Undergraduate Study

Mathematics is the study of universal patterns and structures and is the quantitative language of the world. Mathematics underpins information technology, computer science, engineering, and the physical sciences, and is playing an increasingly important role in the biological and medical sciences, economics, finance, environmental science, sociology and psychology.

Mathematics makes you flexible! Students with a good background in fundamental or cross disciplinary mathematics have many more options in terms of career possibilities, and are highly sought after for postgraduate study in almost every quantitative field. "Employers set a lot of store by mathematical ability and are more likely to hire someone with a good background in mathematics" (Ross Gittins, economics editor, Sydney Morning Herald).

The symbiosis between the process of mathematical abstraction on the one hand and the need to achieve practical ends on the other has always been crucial to the progress of mathematics; it leads to great diversity in what mathematicians do and greatly increases the utility of mathematics. The development of the modern computer stemmed directly from the work of John von Neumann, one of the twentieth century's most brilliant mathematicians, and has totally changed the face of the subject and of society. The increasing pervasiveness of mathematics in every area of human activity, together with the enormous advances in the subject itself, indicates that the next 100 years will be exciting indeed.

The Department of Mathematics offers a wide range of courses and programs, catering to students who wish to study the subject for its own interest, its applications, or a mixture of both:

• Fundamental (or Theoretical) Mathematics for those with a significant interest in the subject in its own right, either from a vocational standpoint or because of its intrinsic interest

• Cross Disciplinary Mathematics (Contemporary Applied Mathematics). This is an excellent way to acquire mathematical skills together with a broad knowledge of one or more major areas of contemporary science and technology, including bioinformatics (human genome project), computational science, information technology, astrophysics, and other modern applied mathematics

• Complementary Programs for those whose major interest is in another area (eg biology, chemistry, computing, economics, engineering, geography, information technology, physics, statistics) for which they need to make use of mathematical tools and techniques at a range of different levels.

Major and Double Major in Mathematics

Students can complete a single or a double Major in Mathematics. Refer to the Bachelor of Science entry for further details. In addition, Mathematics is an integral part of the following cross disciplinary majors: Astronomy and Astrophysics, Computational Modelling, Environmental Modelling, Mathematics and Statistics, Mathematical Economics, Mathematical Finance, Mathematical Physics and Quantitative Biology and Bioinformatics.

Combined programs

Students undertaking a combined Science program can still obtain a good knowledge of more than one area of contemporary science by studying cross disciplinary and fundamental mathematics courses as the major part of their Science program. See the later information on the cross disciplinary program. Note that a combined program in Science and Actuarial Studies is now available.

Programs for the PhB, Graduate Diploma, Masters and PhD programs are available to students with the appropriate background.

More complete information about the Department of Mathematics and mathematics courses may be found on the website www.maths.anu.edu.au/DoM.

First Year courses

Students may undertake their mathematics programs at several different levels. The choice of level and the amount of mathematics studied will depend on the student's interest, background, and need for mathematical support in the study of other disciplines. Mathematics topics available to students in their first year of study are arranged in three streams with prerequisites as shown:

Modelling stream

Math1003 Mathematical Modelling 1 (Calculus and Matrix Techniques)

Prerequisites: Assumed Knowledge: ACT Mathematical Methods or NSW HSC Mathematics or equivalent.

Math1005 Mathematical Modelling 2 (Discrete Mathematics)

Prerequisites: ACT Mathematical Methods or NSW HSC Mathematics or equivalent. (MATH1003 is not a prerequisite for this course.)

These courses are designed for students with a wide variety of backgrounds and will cover important areas in mathematics and its applications. Modelling 1 is not a required prerequisite for Modelling 2. The courses are suitable for students whose main area of study is in the application of mathematics to areas such as: social, biological, physical, environmental sciences, computational science and economics. Extensive use will be made of computer packages and the emphasis will be on the applicability of mathematics for solving interesting problems. It is possible to mix-and-match these courses with semester courses in other areas (eg statistics).

MATH1003 Modelling 1 now provides a pathway into higher level mathematics courses.

Advanced stream

Math1013 Mathematics and Applications 1, Math1014 Mathematics and Applications 2

Prerequisites: MATH1003 or a satisfactory result in ACT Specialist Mathematics or NSW HSC Mathematics Extension 1 or equivalent. Students with a good pass in ACT Mathematical Methods or NSW HSC Mathematics or equivalent will be considered. Students with excellent results in Advanced Mathematics in the ACT, or NSW HSC Mathematics, or the equivalent from elsewhere, may also be permitted to enrol in MATH1013 Mathematics and Applications 1.

These courses form the basic sequence of mathematics applicable to other disciplines (in particular to the physical sciences, computer science, statistics or economics) and introductory to a wide range of later year courses in mathematics.

Note that these courses are available in both semesters.

