Mathematics in Economics

A valuable guide to the mathematical apparatus that underlies so much of modern economics. The approach to mathematics is rigorous and the mathematical techniques are always presented in the context of the economics problem they are used to solve. Students can gain insight into, and familiarity with, the mathematical models and methods involved in the transition from 'phenomenon' to quantitative statement. Part I:.

1. Sets and Numbers.

2. Matrices and Vectors.

3. Modelling Consumer Choice.

4. Discrete Variables.

5. Functions.

6. Equilibrium.

7. Eigenvalues and Eigenvectors.

Part II:.

1. Limits and Their Uses.

2. Continuity and Its Uses.

3. Uses of the Derivative.

4. Continuous Compounding and Exponential Growth.

5. Partial Differentiation.

6. The Gradient.

7. Taylor's Theorem - An Approximation Tool.

8. Optimisation in Two Variables.

9. Economic Dynamics: Differential Equations.

"I wish Adam Ostaszewski good luck with this book. May it enjoy the success it deserves." Ken Binmore, University of Michigan

"I believe Mathematics in Economics to be an excellent book, which is much needed in first year UK degree programmes. Its coverage of syllabus is better than its rivals and its treatment of the economics and the mathematics indicates that considerable rigour is needed to do things properly." Martin Cripps, University of Warwick

"In this book the build-up in confidence is done gradually by means of carefully chosen examples."

"Throughout the book the approach to mathematics is rigorous, and excellent use is made of graphs and other figures."

"A valuable guide to the ways in which mathematics provides a basis for modern economics." Tony Whitford

Adam Ostaszewski is currently Senior Lecturer in Mathematics at the London School of Economics. He teaches matematical methods appropriate to economic theory (including game thoery and control theory) and special topic courses to graduates and undergraduates. His main research interets include set-theoretic topology and theoretical economics, concentrating on mathematical problems ansd spanning a wide field of applications. Mathematics in Economics is a valuable guide to the mathematical apparatus that underlies so much of modern economics. The approach to mathematics is rigorous and the mathematical techniques are always presented in the context of the economics problem they are used to solve. Students can therefore gain insight into, and familiarity with, the mathematical models and methods involved in the transition from "phenomenon" to quantitative statement.

Topics covered include:

• Sets and Numbers
• Matrices and Vectors
• Modelling Consumer Choice
• Discrete Variables
• Functions
• Equilibrium
• Eigenvalues and Eigenvectors
• Limits and their Uses
• Continuity and Its Uses
• Partial Differentiation
• The Gradient
• Taylor's Theorem - An Approximation Tool
• Economic Dynamics: Differential Equations.

Each chapter ends with exercises designed to help students understand and practice the techniques they have learnt. The author has provided solutions to selected problems so that the book will function as an effective teaching tool on introductory courses in mathematics for economics, quantitative methods and for mathematicians taking a first course in economics. Mathematics in Economics has been developed from a course taught jointly by Ken Binmore (Professor of Economics) and Adam Ostaszewski (Senior Lecturer in Mathematics).