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Mathematics : A Practical Odyssey

ISBN: 9780534350758 | 0534350755
Edition: 3rd
Format: Paperback
Publisher: Brooks Cole
Pub. Date: 12/30/1997

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Table of Contents
... MORE
1 LOGIC
1(53)
1.1 Deductive vs. Inductive Reasoning
2(10)
Problem Solving
2(1)
Deductive Reasoning
3(1)
Deductive Reasoning and Venn Diagrams
4(1)
Historical Note: Aristotle
5(4)
Inductive Reasoning
9(1)
Exercises 1.1
10(2)
1.2 Symbolic Logic
12(8)
Statements
12(1)
Compound Statements and Logical Connectives
13(1)
The Negation XXXp
13(1)
Historical Note: Gottfried Wilhelm Leibniz
14(1)
The Conjunction p XXX q
15(1)
The Disjunction p XXX q
16(1)
The Conditional p XXX q
17(1)
Exercises 1.2
18(2)
1.3 Truth Tables
20(14)
The Negation XXXp
20(1)
The Conjunction p XXX q
21(1)
The Disjunction p XXX q
21(4)
The Conditional p XXX q
25(4)
Historical Note: George Boole
29(1)
Equivalent Expressions
30(2)
De Morgan's Laws
32(1)
Exercises 1.3
33(1)
1.4 More on Conditionals
34(7)
Variations of a Conditional
34(2)
Equivalent Conditionals
36(1)
The "Only If" Connective
37(1)
The Biconditional p XXX q
38(1)
Exercises 1.4
39(2)
1.5 Analyzing Arguments
41(10)
Valid Arguments
41(4)
Tautologies
45(1)
Historical Note: Charles Lutwidge Dodgson
46(4)
Exercises 1.5
50(1)
CHAPTER 1 REVIEW
51(3)
2 SETS AND COUNTING
54(58)
2.1 Sets and Set Operations
55(11)
Notation
55(2)
Universal Set and Subsets
57(1)
Intersection of Sets
58(1)
Mutually Exclusive Sets
58(1)
Union of Sets
59(1)
Complement of a Set
60(2)
Historical Note: John Venn
62(1)
Set Theory and Logic (prerequisite: Chapter 1)
63(1)
Exercises 2.1
63(3)
2.2 Applications of Venn Diagrams
66(11)
Surveys
66(4)
De Morgan's Laws
70(2)
Historical Note: Augustus De Morgan
72(1)
Exercises 2.2
73(4)
2.3 Introduction to Combinatorics
77(8)
The Fundamental Principle of Counting
77(3)
Factorials
80(2)
Exercises 2.3
82(3)
2.4 Permutations and Combinations
85(13)
With versus Without Replacement
85(1)
Permutations
85(2)
Combinations
87(7)
Historical Note: Chu Shi-chieh
94(1)
Exercises 2.4
95(3)
2.5 Infinite Sets
98(12)
One-to-One Correspondence
98(2)
Historical Note: Georg Cantor
100(1)
Countable Sets
101(4)
Uncountable Sets
105(1)
Points on a Line
106(2)
Exercises 2.5
108(2)
CHAPTER 2 REVIEW
110(2)
3 PROBABILITY
112(73)
3.1 History of Probability
113(7)
Roulette
113(2)
Dice and Craps
115(1)
Cards
115(1)
Historical Note: Blaise Pascal
116(1)
Historical Note: Gerolamo Cardano
117(1)
Exercises 3.1
118(2)
3.2 Basic Terms of Probability
120(15)
Finding Probabilities and Odds
121(3)
Relative Frequency versus Probability
124(1)
Mendel's Use of Probabilities
125(1)
Historical Note: Gregor Johann Mendel
126(2)
Probabilities in Genetics
128(1)
Genetic Screening
129(1)
Historical Note: Nancy Wexler
130(2)
Exercises 3.2
132(3)
3.3 Basic Rules of Probability
135(9)
Mutually Exclusive Events
135(1)
Pair-of-Dice Probabilities
136(2)
More Probability Rules
138(1)
Probabilities and Venn Diagrams
139(1)
Exercises 3.3
140(3)
Fractions on a Graphing Calculator
143(1)
3.4 Combinatorics and Probability
144(8)
Historical Note: Lotteries and Keno
147(3)
Exercises 3.4
150(2)
3.5 Expected Value
152(7)
Why the House Wins
154(1)
Decision Theory
155(1)
Betting Strategies
155(1)
Exercises 3.5
156(3)
3.6 Conditional Probability
159(11)
Probabilities and Polls
159(3)
The Product Rule
162(1)
Tree Diagrams
163(3)
Exercises 3.6
166(4)
