Honours Projects Grant Keady is prepared to supervise

General

Abbreviation: CAS= Computer Algebra System.

I am prepared to co-supervise any project involving use of computer algebra systems AXIOM, Maple or Mathematica. (AXIOM is the best of the open source CAS, first open source distribution being in 2003.)

I will only have time, I'm afraid, to supervise a maximum of 1.5 projects. My favorites are the three topics given next.

Minkowski sums and moments of inertia for plane convex domains

Something publishable might come from the endeavour. A collection of the known inequalities is being assembled here.
I have a couple of papers in the general area, submitted around 2006/07.
Regrettably, many other proofs are still in my hand-written notes and need some tidying.

The rolling of a disk on a horizontal plane and in a sphere

This could possibly be jointly supervised by Lyle Noakes - for the 'in a sphere' version.
I have papers submitted concerning the `on a horizontal plane' problem. For more see RollingDisk/index
I also used the problem in the 2008/09 MATH2200 Unit.

Weakly nonlinear developments of the linear stability analyses of inviscid parallel flows in a channel, flows with piecewise constant vorticity

If this is selected, it would have to be jointly supervised with Andrew Bassom. Various bits and pieces are here

Computer Aided Assessment in Maths with systems underpinned by CAS
NOT offered in 2009.

The student doing the project would only work with one of these.
The skills developed in this project are useful in various areas of education.

• Commercial
  • calmaeth. calmaeth uses mathematica as its CAS. I have 2nd year linear algebra questions written with an old authoring system for calmaeth. Those of these questions which parallel those I now have in AiM or mapleTA, I would very much like translated into the current calmaeth authoring system. A project like this would have to be joint with Kevin Judd, if he is at UWA at the time of the project.
  • NOT in 2009: mapleTA. mapleTA was evaluated in 2008, as a possible replacement to AiM at UWA (and, eventually perhaps, at Curtin). There is an acceptable LaTeX-underpinned authoring system. Translation of some of my calmaeth and AiM 2nd year linear algebra/linear systems questions is one possible project.
• Free, Open Source systems. More details via links from here.
  • stack and cable are two recent systems, both based on free open-source CAS (maxima and AXIOM, resp.). Systems like these would be very good for the upper levels of high school as there are licencing issues associated with using AiM outside an institution with a maple licence. Links associated with stack are at the general CAA URL above.
    Both AiM and stack will run in tandem with moodle as used in EnvironmentalEng/ENVE3605. (We began with AiM in 2006.)

Algorithms and Data Structures of Classical Computer Algebra Systems

The project title could, equally well, have been
"CAS: how do they work?"

Background, and advertisement that there is good reading for the project. At various other Universities there are courses on this. During Sept 96-Dec 96 I gave such a course at Queen Mary and Westfield College University of London. I have LaTeX-ed notes, and excellent Maple Worksheets and problem sets. These were re-used in Sept97-Dec 97 by the lecturer who at QMW who gave the course then: parts were used in a similar course at University of Galway (in early 97, possibly in 98 too). The core of the course concerns algorithms for factorizing univariate polynomials over the rationals -- for example, the Berlekamp and Hensel algorithms.

The output from the project will be an interactive 'book' (well, 'collection') on the subject, and we might make it attractive to commercial publishers (in the sense of them liking it, and providing appropriate links to it) by relating it to an appropriate book, e.g.
Childs "A concrete introduction to higher algebra" (Springer).

For more on this project, click here

Projects suitable for eng. science students

... who want a more "applied"/engineering flavour to their project.

For more see here.

Projects suitable for people who like Euclidean geometry,
e.g. intending school teachers

An engineer and I accidentally became involved with hobbyist Euclidean geometry. It is fun with a Computer Algebra system. (Any would do.)

For more see here.

Recent projects supervised

• 2008 assisting Alan Woods.
  This was Daniel Hawtin's project on the "numbers of solutions of systems of multivariate quadratic equations over finite fields". (The main computational work is in GAP. Some of the graphics is my Mathematica.) Notes are here.