Finite Mathematics and Its Applications

by Goldstein, Larry Joel; Schneider, David I.; Siegel, Martha J.

• ISBN13: 9780130186782
• ISBN10: 0130186783
• Edition: 7th
• Format: Hardcover
• Copyright: 2000-08-01
• Publisher: PRENTICE HALL

Summary

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.

Table of Contents

Preface	xiii
Linear Equations and Straight Lines	1	(52)
Coordinate Systems and Graphs	1	(9)
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: Tables	A1
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 Calculators	A9
Answers to Odd-Numbered Exercises and Chapter Tests	A15
Index	I1