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This book provides a comprehensive introduction to the mathematical foundations of eco-
nomics, from basic set theory to fixed point theorems and constrained optimization. Rather
than simply offer a collection of problem-solving techniques, the book emphasizes the unifying
mathematical principles that underlie economics. Features include an extended presentation
of separation theorems and their applications, an account of constraint qualification in con-
strained optimization, and an introduction to monotone comparative statics. These topics are
developed by way of more than 800 exercises. The book is designed to be used as a graduate
text, a resource for self-study, and a reference for the professional economist. See the author’s
website (link at left) for additional information on this title, including solutions to each of the
845 exercises in the book.
Contents
Chapter 1 Sets and Spaces
1.1 Sets 1.2 Ordered sets 1.3 Metric spaces 1.4 Linear spaces 1.5 Normed linear spaces
1.6 Preference relations
Chapter 2 Functions
2.1 Functions as mappings 2.2 Monotone functions 2.3 Continuous functions 2.4 Fixed
point theorems
Chapter 3 Linear Functions
3.1 Properties of linear functions 3.2 Affine functions 3.3 Linear functionals 3.4 Bilinear
functions 3.5 Linear operators 3.6 Systems of linear equations and inequalities 3.7 Convex
functions 3.8 Homogeneous functions 3.9 Separation theorems
Chapter 4 Smooth Functions
4.1 Linear approximation and the derivative 4.2 Partial derivatives and the Jacobian 4.3Properties of differentiable functions 4.4 Polynomial approximation 4.5 Systems of nonlin-
ear equations 4.6 Convex and homogeneous functions
Chapter 5 Optimization
5.1 Introduction 5.2 Unconstrained optimization 5.3 Equality constraints 5.4 Inequality
constraints
Chapter 6 Comparative statics
6.1 The envelope theorem 6.2 Optimization models 6.3 Equilibrium models
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