Mathematical methods and economic theory

This textbook - for postgraduate students learning mathematical methods in economics - provides a comprehensive account of mathematics required to analyse and solve problems of choice encountered by economists. It looks at a wide variety of decision-making problems, both static and dynamic, in various contexts and provides mathematical foundations for the relevant economic theory. The book consists of three sections, each containing applications to fundamental constructs of economic theory: mathematical logic and functions of single variable, with applications to problems of choice and group decisions; " functions of several variables, presenting applications to demand and supply theory and its extension to interactive decision-making (game theory); dynamic problems, with applications relating to optimal economic growth and stability of competitive equilibrium. Written in an accessible style, the book provides clearly-defined concepts, numerous examples and exercises, suggested further readings, key terms, and useful web links. It will be an indispensable resource for students and teachers of mathematical economics and economic theory. Students of optimization techniques, operations research, and all those seeking an analytical introduction to decision-making problems will also find this book useful

PREFACE;; SECTION I; 1. Introduction (The Objective);; 2. Basic Mathematical Logic;; 3. . Set Theory;; 4. Functions of a Single Variable;; 5. . Economic Applications I: Choice, Utility, and Aggregation; Further Readings for Section I;; SECTION II. ; 6. Introduction (Objective of Section II);; 7. Real Linear Algebra;; 8. Functions of Several Variables;; 9. Static Optimization;; 10. Economic Applications II: Demand and Supply;; 11. Decision-Making under Alternative Scenarios; Further Readings for Section II;; SECTION III; 12. Introduction (Objective and Tools);; 13. . Dynamical Systems;; 14. Dynamic Optimization;; 15. Economic Applications III: Economic Dynamics; Further Readings for Section III; References