Pure Mathematics proves theorems in a wide range of topics usually motivated and illustrated by problems in physics, engineering and computer science.

Topics can be categorised roughly as “algebra” and “analysis”. Algebra has a discrete feel to it (like constructing or breaking codes), whereas analysis has a continuous flavour (like studying properties of mechanical systems).

Members

• Adj. A/Professor Alan Woods  
  Mathematical logic, especially limit laws and axiom systems of bounded arithmetic. Computational complexity theory, especially complexity of propositional proofs, formulas and circuits. Connections of number theory, combinatorics and algebra with logic and computational complexity.
• Dr Alice Devillers
  Group theory, graph theory, combinatorics, geometry.
• A/Professor Alice Niemeyer  
  Computational group theory: soluble groups, black box groups, matrix groups, designs.
• Dr Bob Sullivan  
  Transformation semigroups, history of mathematics.
• A/Professor Cai Heng Li  
  Algebraic combinatorics (especially, group-actions on graphs, maps and polytopes).
• Professor Cheryl Praeger
  Theory for finite permutation groups, design and analysis of randomised algorithms for groups of matrices acting on finite vector spaces.
• Dr John Bamberg
  Finite geometry, group actions and algebraic combinatorics.
• A/Professor Luchezar Stoyanov   
  Dynamical systems, inverse spectral problems, scattering theory.
• Professor Lyle Noakes   
  Applications of differential geometry in engineering, approximation theory, and computer vision.
• Dr Michael Giudici
  Permutation groups and their action on various combinatorial structures, s-arc transitive graphs, fixed point free elements of prime order and graph decompositions.
• Dr Mike Alder   
  Cognitive modelling and pattern recognition.
• Dr Nandita Rath (Honorary)   
  Matrix transformations of sequence spaces, general topology, completions of filter spaces, convergence, actions of convergence groups, the category of G-spaces.
• Adj. A/Professor Phillip Schultz 
  Abelian groups and modules, associative rings and algebras, endomorphism rings and automorphism groups, history of mathematics.
• Dr Sükrü Yalçinkaya
  Group theory, algorithms for groups.
• Dr Tomasz Popiel
  Geometrical methods of interpolation in Riemannian manifolds and their engineering applications, estimation of proportions of elements in finite classical groups.
• A/Prof. William Longstaff   
  Non-self-adjoint operator algebras and subspace lattice theory, matrix theory, basis theory, operator theory, functional analysis, linear algebra.