The Mathematics Department offers both fulltime and parttime 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 wellrounded 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 gradepoint average of at least 2.5 in 300level mathematics units and an overall gradepoint 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 fulltime course takes one year and the parttime course takes two years. For both programs the coursework requirements are that students take six halfyear units. For the fulltime program the student will take three units in each half year. For the parttime program the student will take two units in each of the first three halfyears 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 midyear. 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 halfyear 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:
Analysis 
Algebra 
Topology 
Number Theory 
In both semesters a third unit is offered. These units may vary from yeartoyear 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 takehomeexams.
Grades of honours
Honours are awarded with the following grades:
which are based on the average percentage marks achieved in all components.
The lower cutoffs for each grade of honours are:
First Class 
85% 
Upper Second Class 
70% 
Lower Second Class 
60% 
Third Class 
50% 
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 PostGraduate 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 
Email: 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 

AUSTRALIA 

Application forms may be obtained by contacting:
Ms Marilyn Orr 
Email: 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.
Scholarships
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 
Email: chris@ics.mq.edu.au 
Wallent Scholarship Administrator 
Ph: 9850 8920 
Mathematics Department 
Facs: 9850 8114 
Macquarie University NSW 2109 

Some Recent Honours Essays
2001 
Gabriel Abramowitz 
Connections and General Relativity 
2000 
Oldrich Klima 
The CalderonZygmund Theory of Singular Integrals 
2000 
Mark White 
Pohozaev's Identity and Uniqueness for Elliptic Equations and Systems 
1999 
Samantha Higgins 
An Introduction to Noncooperative Game Theory 
1999 
Alana Flentje 
Mathematical logic: Classical v. Quantum v. Intuitionistic 
1998 
Amy Young 
Trace Monoidal Categories 
1998 
Nicole Sharp 
Elementary Integrals and Differential Galois Theory 
1999 
Dilshara Abayasekara 
Species of Structures 
1999 
Edwin ElMahassni 
The NTRU Cryptosystem 
1997 
Daniel O'Neill 
Estimation and Control of Linear Stochastic Systems 
1997 
Jarrod Bayl 
Elliptic Curves of High rank 
1996 
Oded Rotem 
Quadratic Forms and Quadratic Fields 
1996 
Mark Weber 
A Mathematical Analogy (Grothendieck Topos Theory) 
1996 
Frances Griffin 
Symmetry and Inflation properties of Penrose Tilings 
1996 
Stephen Keith 
The Holomorphic Functional Calculi of Unbounded Operators With Polynomially Bounded Resolvent 
Staff in Mathematics
Professor 
BSc PhD Syd., FAA, FAustMS  
Associate Professors 
BSc PhD Lond. ARCS, DIC, FAustMS  

BSc PhD Adel.  
Senior Lecturers 
Ron J. Andrews 
BA DipEd Syd., MA 

BSc Wales, PhD Lond., DIC  

MSc Syd., PhD Lond.  

Xuan Thinh Duong 
BSc Saigon, PhD Macq. 

BSc MSc Flinders, PhD Univ. of Washington  

MSc Melb., PhD Oxon.  

Gerry Myerson 
AB Harvard, MSc Stanford, PhD Mich. 
Lecturers 
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 
BA PhD ANU 
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 differentialboundary 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 linesum 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, Lfunctions.
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 higherdimensional algebraic structures, quantum groups, geometry of tensor calculus, structure of categories of modules over a ring, generalised group and Galois theory.
Dr Michael Batanin: Higherdimensional category theory, algebraic topology.
Dr Alexei Davydov: Monoidal categories, categories of representations of finite groups, Ktheory.
Algebra
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 nonSchmidt decomposable systems and information transfer, scattering theory and group representations, quantisation of fields in curved spacetime.
Algebraic Geometry
Dr Ross R. Moore: Electronic presentation and publishing of mathematics; TeX, pdfTeX, LaTeX2HTML, Xypic; algebraic geometry, patterns of chaos, geomathematical modelling.