Mathematics reading list

For applicants


Credit: Electric-Eye

We advise you to read the Mathematics page thoroughly. For reading and preparation advice, you should find the following sections particularly useful:

Do also keep an eye on the subject resources, which provide more general guidance and examples for developing your academic interests.

For offer holders: preparing for STEP examinations

Many Mathematics offers include particular grades in STEP. We hope that the following information will help you to prepare:

Our STEP Support programme is designed to help you develop your advanced problem-solving skills and prepare for sitting STEP. The programme includes online modules for individual additional study. Each module consists of a structured mathematical problem-solving assignment, leading to work on STEP questions, with support material and partial solutions to help you assess your progress and identify areas that need more work. Additional support is available through an online discussion forum where you can discuss your work or ask for help and hints, mentored by Cambridge students and staff.

Find the free STEP Support programme at:

Further STEP resources:

For offer holders: the summer before you start your course

The three documents below are updated each year in late July. You will find the date at the bottom of the coversheet.

The King's Maths Perspectives, written by current undergraduate mathematicians, include useful discussion of STEP, the transition from school to Cambridge maths, and what to expect on the course.

For offer holders: reading suggestions

Until you have taken the exams, we recommend that you focus on STEP preparation before all else. In the summer before your course, the following books are recommended.

  • M R Spiegel, Vector Analysis and an Introduction to Tensor Analysis, Schaum – Chapters 1 to 4 are essential (except for the parts marked as “hard”) but read as much as you can.
  • R P Feyman, Lectures in Physics – Volume 1 Addison-Wesley, Chapters 1 – 17 and 21 – 25. This is an excellent introduction to the physics side in mathematics. It is especially important if you have not studied physics at school. (Volume II chapters 1 – 8, 12 – 18 and 20 are also interesting and useful).
  • M Spivak, Calculus, Benjaminc – A good introduction which is aimed slightly above A level and concentrates on techniques.
  • R P Burn: Numbers and Functionsc, Cambridge University Press – An alternative which concentrates on ideas.
  • D Smart, Linear Algebra and Geometryc, Cambridge University Press – Provides a good introduction to the algebra and geometry course as well as later material.
  • T W Körner, The Pleasures of Counting, Cambridge University Press – This gives an excellent but relaxed approach to rigorous mathematics.
  • The Faculty of Mathematics website also includes a reading list.

Further information

Reading lists | For offer holders | Undergraduate study