Hello! I aim to type up notes for as much mathematics as I can here - in particular, I am drawing on the courses that I attend at Cambridge, gradually supplementing them with useful tricks, interesting extensions and in-depth background to aid the understanding.

Eventually, I hope to integrate these courses into a more encyclopaedic (less course-focused) reference, but for now, this (and good old Wiki P.) will have to do.

Asides - There may be something of interest to you here too!

Please note the usual disclaimers: I take all responsibility for errors in these notes (and surely I will have introduced more than my fair share!), and notes are never a substitute for a good book.

First-Year Courses

Differential Equations

Based on a course delivered by the amazingly clear Professor Grae Worster in 2009:

Analysis I

Based on a course delivered by the excellent Professor Gabriel Paternain in 2010:

Second-Year Courses

Variational Principles

Based on a course delivered by Dr. David Stuart in 2010:

Other Courses


Based on a course delivered by Sean Lip in 2010 (course homepage):

These materials are all currently in \LaTeX, authored in the immensely convenient LyX, but I hope to write a converter for my CMS here to transform them into HTML books at some point in the near future.

Please note these are very much works in progress - I want to get around to adding more graphics at some point, as well as integrating them into the website - and several sets of notes are incomplete or missing. For now, use your imagination...

I suggest you either check this page regularly for updates, too, by the way - I try to correct errata as soon as I'm told about them, and I'm constantly adding to them anyway. The contact address is at the top of each PDF, so please don't hesitate to get in touch with anything nice/constructive you'd like to say!

Target Audience?

I hope that these notes are a useful guide for everyone, basically. The mathematics is certainly beyond A-level standard, so if you struggle with the content at that level this perhaps isn't a great place to start. (I do hope to get around to documenting the Mathematics A-levels someday.)

However, if you're an enthusiastic student at that level looking for extension material and background, or a university student looking for a reference with a different point of view, I hope this is the place for you!


These materials are distributed under a permissive Creative Commons licence - you are permitted to use the materials as you wish for non-commercial purposes, but you are required to credit me as the author, and any other people mentioned in each case.

If you have problems with Adobe Acrobat reporting "There was a problem reading this document", then please save the file to your hard drive and open it there. This seems to be a bug with the browser plug-in, particularly with Chrome.

Course Notes

Want to learn? :D

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