University maths textbooks

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.

Mathematical Techniques
Dominic Jordan and Peter Smith

Modern Engineering Mathematics
Glyn James and Phil Dyke

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.

Limits, Limits Everywhere
David Applebaum

Introduction to Real Analysis
Robert G. Bartle and Donald R. Sherbert

Introduction to Complex Analysis
H. A. Priestley

Visual Complex Analysis
Tristan Needham

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.

Elementary Linear Algebra
Howard Anton and Anton Kaul

Basic Linear Algebra: 2nd Edition
T.S. Blyth and E.F. Robertson

Probability and Random Variables: A Beginner’s Guide
David Stirzaker

Weighing the Odds
David Williams

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.

Probability and Random Processes: Fourth Edition
Geoffrey Grimmett and David Stirzaker

One Thousand Exercises in Probability: Third Edition
Geoffrey Grimmett

Putnam and Beyond
Răzvan Gelca and Titu Andreescu

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! You can find every past paper, with solutions, in Kiran Kedlaya’s Putnam archive, which is free and goes back to 1985.