Preface 

vii  

Linear Equations and Straight Lines 


1  (56) 

Coordinate Systems and Graphs 


1  (10) 


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) 


54  (1) 

Chapter Project: BreakEven Analysis 


55  (2) 


57  (66) 

Solving Systems of Linear Equations, I 


57  (13) 

Solving Systems of Linear Equations, II 


70  (8) 

Arithmetic Operations on Matrices 


78  (15) 


93  (10) 

The GaussJordan Method for Calculating Inverses 


103  (5) 


108  (15) 


118  (2) 

Chapter Project: Population Dynamics 


120  (3) 

Linear Programming, A Geometric Approach 


123  (36) 

A Linear Programming Problem 


123  (7) 


130  (11) 


141  (18) 


155  (2) 

Chapter Project: Shadow Prices 


157  (2) 


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) 


196  (17) 


211  (1) 

Chapter Project: Shadow Prices 


212  (1) 


213  (60) 


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) 


252  (6) 

Multinomial Coefficients and Partitions 


258  (15) 


267  (2) 

Chapter Project: Pascal's Triangle 


269  (4) 


273  (70) 


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) 


316  (8) 


324  (6) 


330  (13) 


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) 


364  (6) 


370  (11) 

The Variance and Standard Deviation 


381  (11) 


392  (14) 

Normal Approximation to the Binomial Distribution 


406  (13) 


415  (2) 

Chapter Project: An Unexpected Expected Value 


417  (2) 


419  (36) 


419  (11) 

Regular Stochastic Matrices 


430  (8) 

Absorbing Stochastic Matrices 


438  (17) 


451  (1) 

Chapter Project: Doubly Stochastic Matrices 


452  (3) 


455  (30) 


455  (7) 


462  (7) 

Determining Optimal Mixed Strategies 


469  (16) 


482  (1) 

Chapter Project: Simulating The Outcomes of MixedStrategy Games 


483  (2) 

The Mathematics of Finance 


485  (52) 


485  (11) 


496  (10) 


506  (9) 

Personal Financial Decisions 


515  (22) 


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) 


574  (2) 

Chapter Project: Connections to Markov Processes 


576  (1) 


577  


577  (5) 


582  (9) 


591  (8) 

Logical Implication and Equivalence 


599  (9) 


608  (6) 


614  (10) 


624  


632  (2) 

Chapter Project: A Logic Puzzle 


634  


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 TI83/TI83+/TI84+ Graphing Calculators 


9  (3) 

Appendix C Spreadsheet Fundamentals 


12  (4) 

Appendix D Using the TI89 Graphing Calculator 


16  (5) 
Answers to Exercises 

21  (42) 
Solutions to Circled Exercises 

63  
Index 

1  