Finite Mathematics & Its Applications

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

• ISBN13: 9780131873643
• ISBN10: 0131873644
• Edition: 9th
• Format: Hardcover
• Copyright: 2010-01-01
• Publisher: Pearson College Div

Summary

A "tried and true" favorite of both students and instructors alike, this text offers extremely readable coverage of the principles of finite mathematics and their applications in business, social science, and the life sciences. Topics are presented in a straightforward, interesting manner, with considerable attention given to the applications of the mathematics. The goal is for the students'mathematical maturity and appreciation for the usefulness of mathematics to grow simultaneously. Many sections contain specially designed technology exercises.

Table of Contents

Preface	vii
Linear Equations and Straight Lines	1	(56)
Coordinate Systems and Graphs	1	(10)
Linear Inequalities	11	(10)
The Intersection Point of a Pair of Lines	21	(5)
The Slope of a Straight Line	26	(14)
The Method of Least Squares	40	(17)
Chapter Test	54	(1)
Chapter Project: Break-Even Analysis	55	(2)
Matrices	57	(66)
Solving Systems of Linear Equations, I	57	(13)
Solving Systems of Linear Equations, II	70	(8)
Arithmetic Operations on Matrices	78	(15)
The Inverse of a Matrix	93	(10)
The Gauss-Jordan Method for Calculating Inverses	103	(5)
Input-Output Analysis	108	(15)
Chapter Test	118	(2)
Chapter Project: Population Dynamics	120	(3)
Linear Programming, A Geometric Approach	123	(36)
A Linear Programming Problem	123	(7)
Linear Programming I	130	(11)
Linear Programming II	141	(18)
Chapter Test	155	(2)
Chapter Project: Shadow Prices	157	(2)
The Simplex Method	159	(54)
Slack Variables and the Simplex Tableau	159	(9)
The Simplex Method I: Maximum Problems	168	(12)
The Simplex Method II: Minimum Problems	180	(8)
Sensitivity Analysis and Matrix Formulations of Linear Programming Problems	188	(8)
Duality	196	(17)
Chapter Test	211	(1)
Chapter Project: Shadow Prices	212	(1)
Sets and Counting	213	(60)
Sets	213	(7)
A Fundamental Principle of Counting	220	(6)
Venn Diagrams and Counting	226	(6)
The Multiplication Principle	232	(7)
Permutations and Combinations	239	(7)
Further Counting Problems	246	(6)
The Binomial Theorem	252	(6)
Multinomial Coefficients and Partitions	258	(15)
Chapter Test	267	(2)
Chapter Project: Pascal's Triangle	269	(4)
Probability	273	(70)
Introduction	273	(2)
Experiments, Outcomes, and Events	275	(9)
Assignment of Probabilities	284	(11)
Calculating Probabilities of Events	295	(9)
Conditional Probability and Independence	304	(12)
Tree Diagrams	316	(8)
Bayes' Theorem	324	(6)
Simulation	330	(13)
Chapter Test	340	(1)
Chapter Project: Two Paradoxes	341	(2)
Probability and Statistics	343	(76)
Visual Representations of Data	344	(8)
Frequency and Probability Distributions	352	(12)
Binomial Trials	364	(6)
The Mean	370	(11)
The Variance and Standard Deviation	381	(11)
The Normal Distribution	392	(14)
Normal Approximation to the Binomial Distribution	406	(13)
Chapter Test	415	(2)
Chapter Project: An Unexpected Expected Value	417	(2)
Markov Processes	419	(36)
The Transition Matrix	419	(11)
Regular Stochastic Matrices	430	(8)
Absorbing Stochastic Matrices	438	(17)
Chapter Test	451	(1)
Chapter Project: Doubly Stochastic Matrices	452	(3)
The Theory of Games	455	(30)
Games and Strategies	455	(7)
Mixed Strategies	462	(7)
Determining Optimal Mixed Strategies	469	(16)
Chapter Test	482	(1)
Chapter Project: Simulating The Outcomes of Mixed-Strategy Games	483	(2)
The Mathematics of Finance	485	(52)
Interest	485	(11)
Annuities	496	(10)
Amortization of Loans	506	(9)
Personal Financial Decisions	515	(22)
Chapter Test	533	(1)
Chapter Project: Two Items of Interest	534	(3)
Difference Equations and Mathematical Models	537	(40)
Introduction to Difference Equations I	537	(8)
Introduction to Difference Equations II	545	(7)
Graphing Difference Equations	552	(9)
Mathematics of Personal Finance	561	(6)
Modeling with Difference Equations	567	(10)
Chapter Test	574	(2)
Chapter Project: Connections to Markov Processes	576	(1)
Logic	577
Introduction to Logic	577	(5)
Truth Tables	582	(9)
Implication	591	(8)
Logical Implication and Equivalence	599	(9)
Valid Argument	608	(6)
Predicate Calculus	614	(10)
Logic Circuits	624
Chapter Test	632	(2)
Chapter Project: A Logic Puzzle	634
Appendix A Tables	1	(8)
Table 1 Areas under the standard normal curve	2	(1)
Table 2 (1 + i)n Compound amount of $1 invested for n interest periods at interest rate i per period	3	(1)
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	4	(1)
Table 4 s n 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	5	(1)
Table 5 1/s n i Rent per period for an ordinary annuity of n payments, with compounded interest rate i per period, and future value $1	6	(1)
Table 6 ani Present value of an ordinary annuity of n payments of $1 one period before the first payment, with interest compounded at i per period	7	(1)
Table 7 1/a n i Rent per period for an ordinary annuity of n payments whose present value is $1, with interest compounded at i per period	8	(1)
Appendix B Using the TI-83/TI-83+/TI-84+ Graphing Calculators	9	(3)
Appendix C Spreadsheet Fundamentals	12	(4)
Appendix D Using the TI-89 Graphing Calculator	16	(5)
Answers to Exercises	21	(42)
Solutions to Circled Exercises	63
Index	1