications and build upon the existing knowledge. They also use computational techniques to understand the solution better and reveal its properties. A key feature of applied mathematics is its emphasis on the mathematical techniques and approaches used, and what they are able to reveal about each application, rather than a detailed understanding of the application area itself.
The School of Mathematical Sciences offers a comprehensive program of mathematics units at all undergraduate levels. It encompasses a wide range of areas of modern mathematics, from mathematical methods to statistics to pure mathematics, as well as demonstrating the applications of mathematics across a variety of fields. In addition to the major and extended major in applied mathematics, a broader major and extended major is offered in mathematics, along with specialised programs in mathematical statistics, pure mathematics and financial and insurance mathematics. There are cross links between applied and pure mathematics and statistics, and this is reflected in the mix of units that students can select to complete a major or extended major. Our curriculum is continuously updated to ensure that our students are exposed to the latest developments in mathematics, and acquire skills relevant to the current needs of industry.
Applied mathematics is used to solve problems from many branches of science, engineering, information technology and commerce. For example, it can help understand how cells divide, generate new financial tools, or predict weather. By studying applied mathematics at university, students will also develop general skills in problem-solving, critical thinking, modelling, scholarship, analysis, research and creativity, which can be used wherever their career may take them. Mathematics and statistics are also the two cornerstones for decision making and quantitative activities in commerce, industry, education and defence. Successful companies and organisations know their competitive edge depends on the analytical and quantitative skills of their workforce, and therefore seek employees with a sound mathematical training. Applied mathematics graduates work in a variety of fields, such as the finance, computing and insurance industries, medical and scientific research, the public service, journalism and teaching.
Availability
Applied mathematics is listed in S2000 Bachelor of Science, S3001 Bachelor of Science Advanced - Global Challenges (Honours) and S3002 Bachelor of Science Advanced - Research (Honours) at Clayton as a major or extended major.
Outcomes
In addition to achieving the broad outcomes of their course, students successfully completing this major or extended major will be able to:
- display basic knowledge and key technical skills in advanced calculus, linear algebra, differential equations and computational methods as well as high-level knowledge of and skills in the important techniques, terminology and processes of applied mathematics
- develop, apply, integrate and generate knowledge through abstraction and insight, and use high-level critical thinking skills to model, analyse, use and interpret the mathematics that arises across a range of applications in science, medicine, economics or engineering
- demonstrate skills in the written presentation of a mathematical argument that enable mathematical models, concepts, processes and results to be communicated effectively to diverse audiences.
Major requirements (48 points)
No more than 12 points at level 1 and at least 18 points at level 3.
Students complete:
- One level 1 sequence (12 points) from the following:
- MTH1030 Techniques for modelling and MTH2010 Multivariable calculus
- MTH1030 Techniques for modelling and STA1010 Statistical methods for science
- MTH1030 Techniques for modelling and MAT1830 Discrete mathematics for computer science
Students studying the double degree E3007 Bachelor of Engineering (Honours) and Bachelor of Science choose from the following:
- ENG1005 Engineering mathematics and MTH2040 Mathematical modelling
- ENG1005 Engineering mathematics and STA1010 Statistical methods for science
- ENG1005 Engineering mathematics and MAT1830 Discrete mathematics for computer science
Note 1: Students with a strong mathematics background and an interest in the subject could replace the units MTH1030 and/or MTH2010 with their advanced versions MTH1035 and/or MTH2015. Students will need to seek permission to enrol in these units at the Science Student ServicesScience Student Services (http://www.monash.edu/science/current/undergraduate/help) office.
- One of the following units (6 points):
- MTH2010 Multivariable calculus
- MTH2015 Multivariable calculus (advanced)
Note 2: If MTH2010 or MTH2015 was completed as part of the level 1 science sequence, replace it with a level 3 unit from list f. below.
Students studying the double degree E3007 Bachelor of Engineering (Honours) and Bachelor of Science complete the following unit:
- ENG2005 Advanced engineering mathematics
Note 3: For students in the double degree E3007 Bachelor of Engineering (Honours) and Bachelor of Science units ENG1005 and ENG2005 can count as part of the major for the purpose of this requirement; these units do not count towards the 96 points of Science units required for the Bachelor of Science.
