# Computer-Aided Teaching of All Mathematics (CATAM)

Please note: this edition is valid only for the Part II academic year 2021-22.

## Background

This is the on-line version of the Part II Computational Projects Manual for the academic year 2021-22.

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, say, Adobe Reader.

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.

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)
3.9 Viscous Flow in a Collapsible Channel (9)
3.10 Smoke rings (8)
4. Dynamics
4.5 Euler's Equations (8)
5. Quantum Mechanics

5.2 S-Wave Scattering (7)
5.3 Bound State Energies for One-Dimensional Potentials (9)
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)
10.16 The Tennis Modelling Challenge (8)
11. Statistical Physics
11.3 Classical Gases with a Microscopic Thermometer (8)
12. Nonlinear Dynamics & Dynamical Systems
12.3 The Lorenz Equations (10)
13. Logic & Computation
13.1 Minimisation of Deterministic Finite-State Automata (10)
14. General Relativity
14.5 Cosmological Distances (8)
14.6 Isolating Integrals for Geodesic Motion (8)
15. Number Theory
15.1 Primality Tests (9)
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)