Mathematics for economists

An introductory textbook (new edition)

By Malcolm Pemberton and Nicholas Rau

Mathematics for economists

Book Information

  • Format: Paperback
  • ISBN: 978-1-7849-9148-7
  • Pages: 776
  • Publisher: Manchester University Press
  • Price: £35.00
  • Published Date: September 2015
  • BIC Category: BUSINESS & ECONOMICS / General, Economics, finance, business & management / Economic theory & philosophy, Mathematics & science / Mathematics, Economics, finance, business & management / Business mathematics & systems, Business mathematics & systems, Business & Management, Applied mathematics, MATHEMATICS / Applied, Economic theory & philosophy, Mathematics, Economics


This book is a self-contained treatment of all the mathematics needed by undergraduate and masters-level students of economics. Building up gently from a very low level, the authors provide a clear, systematic coverage of calculus and matrix algebra. The second half of the book gives a thorough account of probability, optimisation and dynamics. The final two chapters are an introduction to the rigorous mathematical analysis used in graduate-level economics. The emphasis throughout is on intuitive argument and problem-solving. All methods are illustrated by examples, exercises and problems selected from central areas of modern economic analysis.

The book's careful arrangement in short chapters enables it to be used in a variety of course formats for students with or without prior knowledge of calculus, for reference and for self-study.

This new fourth edition includes two chapters on probability theory, providing the essential mathematical background for upper-level courses on economic theory, econometrics and finance. Answers to all exercises and complete solutions to all problems are available online from a regularly updated website.


'In spite of the wide scope of this textbook, its presentation is clear and crisp. The materials are very carefully organised. The transition from mathematical principles to economic propositions is remarkably lucid throughout the book. If a first-year undergraduate student in economics comes to ask me which one, among many books on mathematics for economists, to buy for years to come, then I would definitely tell them that this is the one.'
Chiaki Hara, Institute of Economic Research, Kyoto University

'This is a great text to learn from - the authors do an excellent job providing intuitive explanations, making connections between results and illustrating the use of mathematics in solving economics problems, and there is a host of solved exercises which perform two roles: providing essential practice material and introducing further applications in economics.'
Andrew Chesher, Director of The Centre for Microdata Methods and Practice, IFS and UCL


Malcolm Pemberton is Senior Lecturer in Economics at University College London

Nicholas Rau is Honorary Senior Lecturer in Economics at University College London


1. Linear equations
2. Linear inequalities
3. Sets and functions
4. Quadratics, indices and logarithms
5. Sequences, series and limits
6. Introduction to differentiation
7. Methods of differentiation
8. Maxima and minima
9. Exponential and logarithmic functions
10. Approximations
11. Matrix algebra
12. Systems of linear equations
13. Determinants and quadratic forms
14. Functions of several variables
15. Implicit relations
16. Optimisation with several variables
17. Principles of constrained optimisation
18. Further topics in constrained optimisation
19. Integration
20. Aspects of integral calculus
21. Probability
22. Expectation
23. Introduction to dynamics
24. The circular functions
25. Complex numbers
26. Further dynamics
27. Eigenvalues and eigenvectors
28. Dynamic systems
29. Dynamic optimisation in discrete time
30. Dynamic optimisation in continuous time
31. Introduction to analysis
32. Metric spaces and existence theorems
Notes on further reading

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