Fundamentals of University Mathematics


  • Colin McGregor, Glasgow University, UK
  • Jonathan Nimmo, Glasgow University
  • Wilson Stothers, formerly Glasgow University, UK

The third edition of this popular and effective textbook provides in one volume a unified treatment of topics essential for first year university students studying for degrees in mathematics. Students of computer science, physics and statistics will also find this book a helpful guide to all the basic mathematics they require. It clearly and comprehensively covers much of the material that other textbooks tend to assume, assisting students in the transition to university-level mathematics.

Expertly revised and updated, the chapters cover topics such as number systems, set and functions, differential calculus, matrices and integral calculus. Worked examples are provided and chapters conclude with exercises to which answers are given. For students seeking further challenges, problems intersperse the text, for which complete solutions are provided. Modifications in this third edition include a more informal approach to sequence limits and an increase in the number of worked examples, exercises and problems.

The third edition of Fundamentals of university mathematics is an essential reference for first year university students in mathematics and related disciplines. It will also be of interest to professionals seeking a useful guide to mathematics at this level and capable pre-university students.
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University students


Book information

  • Published: October 2010
  • Imprint: Woodhead Publishing
  • ISBN: 978-0-85709-223-6


I found this book to be extremely helpful over a wide range of topics. I must have used this to aid my revision for at least 7 or 8 exams and would probably have struggled without it. Particularly useful sections include those on Complex Numbers, Matrices, Vectors, and Differential Equations. If you can only afford to buy one or two books for your course or study, make sure this is one of them!, Rg Ellam "rob_ellam (review on
This book is excellent preparation for 2nd year undergraduate Mathematics courses. It is detailed and step-by-step, so you don't get lost on certain topics. The proofs are complex, but then that's Mathematics for you!, Jon Baldie (review on
If you are looking for a first year university text you should carefully look at this, a unifier of mathematical ideas at this level. I found it most valuable., The Mathematical Gazette (review of a previous edition)

Table of Contents

Functions and inverse functions; Polynomials and rational functions; Induction and the binomial theorem; Trigonometry; Complex numbers; Limits and continuity; Differentiation - fundamentals; Differentiation - applications; Curve sketching; Matrices and linear equations; Vectors and three-dimensional geometry; Products of vectors; Integration - fundamentals; Logarithms and exponentials; Integration - methods and applications; Ordinary differential equations; Sequences and series; Numerical methods; Appendix A Answers to exercises; Appendix B Solutions to problems; Appendix C Limits and continuity - a rigorous approach; Appendix D Properties of trigonometric functions; Appendix E Tables of integrals; Appendix F Standard Maclaurin series.