This page contains books that you might use to help you with your core studies on a Mathematics degree, and sometimes for other subjects too. Keen A-level students could probably also pick up one of these for some extra maths or preparation, or if you want to see some of what you’re studying done in a more rigorous way than at A-level.
Many of these books are also great as Audiobooks – get a free trial of Audible here:
General ‘Applied’ Maths
These books cover a very wide range of topics and will also overlap with and feel more in the style of A-level maths than most of what you’ll use in a maths degree. These books are often core for physics, engineering etc, but most maths students will use something like this as a frequent reference in a wide range of settings.
Real Analysis
Perhaps the biggest ‘surprise’ of a maths degree is how different ‘pure’ mathematics is. Most ‘core’ maths at A-level is considered applied at university. Limits limits everywhere is a great bridge to this new material, and Bartle and Sherbert, whilst expensive these days is exceptional.
Complex Analysis
Priestley’s book is an excellent introduction to this tough subject. Needham’s Visual Complex Analysis is a little nonstandard but has lots of nice pictures for those searching for intuition.
Linear Algebra
These books take the theories of vectors and matrices you met at A-level to a new level.
Introductory Probability and Statistics
Strizaker’s Probability and Random Variables is a great transition from A-level to more rigorous advanced probability. Williams’ Weighing the Odds does a great job of unifying the central ideas of probability and statistics whilst being very entertaining and informative.
Probability – Grimmett and Stirzaker
These books are considered an ultimate reference in probability, and the second book gives solutions to all the problems in the first. A great reference, and can be used as an introduction, but they are tough so you might want to consider one of the books above first.
Putnam and Beyond
The Putnam competition is like a super hard mathematics challenge competition for undergraduate students. So if you want something that takes you beyond and around the courses you’re studying this could be a great book for you!