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Mathematics : A Practical Odyssey

ISBN: 9780534378912 | 0534378919
Edition: 4th
Format: Paperback
Publisher: Brooks Cole
Pub. Date: 10/26/2000

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SummaryTable of Contents
Discover the many ways mathematics is relevant to your life with MATHEMATICS: A PRACTICAL ODYSSEY and its accompanying online resources. You'll master problem solving skills in such areas as calculating interest and understanding voting systems and come to recognize the relevance of mathematics and to appreciate its human aspect. Included with your purchase is access to the ThomsonNOW, an online tutorial that allows you to work with real math notation in real time, with unlimited practice problems, instant analysis and feedback, and streaming video to illustrate key concepts and Personal Tutor with SMARTHINKING a live, online mathematics tutor.
1 LOGIC
1(53)
Deductive vs. Inductive Reasoning
2(10)
Problem Solving
... MORE(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)
Symbolic Logic
12(9)
Statements
12(1)
Compound Statements and Logical Connectives
13(1)
The Negation ≈p
14(1)
Historical Note: Gottfried Wilhelm Leibniz
15(1)
The Conjunction p q
16(1)
The Disjunction p q
16(1)
The Conditional p → q
17(2)
Exercises 1.2
19(2)
Truth Tables
21(13)
The Negation ≈p
21(1)
The Conjunction p q
21(1)
The Disjunction p q
22(3)
The Conditional p &rarrl q
25(3)
Equivalent Expressions
28(1)
Historical Note: George Boole
29(2)
De Morgan's Laws
31(2)
Exercises 1.3
33(1)
More on Conditionals
34(7)
Variations of a Conditional
34(1)
Equivalent Conditionals
35(2)
The ``Only If' Connective
37(1)
The Biconditional p ↔ q
38(1)
Exercises 1.4
39(2)
Analyzing Arguments
41(13)
Valid Arguments
41(3)
Tautologies
44(2)
Historical Note: Charles Lutwidge Dodgson
46(3)
Exercises 1.5
49(2)
Chapter 1 Review
51(3)
Sets and Counting
54(58)
Sets and Set Operations
55(12)
Notation
55(2)
Universal Set and Subsets
57(1)
Intersection of Sets
58(1)
Mutually Exclusive Sets
58(1)
Union of Sets
58(3)
Complement of a Set
61(1)
Historical Note: John Venn
62(1)
Shading Venn Diagrams
63(1)
Set Theory and Logic (prerequisite: Chapter 1)
63(1)
Exercises 2.1
64(3)
Applications of Venn Diagrams
67(11)
Surveys
67(4)
De Morgan's Laws
71(2)
Historical Note: Augustus De Morgan
73(1)
Exercises 2.2
74(4)
Introduction to Combinatorics
78(8)
The Fundamental Principle of Counting
78(3)
Factorials
81(2)
Exercises 2.3
83(3)
Permutations and Combinations
86(13)
With versus Without Replacement
86(1)
Permutations
86(3)
Combinations
89(6)
Historical Note: Chu Shi-chieh
95(1)
Exercises 2.4
96(3)
Infinite Sets
99(13)
One-to-One Correspondence
99(2)
Historical Note: Georg Cantor
101(1)
Countable Sets
102(3)
Uncountable Sets
105(1)
Points on a Line
106(2)
Exercises 2.5
108(2)
Chapter 2 Review
110(2)
Probability
112(75)
History of Probability
113(7)
Roulette
114(1)
Dice and Craps
115(1)
Cards
116(1)
Historical Note: Blaise Pascal
117(1)
Historical Note: Gerolamo Cardano
118(1)
Exercises 3.1
119(1)
Basic Terms of Probability
120(15)
Finding Probabilities and Odds
122(2)
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(2)
Historical Note: Nancy Wexler
131(1)
Exercises 3.2
132(3)
Basic Rules of Probability
135(9)
Mutually Exclusive Events
136(1)
Pair-of-Dice Probabilities
136(3)
More Probability Rules
139(1)
Probabilities and Venn Diagrams
140(1)
Exercises 3.3
140(3)
Fractions on a Graphing Calculator
143(1)
Combinatorics and Probability
144(10)
Lotteries
146(2)
Historical Note: Lotteries
148(1)
Keno
149(1)
Cards
150(2)
Exercises 3.4
152(2)
Expected Value
154(7)
Why the House Wins
156(1)
Decision Theory
157(1)
Betting Strategies
158(1)
Exercises 3.5
158(3)
Conditional Probability
161(11)
Probabilities and Polls
161(3)
The Product Rule
164(1)
Tree Diagrams
165(4)
Exercises 3.6
169(3)