3.7 Independence; Trees in Genetics
170(12)
Dependent and Independent Events
170(3)
Product Rule for Independent Events
173(1)
Trees in Medicine and Genetics
173(4)
Hair Color
177(1)
Exercises 3.7
178(4)
CHAPTER 3 REVIEW
182(3)
4 STATISTICS
185(91)
4.1 Population, Sample, and Data
186(17)
Population versus Sample
186(1)
Frequency Distributions
186(2)
Grouped Data
188(2)
Histograms
190(2)
Histograms and Relative Frequency Density
192(3)
Pie Charts
195(2)
Exercises 4.1
197(4)
Histograms on a Graphing Calculator
201(2)
4.2 Measures of Central Tendency
203(11)
The Mean
204(4)
The Median
208(1)
The Mode
209(1)
Exercises 4.2
210(4)
4.3 Measures of Dispersion
214(14)
Deviations
214(1)
Variance and Standard Deviation
215(3)
Alternate Methods for Finding Variance
218(4)
Exercises 4.3
222(4)
Measures of Central Tendency and Dispersion on a Graphing Calculator
226(2)
4.4 The Normal Distribution
228(18)
Discrete versus Continuous Variables
228(1)
Normal Distributions
229(2)
Probability, Area, and Normal Distributions
231(1)
Historical Note: Carl Friedrich Gauss
232(2)
The Standard Normal Distribution
234(6)
Converting to the Standard Normal
240(4)
Exercises 4.4
244(2)
4.5 Polls and Margin of Error
246(12)
Sampling and Inferential Statistics
247(1)
Sample Proportion versus Population Proportion
247(2)
Margin of Error
249(1)
Historical Note: George H. Gallup
250(6)
Exercises 4.5
256(2)
4.6 Linear Regression
258(14)
Linear Trends and Line of Best Fit
259(3)
Coefficient of Linear Correlation
262(5)
Exercises 4.6
267(2)
Linear Regression on a Graphing Calculator
269(3)
CHAPTER 4 REVIEW
272(4)
5 FINANCE
276(79)
5.1 Simple Interest
277(9)
National Debt
280(1)
Add-On Interest
281(1)
Credit Card Finance Charge
282(1)
Historical Note: Credit Card History
283(1)
Exercises 5.1
284(2)
5.2 Compound Interest
286(14)
Annual Yield
292(3)
Exercises 5.2
295(3)
Doubling Time on a Graphing Calculator
298(2)
5.3 Annuities
300(13)
Calculating Short-Term Annuities
301(3)
Calculating Long-Term Annuities
304(2)
Tax-Deferred Annuities
306(1)
Sinking Funds
307(1)
Present Value of an Annuity
308(2)
Exercises 5.3
310(3)
Annuities on a Graphing Calculator
313(1)
5.4 Amortized Loans
313(21)
Amortization Schedules
315(5)
Finding an Unpaid Balance
320(3)
Exercises 5.4
323(5)
Amortization Schedules on a Computer
328(6)
5.5 Annual Percentage Rate on a Graphing Calculator
334(9)
Historical Note: The Truth in Lending Act
335(2)
Finance Charges
337(3)
Estimating Prepaid Finance Charges
340(1)
Exercises 5.5
341(2)
5.6 Payout Annuities
343(9)
Calculating Short-Term Payout Annuities
344(1)
Comparing Payout Annuities and Savings Annuities
345(1)
Calculating Long-Term Payout Annuities
345(2)
Payout Annuities with Inflation
347(2)
Exercises 5.6
349(3)
CHAPTER 5 REVIEW
352(3)
6 GEOMETRY
355(96)
6.1 Perimeter and Area
356(15)
Polygons
357(3)
Heron's Formula for the Area of a Triangle
360(3)
Right Triangles
363(2)
Circles
365(2)
Exercises 6.1
367(4)
6.2 Volume and Surface Area
371(12)
Problem Solving
371(2)
Surface Area
373(2)
Spheres
375(3)
Cones and Pyramids
378(1)
Exercises 6.2
379(4)
6.3 Egyptian Geometry
383(13)
Units of Measurement
385(1)
Empirical Geometry (If It Works, Use It)
386(2)
The Great Pyramid of Cheops
388(1)
The Rhind Papyrus
389(2)
Pi and the Area of a Circle
391(3)
Exercises 6.3
394(2)
6.4 The Greeks
396(12)
Thales of Miletus
396(1)
Pythagoras of Samos
397(2)
Euclid of Alexandria
399(1)
Deductive Proof
400(2)
Historical Note: Archimedes of Syracuse
