Macquarie University

MATH300: Geometry and Topology

This unit is designed to widen geometric intuition and horizons by studying topics such as projective geometry, topology of surfaces, graph theory, map colouring, ruler-and-compass constructions, knot theory and isoperimetric problems. This unit is especially recommended for those students preparing to become teachers of high school mathematics

Credit Points:	3
Contact Hours:	4
When Offered:	D1 - Day; Offered in the first half-year
Staff Contact(s):	Mathematics Staff
Prerequisites:	MATH235(P)
Corequisites:
NCCW(s):
Unit Designation(s):	Science
Assessed As:	Graded
Offered By:	Department of Mathematics

MATH331: Waves

This unit introduces the theory of waves by a systematic study of the underlying partial differential equations. Waves involve the transfer, without bulk motion, of both energy and information. Fundamental properties of waves are first examined in the simplest one dimensional setting. The treatment is then broadened to two dimensional and three dimensional waves, particularly for acoustic and electromagnetic waves. Resonators and waveguides provide some examples of how waves behave in confined regions. In contrast, the scattering and diffraction of waves by obstacles in free space carries information about the scatterer itself; this is the basis of many imaging technologies.

Credit Points:	3
Contact Hours:	4
When Offered:	D1 - Day; Offered in the first half-year
Staff Contact(s):	Mathematics staff
Prerequisites:	MATH235(P) and (MATH232(P) or MATH236(P))
Corequisites:
NCCW(s):
Unit Designation(s):	Science Technology
Assessed As:	Graded
Offered By:	Department of Mathematics

MATH332: Nonlinear Dynamics and Chaos

The remarkable fact that determinism does not guarantee regular or predictable behaviour is having a major impact on many fields of science and engineering, as well as mathematics. The discovery of chaos, or of chaotic motions, in simple dynamical systems changes our understanding of the foundations of physics and has many practical applications as well, shedding new light on the workings of lasers, fluids, mechanical structures and chemical reactions. Dynamical systems involve the study of maps and systems of differential equations. In this unit, the diversity of nonlinear phenomena is explored through the study of second-order differential equations, and one dimensional and two dimensional maps. Chaotic motions are introduced by a study of the driven pendulum, a second-order system that includes nonlinear aspects usually ignored in simpler treatments. An appropriate balance between forcing and damping leads to irregular, but bounded, motions that do not repeat themselves, even approximately - truly chaotic motion in a simple deterministic system.

Credit Points:	3
Contact Hours:	4
When Offered:	D2 - Day; Offered in the second half-year
Staff Contact(s):	Mathematics staff
Prerequisites:	MATH235(P) and (MATH232(P) or MATH236(P))
Corequisites:
NCCW(s):
Unit Designation(s):	Technology Science
Assessed As:	Graded
Offered By:	Department of Mathematics

MATH335: Mathematical Methods

This unit develops the ideas and techniques of analysis important in many branches of pure and applied mathematics. Topics include the theory of ordinary differential equations, including linear and nonlinear systems and their stability. Some special functions are also discussed, together with important applications in various branches of mathematics.

Credit Points:	3
Contact Hours:	4
When Offered:	D1 - Day; Offered in the first half-year
Staff Contact(s):	Mathematics Staff
Prerequisites:	MATH235(P) and (MATH232(P) or MATH236(P))
Corequisites:
NCCW(s):
Unit Designation(s):	Science Technology
Assessed As:	Graded
Offered By:	Department of Mathematics

MATH336: Partial Differential Equations

Partial differential equations form one of the most fundamental links between pure and applied mathematics. Many problems that arise naturally from physics and other sciences can be described by partial differential equations. Their study gives rise to the development of many mathematical techniques, and their solutions enrich both mathematics and their areas of origin. This unit explores how partial differential equations arise as models of real physical phenomena, and develops various techniques for solving them and characterising their solutions. Special attention is paid to three partial differential equations that have been central in the development of mathematics and the sciences - Laplace's equation, the wave equation and the diffusion equation.

Credit Points:	3
Contact Hours:	4
When Offered:	D2 - Day; Offered in the second half-year
Staff Contact(s):	Mathematics Staff
Prerequisites:	MATH235(P) and (MATH232(P) or MATH236(P))
Corequisites:
NCCW(s):
Unit Designation(s):	Technology Science
Assessed As:	Graded
Offered By:	Department of Mathematics

MATH337: Algebra IIIA

This unit develops the basic ideas of modern abstract algebra by concentrating on the many facets of group theory. As well as the standard material leading to the isomorphism theorems, we cover combinational aspects such as presentations of groups, the Todd-Coxeter algorithm, and subgroups of free groups via groupoids. Also studied are permutation groups, finitely generated abelian groups, soluble groups and group representations. The unit is especially suitable for students majoring in the theoretical aspects of physics or computing science.

Credit Points:	3
Contact Hours:	4
When Offered:	D1 - Day; Offered in the first half-year
Staff Contact(s):	Mathematics Staff
Prerequisites:	MATH235(P)
Corequisites:
NCCW(s):
Unit Designation(s):	Science
Assessed As:	Graded
Offered By:	Department of Mathematics

This unit further develops the theory of algebraic structures commenced in MATH337 Algebra IIIA, and involves the study of a selection of topics in Ring Theory and Field Theory. The Ring Theory strand develops the basic theory, including the study of integral domains, ideals, quotient rings, principal ideal domains, unique factorisation domains and Euclidean domains, followed by a study of one or two topics related to ring theory such as ideals in quadratic fields, the first case of Fermat's last theorem, Hopf algebras or the Wedderburn Structure Theorem. The Field Theory strand also develops the basic theory, including the notion of irreducibility, simple, algebraic and transcendental extensions, and the tower law. The ideas of group theory studied inMATH337 are then applied to the study of field extensions via the notion of automorphisms, culminating in the study of the Galois correspondence theorem.

Credit Points:	3
Contact Hours:	4
When Offered:	D2 - Day; Offered in the second half-year
Staff Contact(s):	Mathematics Staff
Prerequisites:	MATH337(P)
Corequisites:
NCCW(s):
Unit Designation(s):	Science
Assessed As:	Graded
Offered By:	Department of Mathematics

MATH339: Real and Functional Analysis

This unit is concerned with a review of the limiting processes of real analysis and an introduction to functional analysis. Through the discussion of such abstract notions as metric spaces, normed vector spaces and inner product spaces, we can appreciate an elegant and powerful combination of ideas from analysis and linear algebra.

Credit Points:	3
Contact Hours:	4
When Offered:	D2 - Day; Offered in the second half-year
Staff Contact(s):	Mathematics Staff
Prerequisites:	MATH236(P) or MATH331(P) or MATH332(P) or MATH335(P) or MATH336(P)
Corequisites:
NCCW(s):
Unit Designation(s):	Science
Assessed As:	Graded
Offered By:	Department of Mathematics

MATH388: Mathematics III Advanced

This unit provides an introduction to a range of topics in mathematics which do not form part of the traditional undergraduate curriculum. It is designed to prepare students to engage with mathematical research literature and areas of current research interest.

Credit Points:	3
Contact Hours:	4
When Offered:	D1 - Day; Offered in the first half-year
Staff Contact(s):	Mathematics Staff
Prerequisites:	(Admission to Advanced Program BSc or BAdvSc) and GPA of 3.00
Corequisites:	MATH335 and MATH337
NCCW(s):
Unit Designation(s):	Science
Assessed As:	Graded
Offered By:	Department of Mathematics