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)

# Remarks

Please email any comments to dexter@math.harvard.edu. 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

# What do you use to produce your notes?

The notes themselves are typeset in LaTeX, and most diagrams are drawn with TikZ.

To type the notes, I `vim`

, 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).

# 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
- 204849 lines of source code
- 1610767 words in the source code
- 10610696 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 https://github.com/dalcde/cam-notes`

. 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`

.