Pure mathematics deals with the abstract, the rigour and the beauty of perfection. Although pure mathematics is motivated by reasons other than applications, it often becomes the basis for applied mathematics to solve the most concrete problems: the theory of prime numbers is fundamental to the security systems in electronic banking; notions of the curvature of space and time are applied in designing global positioning systems; imaginary numbers are used in everything from signal processing to the analysis of fluid flow. The examples are endless.
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 very applicable mathematical methods to statistics to pure mathematics. In addition to the major and extended major in pure mathematics, a broader major and extended major is offered in mathematics, along with specialised programs in applied mathematics, mathematical statistics, and financial and insurance mathematics. There are many cross links between pure and applied mathematics and statistics, and this is reflected in the mix of units students can choose from 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.
By studying pure mathematics at university, students will also develop general skills in problem-solving, critical thinking, modelling, scholarship, analysis and research, which can be used wherever their career may take them. Successful companies and organisations know their competitive edge depends critically on the level of analytical skills of their workforce and therefore seek employees with a sound mathematical training. Pure mathematics graduates work in a wide variety of fields such as teaching; the finance, computing and insurance industries; medical and scientific research; the public service, and journalism.
Pure 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.
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 and linear algebra, as well as high-level knowledge of and skills in the important techniques, terminology and processes of the core areas of pure mathematics, in particular advanced analysis, algebra and geometry
- develop, apply, integrate and generate knowledge through abstraction and insight, and use high-level critical thinking skills to analyse, use and interpret the mathematics that arises across a range of areas of pure mathematics
- demonstrate skills in the written presentation of a precise mathematical argument that enable mathematical 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.
- One level 1 sequence (12 points) from the following:
- MTH1030 Techniques for modelling and MTH2010 Multivariable calculus
- 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 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 unit from list e. 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 S2000 Bachelor of Science.
- One of the following units (6 points):
- MTH2021 Linear algebra with applications
- MTH2025 Linear algebra (advanced)
Note 4: 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.
- The following units (12 points) with at least one at level 3:
- Two additional units (12 points) from the following, with overall at least three units (18 points) at level 3:
- FIT2014 Theory of computation
- MTH2032 Differential equations with modelling
- MTH2132 The nature and beauty of mathematics
- MTH2222 Mathematics of uncertainty
- MTH3000 Mathematics research project level 3
- MTH3020 Complex analysis and integral transforms
- MTH3110 Differential geometry
- MTH3130 Topology: the mathematics of shape
- MTH3150 Algebra and number theory 2
- MTH3160Metric spaces, Banach spaces, Hilbert spaces
- MTH3170 Network mathematics
Note 5: Students studying the double degree E3007 Bachelor of Engineering (Honours) and Bachelor of Science can replace MTH2032 with MTH2040 (Mathematical modelling).
Extended major requirements (72 points)
No more than 12 points at level 1 and at least 36 points at level 3.
- The requirements for the major in pure mathematics (48 points)
- Four additional units (24 points) from the list e. under the major above or as listed below, with overall at least six units (36 points) at level 3:
- MTH3011 Partial differential equations
- MTH3051 Introduction to computational 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
- MTH3320 Computational linear algebra
- MTH3330 Optimisation and operations research
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 prerequisites table.
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.
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