Summer Scholarships 2007 Subjects

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Projects and Supervisors for Summer Scholarships

These project titles are not rigid. Talk to the lecturer, the project sometimes can be tailored to your needs and background.

  • 1. Language differences and understanding of mathematics. Student will need to be a good English speaker but also to be fluent in at least one other language (2-3 students). Stage 1 Maths is sufficient.
Contact: Bill Barton Rm 303.505, Ext 88779, homepage
  • 2. Numerical methods for differential equations (1-2 students)
Contact: John Butcher Rm , Ext n/a, homepage
  • 3. Problem on flows in a network. The student would presumably use a little functional analysis and measure theory (1 student).
Contact: n/a Rm n/a, Ext n/a, homepage
  • 4. Numerical methods for ordinary differential equations, developing structure-preserving algorithms for Hamiltonian problems (1 student).
Contact: n/a Rm n/a, Ext n/a, homepage
  • 5. Group theory, graph theory or combinatorics (1 student, depending on circumstances)
Contact: Marston Conder Rm 303.417, Ext 88879, homepage
  • 6. Aspects of knot theory (1-2 students)
a) Calculation of the Jones polynomial of a knot from its Dowker presentation (involves computing).
b) Further development of ideas around a knot invariant David proposed.
Contact: David Gauld Rm 303.419, Ext 88697, homepage
  • 7. Geometric approaches to PDE, conformal geometry (1 student)
Contact: A. Rod Gover Rm 303.427, Ext 88792, homepage
  • 8. Nonlinear ODEs and bifurcation theory (2 students).
Minimum background is a good pass in Maths 260.
Contact: Vivien Kirk Rm 303.525, Ext 88812, homepage
  • 9. To investigate rolling harvest techniques as a means of attaining long-term harvest plans (1 student, depending on the circumstances).
The student would need to have done stats 391 (intro to OR) or equivalent and have good computing skills.
Contact: n/a Rm n/a, Ext n/a, homepage
  • 10. Novel Wave Energy Devices'
The project will be an investigation of a theoretical wave energy device based on an array of truncated cylinders. The key to the efficiency of this device is the existence of sharp resonances at critical frequencies. The project will consist of developing the numerical method for the solution of the array and the investigation of its behaviour. The project will require programming a separation of variables solution in MATLAB and coupling this with a mapping theorem for Bessel functions. The project will build on many of the ideas introduced in 361 and 362.
The project would be well suited to one or two people.
Contact:n/a Rm n/a, Ext 85865, homepage
  • 11. Solvable models for partial Differential Equations

In particular, the following projects may be offered:

a) Electrons dynamics on quantum networks and basic nano-electronic devices ( quantum switches and spin filters) (modern computational electronics)
b) Scattering waves by Helmholtz resonator (classical 100-yars old problem of acoustics).
c) Prediction of earthquakes based on Saint-Venant principle and fitted solvable model of the point-wise boundary stress.
Contact: n/a Rm n/a, Ext n/a, homepage
  • 12.
a) Threshold hypergraphs and simple games.
b) Complexity of algorithms for negotiating treaties, e.g. fallback bargaining.
c) Algebraic representation of Nash equilibria in non-cooperative games.
(1-3 students)
No special knowledge beyond MATH 250 is required.
Contact: Arkadii Slinko Rm 303.509, Ext 85749, homepage
  • 13.Mathematical Physiology. The projects will involve modelling and numerical solutions of ODEs and PDEs (1 student)
Contact: James Sneyd Rm 303.519, Ext 87474, homepage
  • 14. Analysis on Q (Rationals)
Contact: Tom ter Elst Rm 303.229D, Ext 86901, homepage
  • 15. Tight frames and their symmetries (2-3 students):
(a) to write a program in MAGMA (computer algebra package) to compute all so called central harmonic tight frames.
(b) constructing nice tight frames for orthogonal polynomials of several variables for a weight with some symmetries,
(c) computing the norm for the projection operator onto polynomials of degree n on the ball in R^d with a radially symmetric weight.

MATHS 253 is desirable.
Contact: Shayne Waldron Rm 303.415, Ext 85877, homepage
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