- One of the following units (6 points):
- MTH2032 Differential equations with modelling
Students studying the double degree E3007 Bachelor of Engineering (Honours) and Bachelor of Science complete the following unit:
Note 4: If MTH2040 was completed as part of the level 1 science sequence, replace it with a level 3 unit from list f. below.
- One of the following units (6 points):
- MTH2021 Linear algebra with applications
- MTH2025 Linear algebra (advanced)
Students studying the double degree E3007 Bachelor of Engineering (Honours) and Bachelor of Science replace MTH2021 or MTH2025 with a level 3 unit from list f. below.
Note 5: MTH2025 is available only to students with a strong mathematics background. Students will need to seek permission to enrol in this unit at the Science Student ServicesScience Student Services (http://www.monash.edu/science/current/undergraduate/help) office.
- One of the following units (6 points):
- MTH2051 Introduction to computational mathematics
- MTH3051 Introduction to computational mathematics
Note 6: Students are strongly advised to enrol in MTH2051 early on in their studies if they are able to do so.
- The remaining units to complete a major (48 points) from the following, with overall at least 18 points at level 3:
- MTH3000 Mathematics research project level 3
- MTH3011 Partial differential equations
- MTH3020 Complex analysis and integral transforms
- MTH3060 Advanced ordinary differential equations
- MTH3310 Applied mathematical modelling
- MTH3320 Computational linear algebra
- MTH3330 Optimisation and operations research
- MTH3360 Fluid dynamics
Extended major requirements (72 points)
No more than 12 points at level 1, and at least 36 points at level 3.
Students complete:
- The requirements for the major in applied mathematics (48 points)
- Three additional level 3 units (18 points) from list f. under the major above.
- One unit (6 points) from list f. under the major or from the following, with overall at least six units (36 points) at level 3:
- MTH2121 Algebra and number theory or MTH3121 Algebra and number theory
- MTH2132 The nature and beauty of mathematics
- MTH2140 Real analysis or MTH3140 Real analysis
- MTH2222 Mathematics of uncertainty
- MTH2232 Mathematical statistics
- MTH3110 Differential geometry
- MTH3121 Algebra and number theory
- MTH3130 Topology: The mathematics of shape
- MTH3150 Algebra and number theory 2
- MTH3160 Metric spaces, Banach spaces, Hilbert spaces
- MTH3170 Network mathematics
- MTH3230 Time series and random processes in linear systems
- MTH3241 Random processes in the sciences and engineering
- MTH3251 Financial mathematics
- MTH3260 Statistics of stochastic processes
Requirements for progressing to honours and other further studies
Students must meet the entry requirements for S3701 Bachelor of Science (Honours), M5021 Graduate Diploma of Health and Science Research or meet the progression requirements to the fourth year of S3002 Bachelor of Science Advanced - Research (Honours).
Students must also complete prerequisite study as per the intended discipline. Refer to the honours prerequisiteshonours prerequisites (http://www.monash.edu.au/pubs/2019handbooks/undergrad/science-honours-prerequisites.pdf) table.
Bachelors
Single degrees
Successful completion of this area of study can be counted towards meeting the requirements for the following single degrees:*
- S2000 Bachelor of Science
- S3001 Bachelor of Science Advanced - Global Challenges (Honours)
- S3002 Bachelor of Science Advanced - Research (Honours)
Students in other single bachelor's degrees may be eligible to complete the major by using 48 points of their free electives.
Double degrees
Successful completion of this area of study can be counted towards meeting the requirements for the Bachelor of Science component in the following double degrees:*
- B2023 Bachelor of Commerce and Bachelor of Science
- B2016 Bachelor of Commerce Specialist and Bachelor of Science
- D3005 Bachelor of Education (Honours) and Bachelor of Science
- E3007 Bachelor of Engineering (Honours) and Bachelor of Science
- C2003 Bachelor of Information Technology and Bachelor of Science
- L3007 Bachelor of Laws (Honours) and Bachelor of Science
- S2006 Bachelor of Science and Bachelor of Arts
- S2007 Bachelor of Science and Bachelor of Biomedical Science
- S2004 Bachelor of Science and Bachelor of Computer Science
- S2003 Bachelor of Science and Bachelor of Global Studies
- S2005 Bachelor of Science and Bachelor of Music
