Division of Information and Communication Science

Honours Program in Mathematics

The Mathematics Department offers both full-time and part-time honours programs leading to the degrees of BA(Hons) or BSc(Hons) in mathematics.

Why Honours?

The mathematics honours course at Macquarie is designed to give training to undergraduates in the major areas of modern mathematics. Students are able to study topics in more depth than is possible in the ordinary degree course. The emphasis is on providing a firm basis for possible further study either at the postgraduate level or independently. We are also seeking to produce a well-rounded graduate in mathematics who can converse intelligently with other mathematicians on most topics arising in modern mathematics. There is also evidence that an honours degree enhances a graduates career prospects in many areas of business and industry. An honours degree also makes easier the possible study for a higher degree at a later date. A good honours degree is the basic requirement for admission to a postgraduate research program in mathematics and related subjects. The honours program will allow a student to assess the prospects for proceeding to a higher research degree.

Entry Requirements

The normal entry requirements are currently at least four of the units MATH300 Geometry and Topology, MATH334 Mathematics III Advanced, MATH335 Mathematical Methods, MATH336 Differential Equations, MATH337 Algebra IIIA MATH338 Algebra IIIB and MATH339 Real and Functional Analysis, or their equivalents elsewhere.

Candidates must normally have obtained a grade-point average of at least 2.5 in 300-level mathematics units and an overall grade-point average of at least 2.5.

It is recommended that any students considering honours include the units MATH335, MATH337, MATH338, MATH339 and two of the units MATH300, MATH334, MATH336.

Honours Program

The full-time course takes one year and the part-time course takes two years. For both programs the coursework requirements are that students take six half-year units. For the full-time program the student will take three units in each half year. For the part-time program the student will take two units in each of the first three half-years and devote the final semester to the honours essay. The honours program usually commences in February but it may be possible for some programs to commence at mid-year. In addition to the coursework units, an honours student will write an honours essay which will contribute the equivalent of 30% the final grade of honours. The essay topic will be chosen in consultation with a member of the mathematics staff who has agreed to supervise the student. The choice of topic is usually confirmed early in the first half-year and the student will have consulted members of the mathematics staff before settling on a final choice of topic. The deadline for submission of essays is towards the end of October. Students will give an oral presentation on their essay which is assessed and counts for 5% towards the final grade.

Coursework Units

Four coursework units, two per semester, comprise a core of the honours program; these are:




Number Theory

In both semesters a third unit is offered. These units may vary from year-to-year and often contain topics which are applications of the core units. Some typical recent examples are:

Distributions and Partial Differential Equations

Lie Groups

Mathematics of Quantum Mechanics

Fourier Theory

Mathematical Control Theory

Differential Equations in Banach Spaces

Clifford Analysis

Each coursework unit involves three class contact hours per week. Some of these units may be offered as a reading course in the case of small enrolments.

Assesment may vary but usually is based on assignments and take-home-exams.

Grades of honours

Honours are awarded with the following grades:

First Class, Upper Second Class, Lower Second Class, Third Class

which are based on the average percentage marks achieved in all components.

The lower cut-offs for each grade of honours are:

First Class


Upper Second Class


Lower Second Class


Third Class


Very occasionally, a candidate will not satisfy the requirements for award of any grade of honours. This is often the case where no thesis has been submitted or the thesis has been assessed as unsatisfactory.

Normally to be considered for an Australian Post-Graduate Award (APA) a candidate must have been awarded a grade of First Class Honours.

Admission to Honours

Prospective candidates for honours should contact the Mathematics Honours convenor:

Dr Bon Clarke

E-mail: bon@maths.mq.edu.au

Mathematics Department

Ph: (02) 9850 8919

Division of Information and Communication Sciences

Facs: (02) 9850 8114

Macquarie University NSW 2109


and refer to the appropriate web-page (by clicking here).

Application forms may be obtained by contacting:

Ms Marilyn Orr

E-mail: morr@remus.reg.mq.edu.au

Admissions and Student Records

Ph: (02) 850 7273

Registrar's Office

Macquarie University NSW 2109

Applications for 2003 close on 31 October 2002.



