Maths Special Topics Class meeting Semester 1, 2026

Date: Monday, 23rd February 2026 
Time: 10am Canberra
Venue: Seminar room - 1.33, HN building #145

Semester 1, 2026 - Topics classes

1. Coxeter groups (Asilata Bapat) 
   This is a reading course on the theory of Coxeter groups, which is a rich collection of groups constrained by a particular kind of presentation. The symmetric groups are examples of Coxeter groups. 
   Coxeter groups are central to many important areas of topology, representation theory, geometric group theory, and combinatorics. They are closely related to the theory of root systems, as well as semisimple Lie algebras. 
   In the first half of the semester, we will cover the basic theory carefully. In the second half of the semester, we may branch out into some of these directions of applications, depending on interest.
    
   Prerequisites: An excellent grasp of Algebra I is essential for succeeding in this course, and thus an HD in Algebra I is required. Additionally you should have passed at least two     regularly scheduled courses at the third-year level or beyond.
    
   Contact: Email asilata.bapat@anu.edu.au with the subject "Coxeter groups reading course interest" by COB on Friday, 20 February.
    
2. Navier-Stokes Equations (Sylvie Monniaux)
   In this course, Convener will present a classical theory (mild solutions) of the Navier-Stokes system: partial differential equations that describe the movement of a fluid. A first part will be dedicated to the functional analysis tools that are crucial for the treatment of the system: Fourier transform, Sobolev spaces, Sobolev embeddings, properties of the Laplacian in Lp spaces, Riesz transforms. A second part will concern the well posedness of the Navier-Stokes system in critical (Sobolev or Lebesgue) spaces: existence, uniqueness and continuity with respect to the initial conditions of the solutions.
   
   The organisation will be as follows: two 1-hour lectures each week, some exercises and projects to be completed by students.
    
   Prerequisites: D or HD in MATH3320 or lecturer permission
    
   Meetings: Wednesday and Friday, 11-12, plus discussion
    
3. Exterior Differential Systems in Geometry and Differential Equations (Peter Vassilou)
   Exterior differential systems occur throughout differential geometry, in mathematical physics and in numerous related fields. This course introduces students to this topic and some of its applications. The main result is the Cartan-Kahler theorem. An exposition of this theorem will be given as well as the elements surrounding it, including the necessary differential geometric background. The method of moving frames, isometric embedding and orthogonal coordinate systems on Riemannian manifolds are some of the possible topics that may be discussed, time permitting. Geometric control theory and the theory of characteristics of hyperbolic PDE are further possible applications.
    
   Prerequisite:  D or HD in MATH2320 or lecturer permission
    
4. Combinatorics, Probability and Algorithms (Marco Yun Kuen Cheung) (undergraduate and Honours only)
   This course explores the profound synergy between combinatorics, probability and algorithms in modern research. We begin by establishing a rigorous foundation in enumerative combinatorics, covering essential combinatorial structures such as permutations, set/integer partitions and trees, alongside fundamental techniques including bijective counting (e.g., Catalan numbers, Cayley's formula), the inclusion-exclusion principle and Möbius inversion.
   Building on these foundations, we transition to analytic combinatorics, an elegant area where algebraic constructions of combinatorial classes translate into operators on generating functions, which are then utilized to perform precise asymptotic analysis. Finally, we explore how probabilistic method/combinatorics serves as a powerful tool for algorithm design, with a particular focus on graph-related problems.
    
   Prerequisite: D or higher in at least one of MATH1116, MATH2320, MATH3228 and D or higher in at least one of MATH2222, MATH3301, COMP3600; or lecturer permission.
    
5. Mathematical Data Science  (Katharine Turner) 
   MATH3349 only.  Please note that this may not be taken as an ASC.
   The course will be taught in an Inquiry Based Learning (IBL) style and will be split into two parts. The first part is a smattering of non-parametric statistics, which is what happens when you lose assumptions about parametrimode: there are no bell-curves here. The second part considers methods for dimensionality reduction: how can we put the data into a low dimensional space while still respecting the structure?  Assessment will include in-class presentations, IBL scripts, a mid-semester exam, a final exam, an oral exam, and a data analysis project.
    
   Prerequisites:  either MATH1115 and MATH1116; OR MATH1013, MATH1014 and MATH2222; or lecturer permission.  Please email katharine.turner@anu.edu.au during O-Week to express interest in this class.
    
6. MATH4201/6201:  Topics in Computational Maths Honours.
   Title: Regularization methods for inverse problems  

Course details

For more information about this course visit the Programs & courses website.