College of Science Discipline Sub-Committee in Mathematics

Proposal to College of Science Teaching Committee 18th June 2007

Curriculum proposals 2008

MATH3101 Real Analysis (New Course, shared lectures with MATH2320)
MATH3104 Groups and Rings (New Course, shared lectures with MATH2322)

The second year courses MATH2320 Analysis 1 Honours and MATH2322 Algebra 1 are foundation courses for entrance to most of the themes within our Honours program. Unfortunately if MATH2320 or MATH2322 are not taken in second year, the degree structure makes it difficult to take them in third year and still complete the 36 units of  level C courses.  Indeed there are a number of  “Applied” students who take our second year Methods courses, MATH2405 Mathematical Methods 1 Honours and

MATH2405 Mathematical Methods 2 Honours who would be advantaged if they had access to courses in third year which cover the content of MATH2320 and MATH2322. 

As such we propose two new courses, MATH3101 Real Analysis and MATH3104 Groups and Rings which will have shared lectures, respectively with MATH2320 Analysis 1 Honours and MATH2322 Algebra 1, but with different tutorials and assessment which will put more of an emphasise the application of the techniques than the second year courses.

We would predict up to 10 students taking these new courses.

Syllabus for MATH3101

This course develops some areas of abstract mathematical analysis which are important for applications in physics, economics and engineering.

Topics include:
Review of the real number system and set theory;  metric spaces and normed spaces, including spaces of functions and sequences; convergence of sequences and continuity of functions; completeness; the contraction mapping principle and its application to the solution of equations; applications to differential and integral equations; compact spaces and their properties (including applications to differential equations and polynomial approximation); foundations of multidimensional calculus including the inverse and implicit function theorems, with applications to the calculus of variations.

Note: This is an HPC. It provides rigorous proofs of theorems in analysis while emphasizing the importance of these results in applications.

Syllabus for MATH3104

This course is an introduction to abstract algebra, emphasising applications to the
mathematical sciences, such as mathematical physics, engineering, and computer science.

Topics include:
Group Theory: permutation groups; abstract groups, subgroups, cyclic and dihedral groups; homomorphisms; cosets, Lagrange's Theorem, quotient groups; group actions; Sylow theory. Ring Theory: rings and fields, polynomial rings, factorisation; homomorphisms, factor rings. Linear algebra: real symmetric matrices and quadratic forms, Hermitian matrices, canonical forms. Set Theory: cardinality.

Note: This is an HPC. It gives a rigorous development of modern algebra, while emphasising its importance in applications.

MATH6117 Real Analysis (New Course, postgraduate version of HPC MATH3101)
MATH6118 Groups and Rings (New Course, postgraduate version of HPC MATH3104)

We have a policy of having 6100 graduate course equivalents for all our standard 3000 courses which have an honours pathway and 6200 graduate equivalents of higher level special topics 3000 courses. The courses above are 6000 graduate versions of the new proposed HPC courses MATH3101 and MATH3104.

Change to wording of Degree Rules for Master of Mathematical Sciences

We propose the following change, in which lists of specific courses in Group 1 and Group 2 are replaced by generic specifications based on course code numbers. The courses in Group 1 correspond to standard third year courses with honours pathway options, whereas the Group 2 courses correspond to special topic courses, usually assuming a prerequisite from Group 1. We also found that the Group 3 research project courses MATH6300 and MATH6301 were not on the system so are using the essentially equivalent existing courses MATH8701 and MATH8702 as the required research courses.

Master of Mathematical Sciences

(Academic Program: 7607 | Academic Plan: 7607XMMASC)

Degree Structure

The Master of Mathematical Sciences program requires 72 units, with at least 12 units from group 1, 18 units from group 2 and 24 units from group 3 including at least 12 units of MATH8701.


Group 1:  Courses with a code in the range MATH6100 – MATH6199

Group 2:  Courses with a code in the range MATH6200 – MATH6299

Group 3:
*MATH8701 Mathematics Research Project
*MATH8702 Mathematics Reading Course

Each student’s program of study and assessment will be individually tailored to the interests and vocational requirements of the student, in consultation with the course coordinator.

Students may enrol in related graduate courses offered by other programs with the permission of the course coordinator and may be permitted to include the following 2 courses in their program if they are necessary background:

*MATH2406 (Mathematical Methods 1 Honours)
*MATH2501 (Mathematical Methods 2 Honours)

Some courses will only be offered if there is staff available and sufficient student interest.

MATH1007 Poetry of the Universe (Addition of an HPO)

The content in this course takes in some very deep concepts and the existence of an HPO would allow a deeper investigation of a number of these concepts.  We feel that the availability of an HPO would attract strong students such as PhB students to the course.

Some of the assignment questions will be replaced by an alternative questions, and the exam will contain alternative questions requiring deeper conceptual understanding.