Manchester University Press - Mathematics for economists

This book is a self-contained treatment of all the mathematics needed by undergraduate and masters-level students of economics, econometrics and finance. 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, dynamics and static and dynamic optimisation. The last four chapters are an accessible 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.

The preface and full table of contents for the new edition, together with answers to exercises and solutions to problems, are available from https://www.manchesterhive.com/mathematics-for-economists-supplementary-materials

Reviews

'This is the best mathematics for economists textbook that I have come across. It is very clearly written, starts at a basic level, and gradually advances all the way up to dynamic optimization in continuous time. I find that students understand dynamic economic models much better after having studied Pemberton and Rau's textbook.'
Paul S. Segerstrom, Professor of International Economics, Stockholm School of Economics

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
33 Further linear algebra
34 Convex analysis

Notes on further reading
Index

Authors

Malcolm Pemberton is Associate Professor of Economics at University College London
Nicholas Rau is Honorary Senior Lecturer in Economics at University College London