Below are the notes I took during lectures in Cambridge. None of this is official (unless otherwise specified). Included as well are stripped-down versions (eg. definition-only; script-generated and doesn't necessarily make sense), example sheets, and the source code. The source code has to be compiled with header.tex, and is also available on GitHub.

Unready notes are greyed out.

Note that the lecture notes are not reliable indicators for what was lectured in my year, or what will be lectured in your year, as I tend to change, add and remove contents from the notes after the lectures occur.

The notes for the courses in the current term will not be available until the term ends. See here for more details. Please email me (or use other methods to contact me) if you want to obtain a copy of the relevant notes for legitimate purposes..

Part IA

Michaelmas Term

Differential Equations (2014, M. G. Worster)full def thm thp trim src eg 
Groups (2014, J. Goedecke)full def thm thp trim src eg official
Numbers and Sets (2014, A. G. Thomason)full def thm thp trim src eg 
Vectors and Matrices (2014, N. Peake)full def thm thp trim src eg 

Lent Term

Analysis I (2015, W. T. Gowers)full def thm thp trim src eg 
Dynamics and Relativity (2015, G. I. Ogilvie)full def thm thp trim src eg 
Probability (2015, R. Weber)full def thm thp trim src eg official
Vector Calculus (2015, B. Allanach)full def thm thp trim src eg official

Part IB

Michaelmas Term

Analysis II (2015, N. Wickramasekera)full def thm thp trim src eg 
Linear Algebra (2015, S. J. Wadsley)full def thm thp trim src eg official
Markov Chains (2015, G. R. Grimmett)full def thm thp trim src eg 
Methods (2015, D. B. Skinner)full def thm thp trim src eg official
Quantum Mechanics (2015, J. M. Evans)full def thm thp trim src eg 

Lent Term

Complex Analysis (2016, I. Smith)full def thm thp trim src eg 
Complex Methods (2016, R. E. Hunt)full def thm thp trim src eg 
Electromagnetism (2015, D. Tong)full def thm thp trim src eg official
Fluid Dynamics (2016, P. F. Linden)full def thm thp trim src eg 
Geometry (2016, A. G. Kovalev)full def thm thp trim src eg 
Groups, Rings and Modules (2016, O. Randal-Williams)full def thm thp trim src eg 
Numerical Analysis (2016, G. Moore)full def thm thp trim src eg 
Statistics (2015, D. Spiegelhalter)full def thm thp trim src eg official

Easter Term

Metric and Topological Spaces (2015, J. Rasmussen)full def thm thp trim src eg 
Optimisation (2015, F. A. Fischer)full def thm thp trim src eg official
Variational Principles (2015, P. K. Townsend)full def thm thp trim src eg official

Part II

Michaelmas Term

Algebraic Topology (2015, H. Wilton)full def thm thp trim src eg 
Galois Theory (2015, C. Birkar)full def thm thp trim src eg 
Integrable Systems (2016, A. Ashton)full def thm thp trim src eg 
Linear Analysis (2015, J. W. Luk)full def thm thp trim src eg 
Probability and Measure (2016, J. Miller)full def thm thp trim src eg 

Lent Term

Logic and Set Theory (2015, I. B. Leader)full def thm thp trim src eg 
Number Fields (2016, I. Grojnowski)full def thm thp trim src eg 
Representation Theory (2016, S. Martin)full def thm thp trim src eg 
Statistical Physics (2017, H. S. Reall)full def thm thp trim src eg 

Part III

Michaelmas Term

Algebraic Topology (2016, O. Randal-Williams)full def thm thp trim src eg 
Differential Geometry (2016, J. A. Ross)full def thm thp trim src eg 
Local Fields (2016, H. C. Johansson)full def thm thp trim src eg 
Quantum Computation (2016, R. Jozsa)full def thm thp trim src eg official
Quantum Field Theory (2016, B. Allanach)full def thm thp trim src eg 
Symmetries, Fields and Particles (2016, N. Dorey)full def thm thp trim src eg 

Lent Term

Advanced Quantum Field Theory (2017, D. B. Skinner)full def thm thp trim src 
Algebras (2017, C. J. B. Brookes)full def thm thp trim src eg 
Logic (2017, T. E. Forster)full def thm thp trim src 
Modular Forms and L-functions (2017, A. J. Scholl)full def thm thp trim src eg 
Ramsey Theory (2017, B. P. Narayanan)full def thm thp trim src 
Riemannian Geometry (2017, A. G. Kovalev)full def thm thp trim src eg 
The Standard Model (2017, C. E. Thomas)full def thm thp trim src eg official

Part IV

Easter Term

Bounded Cohomology (2017, M. Burger)full def thm thp trim src 



Nevertheless, please email any comments to Feel free to point out errors or unclear explanations, as well as general typographic suggestions. Even better, send a GitHub pull request.

Here I'd like to thank the lecturers who delivered the (usually) amazing lectures, and all of those who helpfully pointed out my mistakes and typos.

Usual disclaimer: The notes have been continuously modified since the lectures have taken place, and do not necessarily accurately reflect what the lecturer said or thought. In particular, all errors are (almost certainly) mine.

External resources

Notes from other sources I like.

(Not so) frequently asked questions

What do you use to produce your notes?

The notes themselves are typset in LaTeX, and most diagrams are drawn with TikZ. As of the time of writing, exactly two plots are generated by Mathematica and one is from Wikimedia Commons (all of which are used in IA Differential Equations).

To type the notes, I just use some text editor (not saying which, to avoid causing controversy), and use the TeX Live distribution to compile the files. I tend to use mupdf to view the pdfs. Everything is version-controlled with git and hosted on GitHub.

All of these are run on a linux system, and everything is installed via the package manager (in particular, don't ask me how to install $SOFTWARE on Windows/OS X, since I have completely no idea).

What else do you use to produce your notes?

I have a handful of helper scripts in my "build system":

  • does the compilation and generates the various different versions of my notes.
  • is used to send the files to the SRCF server hosting this site.
  • goes through the source file and looks for certain common errors and things that don't conform to some arbitrary style guide I've set myself.
  • fixes certain simple errors like trailing whitespaces.
  • computes the page/line/word/character count.

How much stuff have you got here?

There are currently

  • 3507 pages of notes;
  • 168894 lines of source code;
  • 1305211 words in the source code; and
  • 8623358 characters in the source code.

How do I compile the tex files?

I assume you already have the appropriate compiler and packages installed (see question 1). The list of all packages needed can be found in header.tex.

The recommended way to compile the source file is to download the source (labeled "src") from the notes page together with header.tex. Put them in the same folder, and then compile the source file with your compiler. For the notes with images, you have to download the images from the GitHub repository and place them in a folder named image.

Alternatively, you can clone the GitHub repository by running git clone Then you can just navigate to the appropriate folder and compile. Note that the header.tex is stored at the root folder and symlinked to every subfolder. Windows does not like this (technically, anything that is on an FAT or NTFS filesystem). You will have to manually replace the header.tex in each subdirectory to the actual header.tex.