Mathematical Introduction to Linear Programming and Game Theory / Edition 1

by Louis Brickman

Overview

Mathematical elegance is a constant theme in this treatment of linear programming and matrix games. Condensed tableau, minimal in size and notation, are employed for the simplex algorithm. In the context of these tableau the beautiful termination theorem of R.G. Bland is proven more simply than heretofore, and the important duality theorem becomes almost obvious. Examples and extensive discussions throughout the book provide insight into definitions, theorems, and applications. There is considerable informal discussion on how best to play matrix games. The book is designed for a one-semester undergraduate course. Readers will need a degree of mathematical sophistication and general tools such as sets, functions, and summation notation. No single college course is a prerequisite, but most students will do better with some prior college mathematics. This thorough introduction to linear programming and game theory will impart a deep understanding of the material and also increase the student's mathematical maturity.

Product Details

ISBN-13:	9780387969312
Publisher:	Springer New York
Publication date:	06/23/1989
Series:	Undergraduate Texts in Mathematics
Edition description:	1989
Pages:	132
Product dimensions:	6.14(w) x 9.21(h) x 0.36(d)

Table of Contents

1 Simultaneous Linear Equations.- 2 Linear Programming Foundations.- 3 The Simplex Algorithm.- 4 Dual Tableaux and Two-Phase Algorithms.- 5 Dual LP Problems.- 6 Matrix Games.

Editorial Reviews

Defines linear programming and its usefulness, and explains the operation and elementary theory of the simplex algorithm. Also presents duality in a simple fashion, and gives an account of matrix games. Required mathematical tools (beyond arithmetic and high school algebra) are essentially limited to summation notation, basic language of sets and functions, and elementary notions of probability. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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