Summer Scholarships 2009 Subjects

From MathsDept

1. Bill Barton (2 students)

• Language differences in Mathematics

Requirements: fluency in some other language.

2. John Butcher: (1 or more students)

• a variety of topics in numerical methods for ordinary differential equations.
• mathematical structures in graph theory and algebra with applications to numerical analysis and other subjects.

Requirements: depend on the topic, ask John.

3. Robert Chan: (1 or more students)

• numerical methods for a variety of problems modelled by ordinary or partial differential equations

Requirements: A passes (or better) in both 150 and 250, and a good knowledge of Matlab.

4. Marston Conder: (1 student)

• symmetric maps on surfaces
• symmetric graphs
• regular polytopes
• finitely-presented groups

Requirements: computing experience, elementary knowledge of abstract algebra or group theory (e.g. from 255, 320 or 328).

5. Steven Galbraith (1 or 2 students)

• Computational number theory motivated by public key cryptography

(Either theoretical questions or projects involving computer programming.)

Requirements: Preferably high mark in 320 and/or 328.

6. David Gauld: (1 or more students).

• differentiability is continuity if you look at it the right way!
• a variety of topics in algebraic and set theoretic topology.

Requirements: good pass in MATHS255 (first topic); MATHS333 (second topic)

7. Vivien Kirk: (2 students)

• a variety of topics in nonlinear differential equations.

Requirements: an A grade in 260 and a good mark in 250.

8. Mike Meylan: (1 or more students)

• Water waves, resonance, and wave power.

We will work on theoretical methods for some simple equations with the aim to apply these theories to practical problems. The project would suit a student who want to understand more about the theory of differential equations and to see how this theory can be applied in real work situations.

Requirements: 260 and 250 with good grades

9. Eamonn O'Brien: (1 or more students).

• Automorphism groups of finite groups
• Subgroups of finite index in finitely presented groups

Requirements: MATHS 320 or MATHS 328.

10. Claire Postlethwaite: (2 students)

• Ordinary differential equations with symmetry.
• Differential equations with delays.
• Constructing a mathematical model for pigeon navigation.

Requirements: a student to have taken 250 and 260.

11. Arkadii Slinko: (1 or 2 students)

• Classification, enumeration and geometric representation of simple games and comparative probability orders

Requirements: excellent mark in MATHS 250, familiarity with GAP or Magma would be an advantage.

12. Philip Sharp: (1 or more students)

• Seven Saturnian Satellites

I have been working with researchers at NASA's Jet Propulsion Laboratory on a new model for the orbits of Saturn's moons Mimas, Enceladus, Tethys, Dione, Rhea, Titan and Iapetus. The first version of the model has been implemented on a computer. :The project for the summer scholarship would involve experimenting with the model and seeing how well it agreed with real data. More than one student could work on the project. Little computer programming would be required.

13. James Sneyd: (1 or more students)

• studying airway smooth muscle and asthma
• studying saliva secretion
• studying neurosecretory cells in the hypothalamus
• studying oscillations and waves of calcium

Requirements: interest in physiology.

14. Steve Taylor: (1 or more students).

• Solution of a system of integral equations and applications to PDEs.

Requirement: Maths 361 and Maths 270.

15. Shayne Waldron: (2 students)

• The relationship between (convex) complex polytopes and harmonic frames
• Three term recurrence relations and zeros of multivariate orthogonal polynomials (on a ball or simplex)
• Cross-correlation properties of Heisenberg frames
• Constructing complex equiangular tight frames from graphs

Requirements: basic (matrix) linear algebra and matlab.

16. Bill Solomon: (1 or more students)

• Topics in Geometric Algebra

Requirements: Maths 340

• Programming in a Scheme: a very powerful programming language

Requirements: Maths 255 or Maths 315

17. Tom ter Elst: (1 student)

• A variety of topics in analysis, depending on the interest of the student.

18. Warren Moors: (2-3 students)

• Fixed Point Theorems in Linear Spaces

Requirements: at the very least, a good grade in Maths 250.

19. Shixiao Wang: (2 or more students).

• Stability of parallel flows and swirling flows
• Vortex dynamics and vortex breakdown

Requirements: Some background of hydrodynamics stability.

20. Mike Thomas: (1 student).

• Investigating graphical understanding of antiderivative. The project involves school students working on a number of modules of work on antiderivative. The summer student would would as part of an international team analysing the data from NZ schools to see how the concepts are constructed and different approaches to the tasks are employed.