Super-curricular reading and activities for maths
15 widely recommended books and 8 free resources for students applying for maths, each with one thing to do with it. A tutor learns little from a title; they learn a lot from what you tried, proved or questioned.
See the reading listHow to use this list
- Choose a little, go deep. One book and one project you can talk about for ten minutes beat a long list.
- Do something with it. Each entry suggests a problem, proof or program to try.
- Write it down. Keep notes of what you tried and what went wrong: that is the material for your statement and an interview.
Books
Getting ready for university maths
- How to Study for a Mathematics Degree, Lara Alcock. What changes between school and university maths: definitions, proofs and how lectures work. Try: Pick one definition from the book and write out, in your own words, an example and a non-example.
- How to Think Like a Mathematician, Kevin Houston. Reading and writing proofs, step by step, with exercises. Try: Do the exercises on proof by contradiction and induction, then write one proof of your own and ask a teacher to criticise it.
- How to Think About Analysis, Lara Alcock. A gentle way into sequences, series and continuity, the first pure course on most degrees. Try: Use the definition of a limit to prove that 1/n tends to 0, then that (n + 1)/n tends to 1.
- Towards Higher Mathematics: A Companion, Richard Earl. Links topics you know (complex numbers, calculus, induction) to how they continue at university. Try: Choose one chapter that extends an A Level topic and note one result you could not have proved before.
Problem solving
- How to Solve It, George Pólya. The classic description of how to attack a problem you have not seen before. Try: Use Pólya's four stages on a hard problem and keep a record of which question unlocked it.
- Advanced Problems in Mathematics, Stephen Siklos. Hard problems with discussion, written for STEP preparation; free to download from the publisher. Try: Try a problem for 30 minutes before reading the discussion, then compare your method with the book's.
Big ideas and stories
- Mathematics: A Very Short Introduction, Timothy Gowers. A short account of what mathematicians mean by abstraction, proof and approximation. Try: Explain to a friend, in a paragraph, why mathematicians care about proving things that look obvious.
- Fermat's Last Theorem, Simon Singh. The story of a 350-year-old problem and Andrew Wiles's proof. Try: Follow up one piece of mathematics in it, for example why there is no solution in the case n = 4 (Fermat's method of infinite descent).
- The Music of the Primes, Marcus du Sautoy. The prime numbers and the Riemann Hypothesis, told through the people who worked on them. Try: Write a short program that counts the primes up to x and compares the count with x / ln x.
- The Joy of x, Steven Strogatz. Short chapters, each on one idea, from numbers to calculus to group theory. Try: Choose the chapter furthest from your syllabus and follow its further reading.
- A Mathematician's Apology, G. H. Hardy. A pure mathematician's view of why maths is worth doing. Try: Decide whether you agree with Hardy about 'useful' mathematics, and find an example that tests his view.
- What Is Mathematics?, Richard Courant and Herbert Robbins. A classic survey of number, geometry, topology and calculus; harder going but rewarding. Try: Work through one section with a pencil, doing every step yourself.
Maths in the world
- Humble Pi, Matt Parker. Real mistakes in engineering, finance and computing caused by maths going wrong. Try: Pick one error, redo the calculation yourself and say what check would have caught it.
- How Not to Be Wrong, Jordan Ellenberg. Mathematical thinking applied to everyday claims: linearity, regression, expected value. Try: Take one argument from the book and test it on data or a news story of your own.
- The Mathematics of Love, Hannah Fry. A light, short book on modelling and probability in everyday decisions. Try: Set up and solve one of its models properly, with your own assumptions.
Free resources
- NRICH : Free problems and articles from the University of Cambridge, including a section on preparing for interviews and university maths.
- STEP Support Programme : Free modules for STEP from the University of Cambridge's Faculty of Mathematics; good practice for interviews as well.
- UKMT challenges and olympiads : The Senior Mathematical Challenge and the British Mathematical Olympiad, entered through your school.
- Plus magazine : Free articles on current mathematics, written for a general reader.
- Chalkdust : A free maths magazine written by maths students and researchers.
- Project Euler : Problems that need both maths and programming; the first fifty are a good start.
- Gresham College : Free public lectures on mathematics, online.
- OpenLearn : Free short courses from the Open University, including introductions to university maths topics.
Activities
Write up a problem you solved
Choose a hard problem (from NRICH, the STEP Support Programme or our competition section), solve it, then write a clear one-page solution. Writing it up is what makes it worth mentioning.
Enter a competition
UKMT challenges and olympiads are entered through school. What you learnt preparing matters more than the award.
Teach or mentor
Helping younger students, running a maths club or explaining a topic online shows you understand something well enough to teach it.
Program something mathematical
Simulate a random process, test a conjecture for the first million cases, or draw a fractal. Say what the program showed you and what it could not prove.
Do an extended project
An EPQ or another independent project on a mathematical question gives you a lot to discuss in questions 2 and 3.
Take a free online course
A short course on a university topic (for example on OpenLearn) shows you can learn new maths on your own.
On this site
- Extension and competition maths: original problems with hints and full solutions.
- 12 university interview problems.
- TMUA preparation.
FAQ
What are super-curriculars for maths?
Things you do to explore maths beyond your course: reading, solving harder problems, competitions, lectures, programming or teaching. They give you evidence for question 3 of the UCAS personal statement.
How many books should I mention?
One or two that you can discuss properly is better than a list. Say what you did with an idea from the book, not only that you read it.
Do I need to pay for super-curriculars?
No. Libraries, NRICH, the STEP Support Programme, Plus magazine and many online lectures are free.
Next: write about it in your personal statement.
A Level Math Revision is independent: it is not affiliated with or endorsed by UCAS or any university. Facts about UCAS and universities are summarised in our own words with links: always check the official page. We give guidance only and never write statements for students.