### General advice

In general, Part III will provide at most a quick review of material covered in Cambridge undergraduate courses. Therefore it is a good idea for students to spend time consolidating their mathematical background in the relevant subject areas before arriving in Cambridge.

A good strategy is to look at the courses offered in the *Part III Guide to Courses*, but bear in mind that courses and their descriptions may change from year to year. In the guide you will find prerequisite pages for some subject areas, as well as prerequisites inside the individual course descriptions. Many of these refer to Cambridge undergraduate courses. Details of the contents of the undergraduate courses can be accessed via the link below. To help you find out whether you need to learn any new material, it is a good idea is to look at the example sheets and past exam questions for the relevant undergraduate courses (links also provided below). Note that the example sheet questions are designed to be challenging problems.

To give you more detailed guidance than the above advice, we also provide advice by subject area below. These resources are not exhaustive, so for courses/areas for which you cannot find enough information in the resources, please use the advice given in the above paragraph.

The expectation is that most students will handle the amount and depth of mathematical learning required without further assistance. However, you will find some sources of support to help you make the transition as detailed in the *Academic Support** *section of the current student webpage.

### Tripos resources

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 examples sheets (and some lecture notes) for pure maths and statistics courses. (Including very few Part III courses at the end.)
- Undergraduate examples sheets (and some lecture notes) for applied maths and theoretical physics courses.
- Part III examples 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.

### Advice by subject area

Listed below are the areas as in the Guide to Courses, linking to pages with preparation suggestions and resources. The materials are split 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.**Prerequisites**: The topics listed under Prerequisites are necessary or extremely useful for Part III courses in this area. If you are not on top of these already, you can most likely catch up on these if you use your summer well, and can continue catching up a little more in parallel to lectures once you are here. Exercises are provided so you can check your level and 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.)

- Algebra
- Algebraic Geometry
- Analysis and PDEs
- Combinatorics
- Differential Geometry and Topology
- Foundations
- Number Theory
- Probability and Finance
- Statistics and Operational Research
- Particle Physics, Quantum Fields and Strings
- Relativity and Gravitation
- Astrophysics
- Quantum Computation, Information and Foundations
- Applied and Computational Analysis
- Continuum Mechanics

### Preparatory workshops

At the beginning of the academic year, we usually offer some preparatory 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. Needless to say, two hours cannot substitute for an entire undergraduate lecture course, so the workshops mostly aim to convey intuition for the core concepts and provide guidance for further study. If you prepare for these topics already over the summer, you will stand a much better chance to be able to make the most of these workshops.

Certain basics will be assumed in the workshops. We have listed these under "first level prerequisites" on this website. If you find yourself struggling with these also, you will want to invest a considerable amount of time in acquiring them over the summer, or possibly reconsider the areas you wish to focus on in Part III (or, in very rare cases, whether Part III is the right course for you to start with).

The workshop descriptions and timetable for 2019-2020 are available for download here.