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

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Springer Science & Business Media, 2004 - Computers - 354 pages
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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
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