Honours stream

Math1115 Mathematics and Applications 1 Honours, Math1116 Mathematics and Applications 2 Honours

Prerequisites: A satisfactory pass in the ACT Specialist Mathematics double major, NSW HSC Mathematics Extension 2 or equivalent. Students with excellent results in either the ACT Specialist Mathematics major-minor, NSW HSC Mathematics Extension 1, or equivalent, may be permitted to enrol. Students with the appropriate background should normally enrol in MATH1115 Mathematics and Applications 1 Honours rather than in MATH1013 Mathematics and Applications 1. It will be possible at several stages to transfer from the Honours stream but transferring into it is difficult.

These courses are of a more advanced nature and are recommended for those with an appropriate background who intend doing advanced work in other mathematically based disciplines, such as physics or statistics, or in more quantitative areas of other sciences, engineering or economics. They are also recommended for students who, because of their interest and advanced background in mathematics from school, would not find the Modelling or Advanced streams by themselves sufficiently challenging: they will appeal to students who are interested in why things are true, not simply in what is true. Finally, they are the first step towards an honours program in mathematics.

Which stream should you choose?

All streams provide a good mathematical background for fields such as the biological and social sciences, economics and information technology. The modelling stream will allow you to do one mathematics course each semester in second year, and the other two streams will allow you to continue on to a full three-year sequence of 2 to 4 mathematics courses each semester. You should choose the stream that is most appropriate to your mathematical preparation. The more mathematics you can do, the greater benefit and the broader the range of options you will have in later years. Many disciplines are mathematically oriented (such as the physical sciences, the theoretical aspects of computer science, statistics and mathematical economics) and students interested in these areas should enrol in the Advanced or Honours stream. Other disciplines such as biology and finance rely increasingly on sophisticated mathematical models, and students with the mathematical background and an interest in such areas should also enrol in the Advanced or Honours streams if possible. If you are uncertain about which stream is best for you, consult the First Year Coordinator or the Head of Department.

Later Year courses and programs

Students may enrol in any courses for which they have the prerequisites. Coordinators for second and third year will be happy to help students choose sequences of courses suited to their needs and interests. To assist students in choosing a coherent program, a number of sequences designed to suit the backgrounds and interests of most students are now described. Other programs are of course possible.

Cross-disciplinary program:

You can do one or more Majors as listed previously. These normally require 12 units of Group A courses including MATH1014 (or MATH1116 for the later year Honours level courses). For some courses, MATH1003 or MATH1005 at a high level may be sufficient, see the lecturer involved, but MATH1003 and MATH1005 are not normally sufficient to carry through to a Major. Students can obtain an excellent background in mathematics with knowledge of important areas of contemporary science and technology, including bioinformatics, computational science, astrophysics and other contemporary applied mathematics by taking some or most of the following.

	Semester 1	Semester 2
Group B courses	MATH2305 Differential Equations and Applications OR MATH2405 Mathematical Methods 1 Hons	MATH2306 Partial Differential Equations and Applications OR MATH2406 Mathematical Methods 2 Hons MATH2307 Bioinformatics and Biological Modelling
Group B or C courses	MATH2320 Analysis 1 Hons OR MATH3116 Real Analysis	MATH2322 Algebra 1 Hons OR MATH3104 Groups and Rings
Group C courses	MATH3501 Scientific and Industrial Modelling MATH3511 Scientific Computing MATH3029 Probability Modelling with Applications	MATH3062 Fractal Geometry and Chaos Dynamics MATH3133 Environmental Mathematics MATH3301 Number Theory and Cryptography MATH3512 Matrix Computations and Optimisation MATH3015 Mathematical Finance

 

Students may also combine these courses with offerings in other Departments; for information on ways in which this can be done see the following entries for the Programs in Computational Science, in Astronomy and Astrophysics and in Bioinformatics or contact members of these Programs or members of the Mathematics Department. Students may also combine these courses with other third year honours level courses in fundamental mathematics.

Students in engineering are strongly recommended to do MATH2305 Differential Equations and Applications or MATH2405 Mathematical Methods 1 Honours.

The following sequence is especially relevant to students interested in the applications of mathematics in information technology. It provides an introduction to the mathematics behind many of the applications in information technology and shows how it is applied.

	Semester 1	Semester 2
Group B courses	MATH2301 Games, Graphs and Machines
Group C courses		MATH3301 Number Theory and Cryptography
This sequence requires 12 units of Group A courses in mathematics, including MATH1005 or MATH1014 or MATH1116.

 

The following sequence is especially relevant to students interested in advanced studies in the physical sciences, statistics and financial analysis. The courses are oriented towards applications and provide a solid grounding in the mathematical techniques needed. This sequence is especially recommended as the Science component of a combined program in Engineering, Economics or Commerce. It may also be included as part of an Economics, Commerce or Actuarial Studies program.