There are a limited numbers of scholarships available for exceptional students to study during an honours year. Details of these scholarships can be obtained from

Dr Christopher Cooper

E-mail: chris@ics.mq.edu.au

Wallent Scholarship Administrator

Ph: 9850 8920

Mathematics Department

Facs: 9850 8114

Macquarie University NSW 2109

Some Recent Honours Essays


Gabriel Abramowitz

Connections and General Relativity


Oldrich Klima

The Calderon-Zygmund Theory of Singular Integrals


Mark White

Pohozaev's Identity and Uniqueness for Elliptic Equations and Systems


Samantha Higgins

An Introduction to Nonco-operative Game Theory


Alana Flentje

Mathematical logic: Classical v. Quantum v. Intuitionistic


Amy Young

Trace Monoidal Categories


Nicole Sharp

Elementary Integrals and Differential Galois Theory


Dilshara Abayasekara

Species of Structures


Edwin El-Mahassni

The NTRU Cryptosystem


Daniel O'Neill

Estimation and Control of Linear Stochastic Systems


Jarrod Bayl

Elliptic Curves of High rank


Oded Rotem

Quadratic Forms and Quadratic Fields


Mark Weber

A Mathematical Analogy (Grothendieck Topos Theory)


Frances Griffin

Symmetry and Inflation properties of Penrose Tilings


Stephen Keith

The Holomorphic Functional Calculi of Unbounded Operators With Polynomially Bounded Resolvent

Staff in Mathematics


Ross H. Street

BSc PhD Syd., FAA, FAustMS

Associate Professors

William W. L. Chen

BSc PhD Lond. ARCS, DIC, FAustMS

John V. Corbett

BSc PhD Adel.

Senior Lecturers

Ron J. Andrews

BA DipEd Syd., MA

Bon M. N. Clarke

BSc Wales, PhD Lond., DIC

Christopher D. H. Cooper

MSc Syd., PhD Lond.

Xuan Thinh Duong

BSc Saigon, PhD Macq.

Chris Meaney

BSc MSc Flinders, PhD Univ. of Washington

Ross R. Moore

MSc Melb., PhD Oxon.

Gerry Myerson

AB Harvard, MSc Stanford, PhD Mich.


Susumu Okada

PhD Flinders

Rod I. Yager (Head of Department)

BSc Syd., PhD ANU

Honorary Associates

Brian J. Day

MSc Syd., PhD NSW

George Ivanov


Research Fellows

Michael Batanin (Scott Russell Johnson Memorial Fellow)

BSc PhD Novosibirsk

Alexei Davydov

BSc PhD Moscow

Lixin Yan

BA Jilin, MSc PhD Zhongshan

Areas of Research

The major research interests in the mathematics discipline are in Number Theory, Functional Analysis and Partial Differential Equations, Category Theory, Harmonic Analysis, and Mathematical Physics.

The following is a list of the main areas of research and available research supervisors:

Functional Analysis, Harmonic Analysis, Partial Differential Equations

Dr Bonnington M. N. Clarke: Control problems for hyperbolic partial differential equations, boundary controllability and observability, hyperbolic differential-boundary systems.

Dr Christopher Meaney: Harmonic analysis on Lie groups and symmetric spaces.

Dr Xuan T Duong: Singular integrals, functional calculi, Hardy spaces and partial differential equations.

Dr Lixin Yan: Singular integrals, function spaces, Clifford analysis.

Number Theory and its Applications

Associate Professor William W. L. Chen: Irregularities of distribution.

Dr Gerry Myerson: Constant line-sum matrices as linear combinations of permutation matrices, covering systems of congruences in higher dimensions, divisibility properties of special sequences, investigation of the distribution of sequences, in particular, sequences as far as possible from uniformly distributed.

Dr Rodney I. Yager: Algebraic number theory, arithmetic of abelian varieties, elliptic curves of large rank, L-functions.

Category Theory

Professor Michael S. J. Johnson: Category theory. Applications of category theory to computer science, homotopy theory and universal algebra.

Professor Ross H. Street: Coherence in category theory, enriched categories, geometric representations of higher-dimensional algebraic structures, quantum groups, geometry of tensor calculus, structure of categories of modules over a ring, generalised group and Galois theory.

Dr Michael Batanin: Higher-dimensional category theory, algebraic topology.

Dr Alexei Davydov: Monoidal categories, categories of representations of finite groups, K-theory.


Dr Christopher D. H. Cooper: Group theory, module invariants for knots.

Mathematical Physics

Associate Professor John V. Corbett: Applications of sheaf theory to the foundations of quantum mechanics, Multipartite non-Schmidt decomposable systems and information transfer, scattering theory and group representations, quantisation of fields in curved space-time.

Algebraic Geometry

Dr Ross R. Moore: Electronic presentation and publishing of mathematics; TeX, pdf-TeX, LaTeX2HTML, Xy-pic; algebraic geometry, patterns of chaos, geo-mathematical modelling.