Preface 

xiii  

Linear Equations and Straight Lines 


1  (52) 

Coordinate Systems and Graphs 


1  (9) 


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) 


50  (2) 

Chapter Project: BreakEven Analysis 


52  (1) 


53  (60) 

Solving Systems of Linear Equations, I 


53  (11) 

Solving Systems of Linear Equations, II 


64  (7) 

Arithmetic Operations on Matrices 


71  (15) 


86  (9) 

The GaussJordan Method for Calculating Inverses 


95  (6) 


101  (12) 


109  (2) 

Chapter Project: Population Dynamics 


111  (2) 

Linear Programming, A Geometric Approach 


113  (33) 

A Linear Programming Problem 


113  (7) 


120  (10) 


130  (16) 


143  (2) 

Chapter Project: Shadow Prices 


145  (1) 


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) 


183  (16) 


197  (1) 

Chapter Project: Shadow Prices 


198  (1) 


199  (55) 


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) 


236  (6) 

Multinomial Coefficients and Partitions 


242  (12) 


250  (1) 

Chapter Project: Pascal's Triangle 


251  (3) 


254  (65) 


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) 


295  (7) 


302  (6) 


308  (11) 


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) 


340  (6) 


346  (10) 

The Variance and Standard Deviation 


356  (11) 


367  (14) 

Normal Approximation to the Binomial Distribution 


381  (11) 


389  (2) 

Chapter Project: An Unexpected Expected Value 


391  (1) 


392  (35) 


392  (10) 

Regular Stochastic Matrices 


402  (9) 

Absorbing Stochastic Matrices 


411  (16) 


423  (2) 

Chapter Project: Doubly Stochastic Matrices 


425  (2) 


427  (28) 


427  (7) 


434  (7) 

Determining Optimal Mixed Strategies 


441  (14) 


452  (1) 

Chapter Project: Simulating the Outcomes of MixedStrategy Games 


453  (2) 

The Mathematics of Finance 


455  (34) 


455  (11) 


466  (10) 


476  (13) 


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) 


525  (2) 

Chapter Project: Connections to Markov Processes 


527  (1) 


528  (51) 


528  (4) 


532  (9) 


541  (7) 

Logical Implication and Equivalence 


548  (9) 


557  (6) 


563  (16) 


576  (2) 

Chapter Project: A Logic Puzzle 


578  (1) 


579  (66) 


579  (13) 


592  (10) 

Hamiltonian Circuits and Spanning Trees 


602  (11) 


613  (11) 


624  (11) 


635  (10) 


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 TI82 and TI83 Graphing Calculators 

A9  
Answers to OddNumbered Exercises and Chapter Tests 

A15  
Index 

I1  