	Semester 1	Semester 2
Group B courses	MATH2305 Differential Equations and Applications OR MATH2405 Mathematical Methods 1 Hons	MATH2306 Partial Differential Equations and Applications OR MATH2406 Mathematical Methods 2 Hons
Group C courses	MATH3501 Scientific and Industrial Modelling MATH3511 Scientific Computing MATH3029 Probability Modelling with Applications	MATH3062 Fractal Geometry and Chaos Dynamics MATH3512 Matrix Computations and Optimization MATH3015 Mathematics of Finance
This sequence requires 12 units of Group A courses in mathematics, including MATH1014 or MATH1116.

 

Honours Pathway level courses:

These sequences require 12 units of Group A courses in mathematics, including MATH1116 at Credit level or better, though students with excellent results in MATH1014 may be eligible to enrol: consult the year coordinator.

As well as catering for students who intend to continue to the fourth honours year in mathematics, honours pathway level courses are used to form mathematics sequences at a high level as part of other programs. Students may consult the year coordinator for further advice.

	Semester 1	Semester 2
Group A courses	MATH1115 Mathematics and Applications 1 Honours	MATH1116 Mathematics and Applications 2 Honours
Group B courses	MATH2405 Mathematical Methods 1 Honours	MATH2306 Mathematical Methods 2 Honours
Group B or C Courses	MATH2320 Analysis 1 Honours OR MATH3116 Real Analysis	MATH2322 Algebra 1 Honours OR MATH3104 Groups and Rings
Group C Courses	MATH3320 Analysis 2 Honours MATH3345 Galois Theory Honours MATH3029 Probability Modelling with Applications MATH3501 Scientific and Industrial Modelling (HPO) MATH3511 Scientific Computing (HPO)	MATH3325 Analysis 3 Honours MATH3228 Complex Analysis Honours MATH3015 Mathematics of Finance (HPO) MATH3133 Environmental Mathematics (HPO) MATH3512 Matrix Computations and Optimisation (HPO)

 

Some fourth year honours courses will be available to third year students with an appropriate background. Students should consult the third year coordinator about what is available.

PhB and Distinguished Scholar Programs

Students with a strong interest in mathematics who are accepted into the University's Bachelor of Philosophy (Honours) or Distinguished Scholar Program will be assigned a mentor by the Department of Mathematics. The mentor will supervise a project or reading program outside the student's normal studies. Distinguished Scholars and other outstanding undergraduate students may be invited to participate in special courses that extend and develop their particular interests.

Honours in Mathematics

The Honours Program in Mathematics is organised within the Mathematical Sciences Institute, with support from the Centre for Mathematics and its Applications (CMA). The Centre for Bioinformation Sciences, the Centre for Resource and Environmental Studies (CRES) and the Research School of Astronomy and Astrophysics (RSAA) also provide support.

Entry to the fourth (honours) year is at the discretion of the Head of Department. Faculty requirements for entry to honours must be met. To qualify for admission to the Honours Year in Mathematics, an ANU student must have successfully completed at least 48 units of Group B or Group C courses relevant to the proposed Honours study, of which at least 24 units must be for Group C courses. At least a Credit average must have been achieved in these 48 units.

It is recommended that all students should include in their program MATH2405, MATH2406, MATH2320 (or MATH3116) and MATH2322 (or MATH3104). Students must also have completed sufficient in the way of prerequisites in mathematics to enable them to pursue an approved course of study in their fourth year.

Proposals for combined honours programs in mathematics and in another subject (such as economics, computer science, philosophy, physics, statistics, or theoretical physics) will be considered in consultation with the department concerned.

Program in Astronomy and Astrophysics

The Departments of Mathematics and Physics and the Research School of Astronomy and Astrophysics support a program of related courses in the area of Astronomy and Astrophysics. Courses at both pass and honours level are offered in the program. A fuller description of the Program is given in the separate Astronomy and Astrophysics entry.

Program in Computational Science

The Departments of Mathematics, Computer Science and Physics support a stream of courses in Scientific Computation that makes up the Bachelor of Computational Science (BComptlSci). A fuller description is given in the separate entry for that program or on the website www.maths.anu.edu.au/bcomptlsci.

Program in Bioinformatics

Mathematical and statistical modelling is the leading approach to the analysis of the huge amount of biological data relevant to the evolution and functions of organisms that is being constantly generated. Together with advances in computing and software technologies, this provides insights into the processes of life based on information obtained by experimental biologists and medical researchers. It is important for furthering our knowledge in life sciences, leading for example to improved drug design and population health. Bioinformatics graduates receive a Bachelor of Science after three years, with an optional fourth honours year. A combination of courses from the program can also be taken towards a Bachelor of Computational Science or a Bachelor of Biotechnology. The two core bioinformatics courses (Bioinformatics and Biological Modelling and Advanced Bioinformatics) are a joint initiative of the Department of Mathematics and the Centre for Bioinformation Science (a collaboration between the John Curtin School of Medical Research and the Mathematical Sciences Institute). Relevant biological material will be explained as the courses progress and these lectures will be given by leading biologists and medical researchers. See www.maths.anu.edu.au/bio.html for further information.

This page was updated on Friday September 14, 2007