Finite Mathematics Book

Chapter 1	Functions and Linear Models	2
1.1	Functions from the Numerical and Algebraic Viewpoints	3
1.2	Functions from the Graphical Viewpoint	15
1.3	Linear Functions	27
1.4	Linear Models	38
1.5	Linear Regression (optional)	54
	You're the Expert: Modeling Spending on Internet Advertising	63
	Chapter 1 review test	67
	Optional Internet Topic: New Functions from Old: Scaled and Shifted Functions
Chapter 2	Systems of Linear Equations and Matrices	70
2.1	Systems of Two Linear Equations in Two Unknowns	71
2.2	Using Matrices to Solve Systems of Equations	85
2.3	Applications of Systems of Linear Equations	105
	You're the Expert: The Impact of Regulating Sulfur Emissions	117
	Chapter 2 review test	121
Chapter 3	Matrix Algebra and Applications	124
3.1	Matrix Addition and Scalar Multiplication	125
3.2	Matrix Multiplication	136
3.3	Matrix Inversion	150
3.4	Input-Output Models	161
	You're the Expert: The Japanese Economy	175
	Chapter 3 review test	177
Chapter 4	Linear Programming	180
4.1	Graphing Linear Inequalities	181
4.2	Solving Linear Programming Problems Graphically	192
4.3	The Simplex Method: Solving Standard Maximization Problems	209
4.4	The Simplex Method: Solving General Linear Programming Problems	227
4.5	The Simplex Method and Duality (optional)	240
	You're the Expert: Airline Scheduling	249
	Chapter 4 review test	252
Chapter 5	The Mathematics of Finance	256
5.1	Simple Interest	257
5.2	Compound Interest	264
5.3	Annuities, Loans, and Bonds	276
	You're the Expert: Saving for College	295
	Chapter 5 review test	299
Chapter 6	Sets and Counting	302
6.1	Sets and Set Operations	303
6.2	Cardinality	313
6.3	The Addition and Multiplication Principles	322
6.4	Permutations and Combinations	331
	You're the Expert: Designing a Puzzle	343
	Chapter 6 review test	345
Chapter 7	Probability	348
7.1	Sample Spaces and Events	349
7.2	Estimated Probability	362
7.3	Empirical Probability	371
7.4	Probability and Counting Techniques (optional)	380
7.5	Abstract Probability	389
7.6	Conditional Probability and Independence	397
7.7	Bayes' Theorem and Applications	411
	You're the Expert: The Monty Hall Problem	420
	Chapter 7 review test	422
Chapter 8	Random Variables and Statistics	426
8.1	Random Variables and Distributions	427
8.2	Bemoulli Trials and Binomial Random Variables	437
8.3	Measures of Central Tendency	443
8.4	Measures of Dispersion	455
8.5	Normal Distributions	468
	You're the Expert: Spotting Tax Fraud with Benford's Law	478
	Chapter 8 review test	481
	Optional Internet Topics
	Sampling Distributions and the Central Limit Theorem
	Confidence Intervals
Chapter 9	Markov Systems	486
9.1	Markov Systems	487
9.2	Distribution Vectors and Powers of the Transition Matrix	495
9.3	Long-Range Behavior of Regular Markov Systems	507
9.4	Absorbing Markov Systems	520
	You're the Expert: Predicting the Price of Gold	532
	Chapter 9 review test	536
Chapter G	Game Theory (Optional Internet Topic)
G.1	Two-Person Zero Sum Games; Reduction by Dominance
G.2	Strictly Determined Games
G.3	Mixing Strategies
G.4	Solving Games using the Simplex Method
	You're the Expert: Harvesting Forests
Chapter L	Introduction to Logic (Optional Internet Topic)
L.1	Statements and Logical Operators
L.2	Logical Equivalence, Tautologies, and Contradictions
L.3	The Conditional and the Biconditional
L.4	Tautological Implications and Tautological Equivalences
L.5	Rules of Inference
L.6	Arguments and Proofs
Appendix A	Real Numbers	1
Appendix B	Table: Area Under a Normal Curve	7
	Answers to Selected Exercises	9
	Index	1