Tripos Resources

A collection of resources I made while studying the maths tripos at Cambridge. I generally try to be as conceptual and intuition-focused as possible. Anecdotally, these resources have been pretty useful to people, so hopefully collecting them in one place is valuable!

For my general thoughts on how to learn things well (especially maths!) see this blog post

Second Year

• Intuition-Focused Revision lectures

  • Complex Analysis Part 1 and Part 2

  • Linear Algebra Part 1 and Part 2

  • Groups, Rings and Modules

• Comprehensive intuition-focused notes for most second year courses

  • Analysis II

    • Covers uniform convergence, normed spaces, formal multivariable differentiation and the inverse function theorem 

  • Metric & Topological Spaces

  • Note: Analysis II and Metric & Topological Spaces have since been merged into Analysis & Topology, but the syllabus hasn’t changed too much. I expect the notes to still be useful

  • Quantum Mechanics

  • Numerical Analysis

  • Geometry

  • Variational Principles (Calculus of Variations)

  • Statistics

  • Markov Chains

  • Complex Methods (& Analysis)

  • Linear Algebra

  • Groups, Rings and Modules

• Anki flashcards for second year maths courses

  • Tries to cover definitions, theorem statements, proof sketches, intuitions, motivations, and exam technique.

  • I think it’s better practice to make your own Anki cards than to use somebody else’s. But, anecdotally, I’ve put enough intuitions into these cards that people at least some people other than me find the deck valuable

  • If you aren’t familiar with Anki, you should definitely check it out. I find Michael Nielsen’s glowing review pretty inspiring

Third Year

• Intuition-focused notes for a handful of third year courses. The quality of these varies a lot more than my second year notes

  • Complete, and fairly high effort

    • Linear Analysis - Introductory functional analysis

    • Galois Theory

    • Graph Theory

    • Number Fields - Introductory Algebraic Number Theory

    • Probability & Measure - Introductory Measure Theory

    • Logic and Set Theory - Introduction to formal logic, ordinals and cardinals

  • Rough and low effort, but hopefully still useful

    • Algebraic Topology

    • Analysis of Functions

    • Maths of Machine Learning - Introduction to Statistical Learning Theory

    • Representation Theory

• Collecting student reviews for Cambridge maths courses (almost at 1000 reviews!)