402(1)
Archimedes of Syracuse
402(3)
Exercises 6.4
405(3)
6.5 Right Triangle Trigonometry
408(14)
Angle Measurement
409(1)
Special Triangles
410(2)
Trigonometric Ratios
412(4)
Using a Calculator
416(1)
Finding an Acute Angle
417(1)
Angles of Elevation and Depression
418(2)
Exercises 6.5
420(2)
6.6 Conic Sections and Analytic Geometry
422(13)
Historical Note: Hypatia
423(1)
Conic Sections
423(1)
The Circle
424(1)
The Parabola
425(3)
The Ellipse
428(2)
The Hyperbola
430(4)
Exercises 6.6
434(1)
6.7 Non-Euclidean Geometry
435(11)
The Parallel Postulate
435(1)
Giralamo Saccheri
436(1)
Carl Friedrich Gauss
437(1)
Janos Bolyai
437(1)
Nikolai Lobachevsky
438(1)
Bernhard Riemann
439(1)
Geometric Models
440(1)
A Comparison of Triangles
441(2)
Geometry in Art
443(2)
Exercises 6.7
445(1)
CHAPTER 6 REVIEW
446(5)
7 MATRICES AND MARKOV CHAINS
451(60)
7.0 Review of Matrices
452(12)
Terminology and Notation
452(1)
Matrix Multiplication
453(3)
Historical Note: Arthur Cayley and James Joseph Sylvester
456(2)
Properties of Matrix Multiplication
458(2)
Identity Matrices
460(1)
Exercises 7.0
460(3)
Matrix Multiplication on a Graphing Calculator
463(1)
7.1 Markov Chains
464(14)
Transition Matrices
466(1)
Probability Matrices
467(1)
Using Markov Chains to Predict the Future
468(2)
Historical Note: Andrei Andreevich Markov
470(5)
Exercises 7.1
475(3)
7.2 Systems of Linear Equations
478(22)
Linear Equations
478(1)
Systems of Equations
479(3)
Solving Systems: The Elimination Method
482(1)
Solving Systems: The Gauss-Jordan Method
483(8)
Exercises 7.2
491(2)
Technology and the Row Operations
493(7)
7.3 Long-Range Predictions with Markov Chains
500(9)
Exercises 7.3
506(3)
CHAPTER 7 REVIEW
509(2)
8 LINEAR PROGRAMMING
511(61)
8.0 Review of Linear Inequalities
513(12)
Systems of Linear Inequalities
516(3)
Finding Corner Points
519(1)
Exercises 8.0
520(1)
Graphing Linear Inequalities on a Graphing Calculator
521(4)
8.1 The Geometry of Linear Programming
525(17)
Creating a Model
526(1)
Historical Note: George Dantzig
527(2)
Analyzing the Model
529(3)
Some Graphing Tips
532(1)
Why the Corner Principle Works
532(7)
Exercises 8.1
539(3)
8.2 Introduction to the Simplex Method
542(11)
Comparison of the Gauss-Jordan and Simplex Methods
548(1)
Karmarkar's New Method
549(1)
Historical Note: Hindu Mathematics
550(1)
Exercises 8.2
551(2)
8.3 The Simplex Method: Complete Problems
553(17)
Pivoting with the Simplex Method
554(1)
When to Stop Pivoting
555(3)
Why the Simplex Method Works
558(5)
Exercises 8.3
563(2)
Technology and the Simplex Method
565(5)
CHAPTER 8 REVIEW
570(2)
9 EXPONENTIALS AND LOGARITHMIC FUNCTIONS
572(74)
9.0A Review of Exponentials and Logarithms
573(12)
Functions
573(1)
Exponential Functions
573(2)
Rational and Irrational Numbers
575(1)
The Natural Exponential Function
575(3)
Logarithms
578(1)
Common Logarithms
578(1)
Historical Note: Leonhard Euler
579(3)
The Natural Logarithm Function
582(2)
Exercises 9.0A
584(1)
9.0B Review of Properties of Logarithms
585(11)
The Inverse Properties
585(1)
Solving Exponential Equations
586(2)
The Exponent-Becomes-Multiplier Property
588(2)
Historical Note: John Napier
590(2)
The Division-Becomes-Subtraction Property
592(1)
The Multiplication-Becomes-Addition Property
593(1)
Solving Logarithmic Equations
594(1)
Exercises 9.0B
595(1)
9.1 Exponential Growth
596(16)
Delta Notation
597(2)
The Exponential Model
599(7)
Exponential Growth and Compound Interest (prerequisite: Chapter 5)
