Rent 9780137418770 | Finite Mathematics and Its Applications | Larry J. Goldstein; David I. Schneider; Martha J. Siegel @knetbooks.com

Summary Table of Contents

This well written text features a wide range of problems sets including graphing utility and Excel problems. The current edition has extensively revised mathematics of finance and statistics.

Preface

1 Linear Equations and Straight Lines

(50)

1.1 Coordinate Systems and Graphs

(10)

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1.2 Linear Inequalities

(9)

1.3 The Intersection Point of a Pair of Lines

(5)

1.4 The Slope of a Straight Line

(12)

1.5 The Method of Least Squares

(14)

2 Matrices

(56)

2.1 Solving Systems of Linear Equations I

(10)

2.2 Solving Systems of Linear Equations II

(8)

2.3 Arithmetic Operations on Matrices

(14)

2.4 The Inverse of a Matrix

(9)

2.5 The Gauss-Jordan Method for Calculating Inverses

(6)

2.6 Input-Output Analysis

(8)

3 Linear Programming, A Geometric Approach

107

(30)

3.1 A Linear Programming Problem

108

(6)

3.2 Linear Programming I

114

(11)

3.3 Linear Programming II

125

(12)

4 The Simplex Method

137

(52)

4.1 Slack Variables and the Simplex Tableau

138

(8)

4.2 The Simplex Method I: Maximum Problems

146

(12)

4.3 The Simplex Method II: Minimum Problems

158

(8)

4.4 Marginal Analysis and Matrix Formulations of Linear Programming Problems

166

(8)

4.5 Duality

174

(15)

5 Sets and Counting

189

(52)

5.1 Sets

190

(6)

5.2 A Fundamental Principle of Counting

196

(6)

5.3 Venn Diagrams and Counting

202

(6)

5.4 The Multiplication Principle

208

(6)

5.5 Permutations and Combinations

214

(7)

5.6 Further Counting Problems

221

(6)

5.7 The Binomial Theorem

227

(5)

5.8 Multinomial Coefficients and Partitions

232

(9)

6 Probability

241

(64)

6.1 Introduction

242

(1)

6.2 Experiments, Outcomes, and Events

243

(9)

6.3 Assignment of Probabilities

252

(11)

6.4 Calculating Probabilities of Events

263

(8)

6.5 Conditional Probability and Independence

271

(11)

6.6 Tree Diagrams

282

(7)

6.7 Bayes' Theorem

289

(6)

6.8 Simulation

295

(10)

7 Probability and Statistics

305

(62)

7.1 Frequency and Probability Distributions

306

(11)

7.2 Binomial Trials

317

(6)

7.3 The Mean

323

(10)

7.4 The Variance and Standard Deviation

333

(11)

7.5 The Normal Distribution

344

(14)

7.6 Normal Approximation to the Binomial Distribution

358

(9)

8 Markov Processes

367

(32)

8.1 The Transition Matrix

368

(9)

8.2 Regular Stochastic Matrices

377

(9)

8.3 Absorbing Stochastic Matrices

386

(13)

9 The Theory of Games

399

(26)

9.1 Games and Strategies

400

(6)

9.2 Mixed Strategies

406

(6)

9.3 Determining Optimal Mixed Strategies

412

(13)

10 The Mathematics of Finance

425

(32)

10.1 Interest

426

(9)

10.2 Annuities

435

(10)

10.3 Amortization of Loans

445

(12)

11 Difference Equations and Mathematical Models

457

(36)

11.1 Introduction to Difference Equations I

458

(8)

11.2 Introduction to Difference Equations II

466

(5)

11.3 Graphing Difference Equations

471

(10)

11.4 Mathematics of Personal Finance

481

(5)

11.5 Modeling with Difference Equations

486

(7)

12 Logic

493

(48)

12.1 Introduction to Logic

494

(4)

12.2 Truth Tables

498

(8)

12.3 Implication

506

(8)

12.4 Logical Implication and Equivalence

514

(8)

12.5 Valid Argument

522

(6)

12.6 Predicate Calculus

528

(13)

13 Graphs

541

13.1 Graphs as Models

542

(12)

13.2 Paths and Circuits

554

(11)

13.3 Hamiltonian Circuits and Spanning Trees

565

(10)

13.4 Directed Graphs

575

(18)

13.5 Matrices and Graphs

593

13.6 Trees

604

Appendix A Tables A1

Table 1 Areas under the standard normal curve

Table 2 (1 + i)(n) Compound amount of $1 invested for n interest periods at interest rate i per period

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

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

Table 5 1/S(n)(i) Rent per period for an ordinary annuity of n payments, compounded interest rate i per period, and future value $1

Table 6 a(n)(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

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 A8

Appendix B Using the Tl-82 and Tl-83 Graphing Calculators A9

Answers to Exercises A15

Index