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 Keith Carne) are available here.
Lecture notes for a similar course (Calculus of Variations) at Edinburgh are available here.
The course has changed somewhat. I recommend reading Grae Worster’s Understanding Fluid Flow to supplement Michael McIntyre’s lecture notes.