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)
- 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.
Official lecture notes (by Keith Carne) are available here.
Lecture notes for a similar course (Calculus of Variations) at Edinburgh are available here.
Official lecture notes (by Richard Jozsa) are available h e r e (each letter links to one of four separate PDF files).
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”?