606(2)
Exercises 9.1
608(4)
9.2 Exponential Decay
612(17)
Half-Life
616(2)
Relative Decay Rate
618(3)
Historical Note: Marie Curie
621(1)
Radiocarbon Dating
622(2)
Historical Note: Willard Frank Libby
624(3)
Exercises 9.2
627(2)
9.3 Logarithmic Scales
629(15)
Earthquakes
629(3)
The Richter Scale
632(4)
Earthquake Magnitude and Energy
636(1)
The Decibel Scale
636(3)
Historical Note: Alexander Graham Bell
639(2)
Exercises 9.3
641(3)
CHAPTER 9 REVIEW
644(2)
10 CALCULUS
646
10.0 Review of Ratios, Parabolas, and Functions
647(13)
Ratios, Proportions, and Rates
647(2)
Similar Triangles
649(2)
Parabolas
651(1)
Secant Lines and Their Slopes
652(2)
Locating the Vertex
654(3)
Functions
657(1)
Exercises 10.0
658(2)
10.1 The Antecedents of Calculus
660(16)
Ancient Mathematics
660(1)
Greek Mathematics
661(2)
Hindu Mathematics
663(1)
Arabic Mathematics
664(4)
Historical Note: Arab Mathematics
668(1)
Mathematics during the Middle Ages
669(1)
Mathematics during the Renaissance
669(4)
Historical Note: Rene Descartes
673(1)
Exercises 10.1
674(2)
10.2 Four Problems
676(17)
Problem 1: Find the Distance Traveled by a Falling Object
677(4)
Problem 2: Find the Trajectory of a Cannonball
681(1)
Historical Note: Galileo Galilei
682(3)
Problem 3: Find the Line Tangent to a Given Curve
685(3)
Problem 4: Find the Area of Any Shape
688(2)
Exercises 10.2
690(3)
10.3 Newton and Tangent Lines
693(9)
Cauchy's Reformulation of Newton's Method
695(3)
Historical Note: Isaac Newton
698(3)
Exercises 10.3
701(1)
10.4 Newton on Falling Objects and the Derivative
702(11)
Average Speed and Instantaneous Speed
702(1)
Newton on Gravity
702(4)
The Derivative
706(3)
Interpreting a Derivative
709(2)
Exercises 10.4
711(2)
10.5 The Trajectory of a Cannonball
713(14)
The Motion Due to the Explosion
714(1)
The Motion Due to Gravity
715(1)
The Equation for the Cannonball's Motion
716(5)
The Generalized Equation for the Cannonball's Motion (prerequisite: Section 6.5)
721(4)
Exercises 10.5
725(2)
10.6 Newton and Areas
727(11)
Find the Area of Any Shape
727(1)
The Area Function A(x)
727(3)
Newton and the Area Function
730(1)
Antiderivatives
731(2)
Antiderivatives and Areas
733(3)
Exercises 10.6
736(2)
10.7 Conclusion
738(2)
Rates of Change
738(1)
Sketching Curves
738(1)
Finding Maximum and Minimum Values
739(1)
Motion
739(1)
Areas and Volumes
739(1)
CHAPTER 10 REVIEW
740
APPENDIXESA-1(81)
Appendix I Using a Scientific CalculatorA-1(10)
The Equals ButtonA-1(1)
The Clear ButtonA-2(1)
The Subtraction Symbol and the Negative SymbolA-2(1)
Order of Operations and Use of ParenthesesA-3(3)
The Shift ButtonA-6(1)
MemoryA-7(1)
Scientific NotationA-8(1)
ExercisesA-9(2)
Appendix II Using a Graphing CalculatorA-11(11)
The Enter ButtonA-11(1)
The 2nd and Alpha ButtonsA-11(1)
Correcting Typing ErrorsA-12(1)
The Subtraction Symbol and the Negative SymbolA-12(1)
The Multiplication SymbolA-13(1)
Order of Operations and Use of ParenthesesA-13(3)
MemoryA-16(3)
Scientific NotationA-19(1)
ExercisesA-20(2)
Appendix III Graphing with a Graphing CalculatorA-22(3)
The Graphing ButtonsA-22(1)
Graphing a LineA-22(1)
ExercisesA-23(2)
Appendix IV Finding Points of Intersection with a Graphing CalculatorA-25(2)
ExercisesA-26(1)
Appendix V Dimensional AnalysisA-27(5)
ExercisesA-29(3)
Appendix VI Body Table for the Standard Normal DistributionA-32(1)
Appendix VII Answers to Selected ExercisesA-33(49)
CreditsA-82(1)
IndexA-83

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