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.

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) - full def thm thp trim src egGroups (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 egDynamics 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 egLinear 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 egComplex 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 egOptimisation (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 egGalois 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 egNumber 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

Advanced Probability (2017, M. Lis) - full def thm thp trim src egAlgebraic Topology (2016, O. Randal-Williams) - full def thm thp trim src eg

Analysis of Partial Differential Equations (2017, C. Warnick) - full def thm thp trim src eg

Combinatorics (2017, B. Bollobas) - full def thm thp trim src

Differential Geometry (2016, J. A. Ross) - full def thm thp trim src eg

Extremal Graph Theory (2017, A. G. Thomason) - full def thm thp trim src

Hydrodynamic Stability (2017, C. P. Caulfield) - full def thm thp trim src

Local Fields (2016, H. C. Johansson) - full def thm thp trim src eg

Modern Statistical Methods (2017, R. D. Shah) - full def thm thp trim src eg official

Percolation and Random Walks on Graphs (2017, P. Sousi) - full def thm thp trim src official

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 egAlgebras (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

Positivity in Algebraic Geometry (2018, S. Svaldi) - 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

Schramm–Loewner Evolutions (2018, J. Miller) - full def thm thp trim src eg official

Stochastic Calculus and Applications (2018, R. Bauerschmidt) - full def thm thp trim src eg

Symplectic Geometry (2018, A. R. Pires) - full def thm thp trim src

The Standard Model (2017, C. E. Thomas) - full def thm thp trim src eg official

Theoretical Physics of Soft Condensed Matter (2018, M. E. Cates) - full def thm thp trim src

## Easter Term

Classical and Quantum Solitons (2017, N. S. Manton and D. Stuart) - full def thm thp trim src# Part IV

## Michaelmas Term

Topics in Geometric Group Theory (2017, H. Wilton) - full def thm thp trim src## Lent Term

Topics in Number Theory (2018, A. J. Scholl) - full def thm thp trim src## Easter Term

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

THESE NOTES ARE PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, LACK OF TYPOS AND FUNNINESS OF PUNS.

Nevertheless, please email any comments to dec41@cam.ac.uk. 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.

- Gareth Taylor's notes. Mostly pure mathematics.
- David Tong's notes. Theoretical physics.
- Richard Weber's notes. Applicable courses.
- Archimedeans' site. Miscellaneous topics from different sources.
- Student Representatives' page. Miscellaneous topics from different sources. May overlap with above.

# (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":

`gen.sh`

does the compilation and generates the various different versions of my notes.`sync.sh`

is used to send the files to the SRCF server hosting this site.`test.sh`

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.`clean.sh`

fixes certain simple errors like trailing whitespaces.`count.sh`

computes the page/line/word/character count.

## 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

- 4240 pages of notes;
- 203680 lines of source code;
- 1600945 words in the source code; and
- 10544110 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`

.