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On this website you will find my notes as I write them throughout my time in Cambridge.

Disclaimer

No content presented on this website is official. It is not endorsed by the University of Cambridge, the Maths Faculty, or any of the Lecturers.
It is not an accurate representation of what was lectured or what is examined.
While some notes were taken during lectures, a big part was created after lectures or during revision and heavily modified to suit my needs. In particular, all errors are my own.
You should also assume that no single course presented here is Complete.

why?

I found that written notes are useless for me because I never look at them.
I also found large PDF style notes inconvenient for finding specific things.
That said, my main goals were:

1. providing quick lookup of all the maths I learn
2. having a wikilink whenever a maths concept appears in text
3. keeping myself entertained during lectures while i struggle with latex and plugins

I have (so far) failed at (1), tried at (2), and sometimes succeeded at (3).
Either way, this database might be useful for some of you.

Navigation

Most of the time you should use the search bar (Ctrl+K) to find the note you need. To find related notes, look for the links in the text and the list of backlinks.
You can also click on the graph view and see all the connections - it’s kinda fun.

The "Click me!" button

There is way too many files for me to check if the markdown, mathjax, tikzjax and everything else is rendering correctly. If you find that some page looks weird, click the button and I will check it out.
Two main issues that I know of are weird indenting after a list, and display math messing up the whole page.

Another word of warning

Some courses are quite detailed, while others look like they have been frantically put together just before exams (because they were :p). I sometimes go back and reorganize stuff - if you want to see a specific course redone, let me know.

Part IA

Group Theory (taken from Groups, Rings and Modules)
some Vectors and Matrices
Probability (taken from Probability and Measure)
Analysis I
See also Algebraic Methods in Combinatorics for some fun

Part IB

Optimisation
Variational principles
Some of Methods
Analysis and Topology
Quantum mechanics
Groups, Rings and Modules (only Group Theory and Ring Theory)
Numerical Analysis
Complex Methods

Part II

Some of Algebraic Topology
Linear Analysis
Numerical Analysis
Asymptotic methods
Automata and formal languages
Some of Principles of Quantum Mechanics
Probability and Measure (mostly just measure)
Some of Number theory
Some of Graph Theory
Coding and Cryptography
Logic and Set Theory
Quantum Information and Computing

Part III

(in progress)
Quantum Information
Algebraic Methods in Combinatorics
Category Theory
Information Theory
Forcing and Continuum Hypothesis

Acknowledgements

• The lecture notes were created in Obsidian

• They were written using artisticat1/obsidian-latex-suite plugin

  • which was inspired by Gilles Castel’s lecture note snippets

• If you want to view them in the app, you can find the setup guide in yarohtar/cam-maths-notes-obsidian

• This website was created using Jacky Zhao’s Quartz

• The commutative diagrams are rendered using benrbray/tikzjax

  • which is a fork of artisticat1/tikzjax
    • which is a fork of drgrice1/tikzjax
      • which is a fork of Jim Fowler’s TikzJax
        • which itself uses Jim Fowler’s web2js and dvi2html

Contributions?

If you want to add your own stuff on here, or fix some of my old notes, let me know and we’ll see what we can do. Setting this up might take some commitment, but I want the website to cover as much as possible, and would be happy to do it.