Pure Mathematics is mainly concerned with understanding and developing the concepts and principles underlying mathematics, rather than with the mechanics of calculating specific numerical answers or finding exact formulae for the solution of various problems. While an Applied Mathematician might be looking for the exact value of the sum of a series or for a rapidly converging approximation to the solution of a differential equation, the Pure Mathematician is more likely to be concerned with whether the series does really converge or whether the differential equation does have a (unique) solution and whether that solution behaves in a particular way.

It is amazing how often the same mathematical principles are found to underlie and unify topics which seem at first to have very little in common. For example, the same mathematical techniques (Fourier analysis, integral geometry and group theory) underlie both medical imaging and mineral exploration, while the idea of chaos links heart attacks with turbulence in fluids and the stability or otherwise of complex ecosystems. Oversimplifying, you could say that pure mathematicians develop the underlying ideas, applied mathematicians apply them to specific problems (taking into account features which a special to each problem) and statisticians try to quantify what happens when random variations are introduced into the picture.

Three `core' second year courses in Pure Mathematics show you the basic principles which support enormous areas of mathematics and its applications. These are MATH2011 Several Variable Calculus, MATH2501 Linear algebra and MATH2520 Complex Analysis (or their Higher counterparts).

These courses are vital for anyone who wants to go further in mathematics.

There are four other Pure courses which are valuable to all mathematicians but particularly relevant if your interests are at all related to computer science. The first is MATH1081 Discrete Mathematics, which you may already have done in first year. This provides the background in logic and abstract modes of thought which is so necessary in(theoretical) computer science. Two others are MATH2400 Finite Mathematics, which shows how to develop codes based on the arithmetic of integers and finite fields, and MATH2430 Symbolic Computing, which considers how computers represent and manipulate symbolic and exact data. (NOTE: MATH2430 is not currently offered.) The fourth is MATH3411 Information Codes and Ciphers

MATH1141 Higher Mathematics 1A

MATH1241 Higher Mathematics 1B

MATH1081 Discrete Mathematics

MATH1000 Modelling Real-World Phenomena

Courses totalling 6 units of credit from Science schools other than Mathematics

Elective courses totalling 18 units of credit

Choose a General Education course of 3 units of credit

MATH2060 Professional and Ethical Issues in Mathematics

MATH2111 Higher Several Variable Calculus

MATH2130 Higher Mathematical Methods for Differential Equations

MATH2601 Higher Linear Algebra

MATH2620 Higher Complex Analysis

MATH2901 Higher Theory of Statistics

Further Level II Mathematics courses totalling 6 units of credit

Elective courses totalling 9 units of credit

Choose one from:

Choose a General Education course of 3 units of credit

Level III Pure Mathematics courses totalling 24 units of credit

Further Level III courses in Mathematics totalling 12 units of credit
Elective courses totalling 6 units of credit

Choose General Education courses totalling 6 units of credit

MATH4603 or MATH4604 Pure Mathematics 4 (Honours)

Note: where two courses are listed on a line, the second is the higher alternative.

MATH1131 or MATH1141 Mathematics 1A

MATH1231 or MATH1241 Mathematics 1B

MATH1081 Discrete Mathematics (Highly Recommended)

MATH2011 or MATH2111 Several Variable Calculus

MATH2060 Professional and Ethical Issues in Mathematics *
MATH2120 or MATH2130 Mathematical Methods for Differential Equations
MATH2501 or MATH2601 Linear Algebra

MATH2520 or MATH2620 Complex Analysis

MATH2801 or MATH2901 Theory of Statistics


* MATH2060 may be omitted if the professional education requirement has been met in the other discipline of a double major

Choose 18 units of credit from level III Mathematics

Students who have performed well in years 1 to 3 of the Science Degree with a major in Mathematics may apply to do Pure Mathematics Honours. See the Honours web page for further details.