Here you will find a collection of resources that we hope can aid with preparation for Part III. The page is under construction and material will be added continually. For a more formal specification of the courses and their prerequisites, please refer to the Guide to Courses.
Note that in Cambridge we call question or exercise sheets "Example sheets". Example sheet questions vary from a few straightforward exercises to really challenging problems. We recommend that you look at the main questions, excluding "extra", "additional" or "starred" questions. Do also check the former exam questions page.
- Formal list of content of Cambridge undergraduate maths courses.
- Past exam questions for undergraduate courses.
- Undergraduate example sheets (and some lecture notes) for pure maths and statistics courses. (Including very few Part III courses at the end.)
- Undergraduate example sheets (and some lecture notes) for applied maths and theoretical physics courses.
- Part III example sheets and some lecture notes for applied maths and theoretical physcis courses.
- Lecture notes collected by the Archimedeans (students maths society) both for undergraduate and some Part III courses. Note some of these are for fairly old versions of the courses.
Particular Advice per Area
Listed below are the areas as in the Guide to Courses, linking to pages with preparation suggestions and resources. Completeness of resources varies as we are still working on building up this preparation material. We have structured these materials into two levels:
- Reality check: These exercises and topic lists are there to provide a reality check for you to test if working over the summer to catch up on the core prerequisites for the subject area is realistic. If you can't do the exercises given here fairly easily, we strongly recommend that you reconsider your choice of area, and/or whether Part III really is for you.
- Core prerequisites: These are necessary or extremely useful for the Part III courses. If you do not have these prerequisites already, we believe you can catch up on these if you use your summer well, and can continue catching up a little more in parallel to the courses once you are here. We try to provide exercises so you can check your level and can determine what you still need to work on.
- (Any course or topic listed in brackets is of secondary importance, but the topics covered in it might still be useful, or certain topics might still be useful for that course, which will be clear from context.)
- Analysis and PDEs
- Geometry and Topology
- Number Theory
- Probability and Finance
- Statistics and Operational Research
- Particle Physics, Quantum Fields and Strings
- Relativity and Gravitation
- Quantum Computation, Information and Foundations
- (Philosophy of Physics)
- Applied and Computational Analysis
- Continuum Mechanics
What are Catch-Up Workshops?
At the beginning of the academic year, we usually give some catch-up workshops. These are aimed at Part III students who have taken undergraduate courses in the relevant areas, but whose courses may not have covered all the material needed for the Part III lecture courses. We know that two hours cannot substitute for a whole undergraduate lecture course, so the workshops aim to give some intuition and a helping hand with further study. If you prepare for these topics already over the summer, you will have a much better chance at reaching the correct level (if you are not there already).
Certain basics will be assumed in the workshops. We have listed these under "first level prerequisites" on this website. If you find you are missing these also, you should definitely be doing some work over the summer, or possibly reconsider which areas you want to study and whether Part III is the correct course for you.
You can see here the abstracts for last year's workshops; you can assume that next year's will be similar but they may not be exactly the same, as we try to keep developing them to the majority need.