Mathematics Reading List

Congratulations on receiving an offer to study Mathematics (including Mathematics and Computer Science and Mathematics and Philosophy) at Balliol! We know that some of you might want to start preparing for the course, and we have put together some suggestions for activities that you might like to do. 

Oxford preparation

There is no compulsory preliminary reading that you need to do, but there are several things that you can do as useful preparation to help you when you arrive in Oxford. The only initial knowledge assumed is common to most A‑level (and equivalent) syllabuses, but it is worth making sure that you are up to speed with certain key topics. There are some sheets of practice problems that you can use to help; please work through them carefully to make sure that you’re happy with the ideas covered, and do some background reading to fill in any gaps. We’d suggest concentrating on this in September, so that the material is fresh in your mind at the start of term. There are some additional materials about bridging the gap.

The Mathematical Institute has a booklet called ‘How do Undergraduates do Mathematics?’ on its website and we suggest you read it carefully before you come to Oxford.

Preparing for a Maths degree

There are some books available to help students make the transition from school mathematics to university mathematics; some of you will like to look at these. They include:

• Lara Alcock, How to Study for a Mathematics Degree (Oxford University Press)
• Kevin Houston, How to Think Like a Mathematician (Cambridge University Press)

Some of you might like to look at the AMSP Transition to University course, to revisit and consolidate topics you’ve met at school/college, or even to explore ideas you haven’t seen in your studies so far.

Introduction to the first-year courses

You will study a range of courses during your first year, and you can read about these on the Mathematics Institute website. In particular, you may wish to browse the synopses and reading lists for the first-year (‘Prelims’) courses, and there is a page of useful information specifically for first-year mathematicians.

You might want to start reading in advance on some topics in the first-year course, particularly in any area which may be completely new to you, but this is not compulsory.

Some suggested books relevant to the topics common to Mathematics, Mathematics and Philosophy, and Mathematics and Computer Science are:

• C. Plumpton, E. Shipton & R.L. Perry, Proof (Macmillan)
• J. Rotman, Journey into Mathematics: An Introduction to Proofs (Prentice Hall)
• G. Smith, Introductory Mathematics: Algebra and Analysis (Springer)
• J. Baylis, What is Mathematical Analysis? (Macmillan)
• T.S. Blyth & E.F. Robertson, Basic Linear Algebra (Springer)

Some books relevant to the Applied Mathematics topics are:

• D. Stirzaker, Probability and Random Variables: A beginner’s guide (Cambridge)
• G. Grimmett & Welsh, Probability, an introduction (Oxford)
• D. Acheson, From Calculus to Chaos: An introduction to dynamics (Oxford)
• M. Lunn, A First Course in Mechanics (Oxford) chapters 1–4
• D.W. Jordan & P. Smith, Mathematical Techniques (Oxford)

Most of these books are included in first-year reading lists, but do not have the status of essential textbooks. The books by Smith, Bayliss, and Blyth & Robertson deal with the mainstream pure mathematics which forms a substantial part of the course. Do not worry if you find them difficult at this stage. If your course is Mathematics and you have not done any mechanics in your A‑levels (or equivalent), you will probably find it useful to look at the early parts of Acheson or Lunn, or some other introduction to the subject.

Don’t rush to buy lots of books before coming to Oxford. The Balliol Mathematics Book Loan Scheme has multiple copies of the books listed above and the key books for all the courses, and we’ll lend you copies in October that you can use throughout the year, or help you to access online versions.

YouTube

On a completely different note, Oxford Mathematics has an extensive collection of recordings of public lectures on YouTube, which you might enjoy browsing.

If you would like any further advice, please do not hesitate to get in touch with the College.

From the Mathematics Tutors, July 2024