# Computer-Aided Teaching of All Mathematics (CATAM)

Please note: this edition is valid only for the Part II academic year 2020-21.

## Background

This is the on-line version of the Part II Computational Projects Manual for the academic year 2020-21.

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.

## Complete Manual

This manual will also be available on the CATAM Part II Moodle site

All Sections

## Manual by Section

Contents
Introduction
1. Numerical Methods
1.3 Parabolic Partial Differential Equations (7)
1.8 Hyperbolic Partial Differential Equations (8)
2. Waves
2.7 Soliton Solutions of the KdV Equation (7)
2.10 Phase and Group Velocity (8)
3. Fluid and Solid Mechanics
3.1 Boundary Layer Flow (6)
3.8 Wind-forced Ocean Currents (10)
4. Dynamic
4.3 The Rotating Top (6)
5. Quantum Mechanics
5.1 Band Structure (8)
6. Electromagnetism
6.1 Diffraction Pattern due to a Current Strip (7)
7. Mathematical Methods
7.6 Insulation (10)
9. Operational Research
9.3 Protein Comparison in Bioinformatics (8)
9.5 The Google PageRank Algorithm (5)
10. Statistics
10.3 Bootstrap Estimation of Standard Error (5)
10.12 Analysis of Performance Data (8)
10.15 Variable Selection and the Bias-Variance Tradeoff (8)
11. Statistical Physics
11.2 The Ising Model in One Dimension (10)
12. Nonlinear Dynamics & Dynamical Systems
12.8 A Nonlinear Map and the Dynamics of Hydrogen Atoms in Electric Fields (7)
12.9 Differential Equations for Nonlinear Oscillators (10)
14. General Relativity
14.1 Particle or Photon Orbits near a Black Hole (8)
14.7 Gravitational Radiation from Point Masses in a Keplerian Orbit (8)
15. Number Theory
15.3 Positive Definite Binary Quadratic Forms (9)
15.6 Computing Roots Modulo p (7)
16. Algebra
16.8 The Character Table of a Finite Group (9)
16.9 Resultants and Resolvants (8)
17. Combinatorics
17.5 Matchings (6)
17.7 Graph Planarity (10)
19. Communication Theory
19.2 Information Content of Natural Language (4)
20. Probability
20.1 The Percolation Model (7)
20.2 Importance Sampling and Fast Simulation (5)
23. Astrophysics
23.1 Generating a Consistent Self-Gravitating System (8)
23.4 Stellar Structure (8)