Here is an aperiodically-updated source of revision sheets for Part IB of the Mathematical Tripos. The same principles apply as in IA revision.

### Groups, Rings and Modules

- Examples of Groups
- Möbius Group
- First Isomorphism Theorem
- Cauchy’s Theorem
- Sylow’s Theorems
- Simple Groups
- EDs, PIDs and UFDs
- Fermat’s Christmas Theorem
- Gauss’s Lemma and Eisenstein’s Criterion
- Structure Theorem (proof and applications)

### Linear Algebra

- Vector spaces and inner products
- Cauchy-Schwarz inequality
- Dot product
- Gram-Schmidt process
- Matrices glossary

Unofficial lecture notes (by Alex Chan) for *Linear Algebra* are available here.

### Analysis II/Met ‘n’ Top

Official lecture notes (by T. W. Körner) for *Metric and Topological Spaces* are available here. Unofficial lecture notes (by Christopher Williams) for *Analysis II* are available here.

### Complex Analysis

Official lecture notes (by Keith Carne) are available here.

### IB Geometry

### Variational Principles

Lecture notes for a similar course (*Calculus of Variations*) at Edinburgh are available here.

### Methods

Official lecture notes (by Richard Jozsa) are available h e r e (each letter links to one of four separate PDF files).

### Quantum Mechanics

### Electromagnetism

### Fluid Dynamics

The course has changed somewhat. I recommend reading Grae Worster’s *Understanding Fluid Flow* to supplement Michael McIntyre’s lecture notes.

How do I access “Cambridge Preparation”?