Faculty of Mathematics: CATAM

Part II Computational Projects Manual (July 2015 Edition)

Please note: this edition is valid only for the Part II academic year 2015-16.

Background

This is the on-line version of the Part II Computational Projects Manual for the academic year 2015-16.

It is available in Portable Document Format (PDF): most computers will be able to read this format automatically, but if not then you should download Adobe Reader. In cases of difficulty, the CATAM demonstrators can help you display or print the files.

Misprints that are discovered in the manual will be announced via CATAM News. The on-line version will be corrected, and so should be up to date. However, it should always be read in conjunction with CATAM News.

The unit allocation for each project is given in brackets after its title. Some of the projects require data files, which can be found here.

Complete Manual

All Sections

Manual by Section

Contents

Introduction
1. Numerical Methods

1.1 Fourier Transforms of Bessel Functions (6)
1.6 Multigrid Methods (10)

2. Waves

2.2 Dispersion (7)
2.11 Fisher's Equation for Population Dispersal Problems (9)

3. Fluid and Solid Mechanics

3.6 Particle Drift in a Periodic Flow Field (4)
3.8 Wind-forced Ocean Currents (10)
3.10 Smoke rings (8)

4. Dynamics

4.5 Euler's Equations (8)

5. Quantum Mechanics

5.2 S-Wave Scattering (7)
5.4 Monte Carlo Simulations in Particle Physics (8)

6. Electromagnetism

7. Mathematical Methods

7.3 Minimisation Methods (8)
7.4 Airy Functions and Stokes’ Phenomenon (9)

9. Operational Research

9.1 Policy Improvement for a Markov Decision Process (4)
9.4 Option Pricing in Mathematical Finance (6)

10. Statistics

10.9 Markov Chain Monte Carlo (6)
10.15 Variable Selection and the Bias-Variance Tradeoff (8)

11. Statistical Physics

11.4 Molecular Dynamics Simulation of a Classical Gas (10)

12. Nonlinear Dynamics & Dynamical Systems

12.3 The Lorenz Equations (10)
12.6 Chaos and Shadowing (10)

14. General Relativity

14.5 Cosmological Distances (8)
14.6 Isolating Integrals for Geodesic Motion (8)

15. Number Theory

15.5 Reduction of Binary Quadratic Forms (10)
15.10 The Continued Fraction Method for Factorisation (8)

16. Algebra

16.1 The Galois Group of a Polynomial (7)
16.5 Permutation Groups (7)

17. Combinatorics

17.1 Graph Colouring (7)
17.3 Hamiltonian Cycles (5)

19. Communication Theory

19.1 Random Codes (5)

20. Probability

20.5 Percolation and the Invasion Process (9)
20.6 Loss Networks (9)

23. Astrophysics

23.5 Ionization of the Interstellar Gas near a Star (8)
23.6 Accretion Discs (8)



This page was last modified in July 2015.