Cambridge Notes

Below are the notes I took during lectures in Cambridge, as well as the example sheets. None of this is official.

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.

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.

Part IA

Michaelmas Term

Differential Equations (2014, M. G. Worster)

Groups (2014, J. Goedecke)

Numbers and Sets (2014, A. G. Thomason)

Vectors and Matrices (2014, N. Peake)

Lent Term

Analysis I (2015, W. T. Gowers)

Dynamics and Relativity (2015, G. I. Ogilvie)

Probability (2015, R. Weber)

Vector Calculus (2015, B. Allanach)

Part IB

Michaelmas Term

Analysis II (2015, N. Wickramasekera)

Linear Algebra (2015, S. J. Wadsley)

Markov Chains (2015, G. R. Grimmett)

Methods (2015, D. B. Skinner)

Quantum Mechanics (2015, J. M. Evans)

Lent Term

Complex Analysis (2016, I. Smith)

Complex Methods (2016, R. E. Hunt)

Electromagnetism (2015, D. Tong)

Fluid Dynamics (2016, P. F. Linden)

Geometry (2016, A. G. Kovalev)

Groups, Rings and Modules (2016, O. Randal-Williams)

Numerical Analysis (2016, G. Moore)

Statistics (2015, D. Spiegelhalter)

Easter Term

Metric and Topological Spaces (2015, J. Rasmussen)

Optimisation (2015, F. A. Fischer)

Variational Principles (2015, P. K. Townsend)

Part II

Michaelmas Term

Algebraic Topology (2015, H. Wilton)

Galois Theory (2015, C. Birkar)

Integrable Systems (2016, A. Ashton)

Linear Analysis (2015, J. W. Luk)

Probability and Measure (2016, J. Miller)

Lent Term

Logic and Set Theory (2015, I. B. Leader)

Number Fields (2016, I. Grojnowski)

Representation Theory (2016, S. Martin)

Statistical Physics (2017, H. S. Reall)

Part III

Michaelmas Term

Advanced Probability (2017, M. Lis)

Algebraic Topology (2016, O. Randal-Williams)

Analysis of Partial Differential Equations (2017, C. Warnick)

Combinatorics (2017, B. Bollobas)

Differential Geometry (2016, J. A. Ross)

Extremal Graph Theory (2017, A. G. Thomason)

Hydrodynamic Stability (2017, C. P. Caulfield)

Local Fields (2016, H. C. Johansson)

Modern Statistical Methods (2017, R. D. Shah)

Percolation and Random Walks on Graphs (2017, P. Sousi)

Quantum Computation (2016, R. Jozsa)

Quantum Field Theory (2016, B. Allanach)

Symmetries, Fields and Particles (2016, N. Dorey)

Lent Term

Advanced Quantum Field Theory (2017, D. B. Skinner)

Algebras (2017, C. J. B. Brookes)

Logic (2017, T. E. Forster)

Modular Forms and L-functions (2017, A. J. Scholl)

Positivity in Algebraic Geometry (2018, S. Svaldi)

Ramsey Theory (2017, B. P. Narayanan)

Riemannian Geometry (2017, A. G. Kovalev)

Schramm–Loewner Evolutions (2018, J. Miller)

Stochastic Calculus and Applications (2018, R. Bauerschmidt)

Symplectic Geometry (2018, A. R. Pires)

The Standard Model (2017, C. E. Thomas)

Theoretical Physics of Soft Condensed Matter (2018, M. E. Cates)

Easter Term

Classical and Quantum Solitons (2017, N. S. Manton and D. Stuart)

Part IV

Michaelmas Term

Topics in Geometric Group Theory (2017, H. Wilton)

Lent Term

Topics in Number Theory (2018, A. J. Scholl)

Easter Term

Bounded Cohomology (2017, M. Burger)


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.

Note that 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.

Frequently asked questions

Do you live TeX these notes?

I live TeX the words and equations. Simple diagrams are drawn in classes as well, but more complicated ones are usually done after lectures. There is usually some significant post-processing after lectures.

How much stuff have you got here?

There are currently

  • 4266 pages of notes
  • 204847 lines of source code
  • 1610863 words in the source code
  • 10611307 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.