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Finite Mathematics and Its Applications

ISBN: 9780130186782 | 0130186783
Edition: 7th
Format: Hardcover
Publisher: PRENTICE HALL
Pub. Date: 8/1/2000

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SummaryTable of Contents
For finite mathematics courses taught to first- and second-year college students, especially those majoring in business and the social and biological sciences. This tried and true text offers extremely readable coverage of the principles of finite mathematics and their applications in business, social science, and the life sciences. The book divides naturally into four parts. The first part consists of linear mathematics: linear equations, matrices, and linear programming (chapters 1-4); the second part is devoted to probability and statistics (chapter 5-7); the third covers topics utilizing the ideas of the first two parts (chapters 8-10); and the fourth covers topics from discrete mathematics sometimes included in the modern finite mathematics curriculum. In revising this book, the authors incorporated a wide range of topics from which the instructor may design a curriculum, as well as a high degree of flexibility in the order in which the topics may be presented.
Prefacexiii
Linear Equations and Straight Lines
1(52)
Coordinate Systems and Graphs
1(9)
... MORE
Linear Inequalities
10(10)
The Intersection Point of a Pair of Lines
20(5)
The Slope of a Straight Line
25(13)
The Method of Least Squares
38(15)
Chapter Test
50(2)
Chapter Project: Break-Even Analysis
52(1)
Matrices
53(60)
Solving Systems of Linear Equations, I
53(11)
Solving Systems of Linear Equations, II
64(7)
Arithmetic Operations on Matrices
71(15)
The Inverse of a Matrix
86(9)
The Gauss-Jordan Method for Calculating Inverses
95(6)
Input--Output Analysis
101(12)
Chapter Test
109(2)
Chapter Project: Population Dynamics
111(2)
Linear Programming, A Geometric Approach
113(33)
A Linear Programming Problem
113(7)
Linear Programming I
120(10)
Linear Programming II
130(16)
Chapter Test
143(2)
Chapter Project: Shadow Prices
145(1)
The Simplex Method
146(53)
Slack Variables and the Simplex Tableau
146(9)
The Simplex Method I: Maximum Problems
155(12)
The Simplex Method II: Minimum Problems
167(8)
Marginal Analysis and Matrix Formulations of Linear Programming Problems
175(8)
Duality
183(16)
Chapter Test
197(1)
Chapter Project: Shadow Prices
198(1)
Sets and Counting
199(55)
Sets
199(7)
A Fundamental Principle of Counting
206(6)
Venn Diagrams and Counting
212(6)
The Multiplication Principle
218(6)
Permutations and Combinations
224(6)
Further Counting Problems
230(6)
The Binomial Theorem
236(6)
Multinomial Coefficients and Partitions
242(12)
Chapter Test
250(1)
Chapter Project: Pascal's Triangle
251(3)
Probability
254(65)
Introduction
254(2)
Experiments, Outcomes, and Events
256(8)
Assignment of Probabilities
264(12)
Calculating Probabilities of Events
276(7)
Conditional Probability and Independence
283(12)
Tree Diagrams
295(7)
Bayes' Theorem
302(6)
Simulation
308(11)
Chapter Test
316(2)
Chapter Project: Two Paradoxes
318(1)
Probability and Statistics
319(73)
Visual Representations of Data
319(9)
Frequency and Probability Distributions
328(12)
Binomial Trials
340(6)
The Mean
346(10)
The Variance and Standard Deviation
356(11)
The Normal Distribution
367(14)
Normal Approximation to the Binomial Distribution
381(11)
Chapter Test
389(2)
Chapter Project: An Unexpected Expected Value
391(1)
Markov Processes
392(35)
The Transition Matrix
392(10)
Regular Stochastic Matrices
402(9)
Absorbing Stochastic Matrices
411(16)
Chapter Test
423(2)
Chapter Project: Doubly Stochastic Matrices
425(2)
The Theory of Games
427(28)
Games and Strategies
427(7)
Mixed Strategies
434(7)
Determining Optimal Mixed Strategies
441(14)
Chapter Test
452(1)
Chapter Project: Simulating the Outcomes of Mixed-Strategy Games
453(2)
The Mathematics of Finance
455(34)
Interest
455(11)
Annuities
466(10)
Amortization of Loans
476(13)
Chapter Test
487(1)
Chapter Project: Individual Retirement Accounts
488(1)
Difference Equations and Mathematical Models
489(39)
Introduction to Difference Equations I
489(8)
Introduction to Difference Equations II
497(6)
Graphing Difference Equations
503(10)
Mathematics of Personal Finance
513(5)
Modeling with Difference Equations
518(10)
Chapter Test
525(2)
Chapter Project: Connections to Markov Processes
527(1)
Logic
528(51)
Introduction to Logic
528(4)
Truth Tables
532(9)
Implication
541(7)
Logical Implication and Equivalence
548(9)
Valid Argument
557(6)
Predicate Calculus
563(16)
Chapter Test
576(2)
Chapter Project: A Logic Puzzle
578(1)
Graphs
579(66)
Graphs as Models
579(13)
Paths and Circuits
592(10)
Hamiltonian Circuits and Spanning Trees
602(11)
Directed Graphs
613(11)
Matrices and Graphs
624(11)
Trees
635(10)
Chapter Test
645
Appendix A: TablesA1
Table 1 Areas under the standard normal curve
A2
Table 2 (1+i)n Compound amount of $1 invested for n interest periods at interest rate i per second
A3
Table 3 1/(1+i)n Present value of $1. Principal that will accumulate to $1 in n interest periods at a compound rate of i per period
A4
Table 4 Sn⌝i Future value of an ordinary annuity of n $1 payments each, immediately after the last payment at compound interest rate of i per period
A5
Table 5 1/Sn⌝i Rent per period for an ordinary annuity of n payments, with compounded interest rate i per period, and future value $1
A6
Table 6 an⌝i Present value of an ordinary annuity of n payments of $1 one period before the first payment, with interest compounded at i per period
A7
Table 7 1/an⌝i Rent per period for an ordinary annuity of n payments whose present value is $1, with interest compounded at i per period
A8
Appendix B: Using the TI-82 and TI-83 Graphing CalculatorsA9
Answers to Odd-Numbered Exercises and Chapter TestsA15
IndexI1

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