# A Beginner’s Guide to Finite Mathematics: For Business, Management, and the Social Sciences

Springer Science & Business Media, 2004 - Computers - 354 pages
This concise text takes a distinctly applied approach to finite mathematics at the freshman and sophomore level. Topics are presented sequentially: the book opens with a brief review of sets and numbers, followed by an introduction to data sets, histograms, means and medians. Counting techniques and the Binomial Theorem are covered, which provides the foundation for elementary probability theory; this, in turn, leads to basic statistics.   Graph theory is defined, with particular emphasis on its use in mathematical modeling. Matrices and vectors are discussed, along with several elementary commercial applications. The book concludes with an introduction to linear programming, including the simplex method and duality. Ample examples and illustrations are provided throughout; each section contains two sets of problems, with solutions provided for the first set.   Requiring little mathematical background beyond high school algebra, the text will be especially useful for business and liberal arts majors.  Its straightforward treatment of the essential concepts in finite mathematics will appeal to a wide audience of students and teachers.

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### Contents

 Numbers and Sets xi 12 Equations and Inequalities 7 13 Sums 14 14 Elements of Set Theory 20 15 Venn Diagrams 28 16 Averages 35 Counting 43 22 Arrangements 50
 44 Eulers Theorem and Eulerizations 155 45 Types of Graphs 164 46 Hamiltonian Cycles 170 47 Graph Representations and Colorings 178 Matrices 185 52 Systems of Linear Equations 192 53 Formal Solution of Systems of Equations 201 54 Matrices and Vectors 209

 23 Selections 55 24 More About Selections 61 Probability 69 32 Probability Measures 76 33 NonUniform Probabilities 83 34 Counting and Probability 91 35 Stochastic Processes 98 36 More About Conditional Probability 106 37 Bayes Formula and Applications 114 38 Further Examples of Bayes Formula 122 39 Expected Values 127 Graph Theory 135 42 Graphs 142 43 Some Properties of Graphs 148
 55 Vector and Matrix Products 217 56 Inverses 225 57 More About Inverses 232 Linear Programming 239 62 The Geometric Method 248 63 Linear Programming in Higher Dimensions 257 64 Pivoting 264 65 The Simplex Method 274 66 The Two Phase Simplex Method 291 Your Turn Solutions 303 Answers to Exercises A 331 Index 349 Copyright