Dear offer holders,

Congratulations again on receiving an offer to study Mathematics (and or its joint schools with one of Computer Science, Philosophy or Statistics). We look forward to meeting you next academic year. This initial reading list gives useful preliminary background reading for any mathematics degree. We will send more detailed information and more reading to new students about 6 weeks before term starts. You will all have different backgrounds and prior mathematical experiences. So experiment a bit to find reading that interests and challenges you, building on and complementing your background and experience — not all the material below will suit everyone equally.

Extensional school exercises / Practice Problems

• Mathematical Institute Practise Problems: https://www.maths.ox.ac.uk/study-here/undergraduate-study/practice-problems. The 11 standard sheets are designed to be suitable bridging material for students with a single maths A level. As most if not all of you doing A levels will have Further maths, if you find them too easy, then you might want to take a look at the second set of sheets on more challenging material.
• S. Siklos. Advanced Problems in Mathematics: Preparing for University. Openbook Publishers. This book is freely available online (https://www.openbookpublishers.com/product/1050. It consists of problems taken from STEP papers, with worked solutions. STEP problems provide good practise in using mathematics from A level in more involved ways, this can be a nice way of complementing revision for further maths by trying some of these harder exercises.

As you’ll all have different backgrounds and prior mathematical experiences, the mathematics tutors are happy to discuss other options to best fit your own background if you are not getting materials through your school or college (please contact jan.obloj@maths.ox.ac.uk or stuart.white@sjc.ox.ac.uk).

Bridging the gap to undergraduate mathematics

The two main novelties of undergraduate mathematics are abstraction as ex­emplified by abstract algebra and rigorous attention to detail as exemplified by analysis. Books which should help you bridge this gap from A Level mathemat­ics include:

• R. Allenby, Numbers and Proofs
• K. Devlin, Introduction to Mathematical Thinking
• M. Liebeck, A Concise Introduction to Pure Mathematics

About the end of August in the year, we will ask new students to do some serious reading of such books, and we will send some detailed notes about some technical aspects of undergraduate mathematics. Meanwhile, you can find the notes at: http://www.maths.ox.ac.uk/r/study-guide
Some other useful material is at https://www.maths.ox.ac.uk/study-here/undergraduate-study/prospectus#preparation

Books for first term

It would also be useful to get a more detailed foretaste of some of the mathe­matics which you will study during your first term. For algebra, consult either of:

• T.S. Blyth & E.F. Robertson, Basic Linear Algebra (Springer)
• D.A. Towers, Guide to Linear Algebra (Macmillan), Ch. 1, 2, 3, 5

For analysis, try any of the following (ordered from least ambitious to most ambitious):

• F.M. Hart, Guide to Analysis (Macmillan)
• R. Bartle and D. Sherbert, Introduction to Real Analysis (Wiley)
• D.J.H. Garling, A Course in Mathematical Analysis, Vol.1 (CUP)

There is no need to wait until August before you read any of these books or notes above. All of them will be useful to you as undergraduate textbooks. It is important with all books to try the problems; you don’t understand a subject until you can solve problems in it.

We find that some of our students educated outside of the UK A-level system feel that they have less prior experience with the material in the first-year Geometry and Dynamics courses than UK students. While one purpose of the course is to bring everyone up to the same level, if this applies to you it may prove useful to take a look at the recommended textbooks for those courses in advance, in particular:

• R. Earl, Towards Higher Mathematics: a Companion (CUP), Ch. 3.1, 3.2, 3.7, 3.10, 4.2, 4.3.
• M.W. McCall, Classical Mechanics: a Modern Introduction (Wiley), Ch. 1-4, 7.

There is no need to wait until August before you read any of these books or notes above. All of them will be useful to you as undergraduate textbooks. It is important with all books to try some of the problems; you don’t understand a subject until you can solve problems in it.

You certainly do not need to know the full content of these books before your courses start, but you might want to get a head start if the material appears very unfamiliar.

Academic grant scheme

St John’s runs an academic grant scheme which provides students with an annual academic allowance for purchasing materials relevant to your degree. In the 2022–2023 academic year the annual allowance was £379; the allowance for 2023–24 has not yet been decided. (You can find information on the academic grant here.) If you buy any books, be sure to keep the receipts so you can claim reimbursement.

General interest books

Other books of general mathematical interest include:

• Simon Singh, Fermat’s Last Theorem, The Code Book, or The Simpsons and their Mathematical Secrets—each book covers a variety of mathemat­ical ideas linked to a particular theme
• David Acheson, 1089 and All That (OUP)—written by an Oxford tutor.
• Avner Ash and Robert Gross. Elliptic Tales—a description of one of the unsolved millennium problems.
• R. Courant and H. Robbins [and I. Stewart], What is Mathematics? (OUP)— a classic.
• Keith Devlin, The Millennium Problems, The Unfinished Game, or Math­ematics: The New Golden Age.
• Marcus Du Sautoy, The Music of the Primes about prime numbers; Find­ing Moonshine about symmetry.
• William Dunham, Journey through Genius (Penguin)—on the great the­orems of mathematics.
• J. Fauvel, R. Flood and R. Wilson, Oxford Figures (OUP)—a history of mathematics in Oxford.
• Martin Gardner—various entertaining books of problems.
• G.H. Hardy, A Mathematician’s Apology (CUP)—on the value of pure mathematics.
• Stuart Hollingdale, Makers of Mathematics (Dover)—a historical account based on the lives of famous mathematicians.
• Alexander Masters, The Genius in my Basement—an account of a math-ematical genius who somehow lost his way.
• George Polya, How to Solve it (Penguin)—a classic
• Ian Stewart—various books, in particular The Great Mathematical Prob­lems, Seventeen Equations that Changed the World, From Here to Infinity (an account of modern research) and Does God play Dice? (about chaos).
• Cedric Villani, Birth of a Theorem, a brilliant eccentric mathematician’s account of how he and a colleague proved a deep theorem.

Christopher Beem
Jane Coons
Nick Jones
Jan Ob l´oj
Stuart White
Tutors in Mathematics
June 2023

Starting at Oxford

Starting a course at Oxford can be very daunting, but there are many resources out there to help you succeed! Here are some useful guides from across the University that you might want to check out:

• Study skills and training: Here you can find advice on academic good practice including avoiding plagiarism, managing your time, reading, note taking, referencing and revision.
• Student life: It’s not all about academics at Oxford; here you can find out about the range of other opportunities available to you as a student, as well as tips on how to navigate student life with your workload. If you prefer podcasts, much of this information is available in that form here!
• Managing the cost: Undergraduate students Helena, Joe and Dan, have teamed up with the University’s Undergraduate Admissions team to discuss the financial support available to students and how they manage the cost of studying at Oxford.

---

Useful contacts

If you have any questions that aren’t answered on this page, you can get in touch with the following people:

Contact	Questions they can answer
Admissions Office: Sarah Jones	Anything to do with offers, visas, UCAS issues, reading lists and preparatory materials
Accommodation Office	Accommodation, what to bring, insurance, electoral roll issues
Bursary	All things financial
College Office	Practical arrangements, bank letters, etc.
Disability enquiries: Elaine Eastgate	Any issues relating to disability or special requirements