Independence; Trees in Genetics
172(15)
Dependent and Independent Events
172(3)
Product Rule for Independent Events
175(1)
Trees in Medicine and Genetics
176(3)
Hair Color
179(2)
Exercises 3.7
181(4)
Chapter 3 Review
185(2)
Statistics
187(101)
Population, Sample, and Data
188(24)
Population versus Sample
188(1)
Frequency Distributions
188(2)
Grouped Data
190(2)
Histograms
192(2)
Histograms and Relative Frequency Density
194(3)
Pie Charts
197(1)
Exercises 4.1
198(10)
Histograms on a Graphing Calculator
208(4)
Measures of Central Tendency
212(10)
The Mean
212(5)
The Median
217(1)
The Mode
218(1)
Exercises 4.2
219(3)
Measures of Dispersion
222(15)
Deviations
223(1)
Variance and Standard Deviation
224(2)
Alternate Methods for Finding Variance
226(4)
Exercises 4.3
230(4)
Measures of Central Tendency and Dispersion on a Graphing Calculator
234(3)
The Normal Distribution
237(19)
Discrete versus Continuous Variables
238(1)
Normal Distributions
238(2)
Probability, Area, and Normal Distributions
240(2)
Historical Note: Carl Friedrich Gauss
242(1)
The Standard Normal Distribution
243(6)
Converting to the Standard Normal
249(5)
Exercises 4.4
254(2)
Polls and Margin of Error
256(13)
Sampling and Inferential Statistics
256(1)
Sample Proportion versus Population Proportion
257(2)
Margin of Error
259(1)
Historical Note: George H. Gallup
260(6)
Exercises 4.5
266(3)
Linear Regression
269(19)
Linear Trends and Line of Best Fit
270(3)
Coefficient of Linear Correlation
273(4)
Exercises 4.6
277(4)
Linear Regression on a Graphing Calculator
281(3)
Chapter 4 Review
284(4)
Finance
288(80)
Simple Interest
289(9)
National Debt
292(1)
Add-On Interest
293(1)
Credit Card Finance Charge
294(1)
Historical Note: Credit Card History
295(1)
Exercises 5.1
296(2)
Compound Interest
298(75)
Annual Yield
304(3)
Exercises 5.2
307(2)
Doubling Time on a Graphing Calculator
309(64)
Annuities
373
Calculating Short-Term Annuities
313(3)
Calculating Long-Term Annuities
316(1)
Tax-Deferred Annuities
317(2)
Sinking Funds
319(1)
Present Value of an Annuity
320(2)
Exercises 5.3
322(3)
Annuities on a Graphing Calculator
325(1)
Amortized Loans
326(21)
Amortization Schedules
327(5)
Finding an Unpaid Balance
332(3)
Exercises 5.4
335(5)
Amortization Schedules on a Computer
340(7)
Annual Percentage Rate on a Graphing Calculator
347(9)
Historical Note: The Truth in Lending Act
349(1)
Finance Charges
349(3)
Estimating Prepaid Finance Charges
352(2)
Exercises 5.5
354(2)
Payout Annuities
356(12)
Calculating Short-Term Payout Annuities
356(1)
Comparing Payout Annuities and Savings Annuities
357(1)
Calculating Long-Term Payout Annuities
358(2)
Payout Annuities with Inflation
360(2)
Exercises 5.6
362(2)
Chapter 5 Review
364(4)
Geometry
368(92)
Perimeter and Area
369(14)
Polygons
369(4)
Heron's Formula for the Area of a Triangle
373(3)
Right Triangles
376(1)
Circles
377(2)
Exercises 6.1
379(4)
Volume and Surface Area
383(12)
Problem Solving
383(2)
Surface Area
385(2)
Spheres
387(2)
Cones and Pyramids
389(2)
Exercises 6.2
391(4)
Egyptian Geometry
395(11)
Units of Measurement
396(1)
Empirical Geometry (If It Works, Use It)
397(2)
The Great Pyramid of Cheops
399(1)
The Rhind Papyrus
400(2)
Pi and the Area of a Circle
402(2)
Exercises 6.3
404(2)
The Greeks
406(12)
Thales of Miletus
407(1)
Pythagoras of Samos
408(2)
Euclid of Alexandria
410(1)
Deductive Proof
411(1)
Historical Note: Archimedes of Syracuse
412(2)
Archimedes of Syracuse'
414(1)
Exercises 6.4
415(3)
Right Triangle Trigonometry
418(14)
Angle Measurement
419(1)
Special Triangles
420(1)
Trigonometric Ratios
421(4)
Using a Calculator
425(1)
Finding an Acute Angle
426(2)
Angles of Elevation and Depression
428(1)
Exercises 6.5
429(3)
Conic Sections and Analytic Geometry
432(13)
Historical Note: Hypatia
433(1)
Conic Sections
433(1)
The Circle
434(1)
The Parabola
435(3)
The Ellipse
438(2)
The Hyperbola
440(4)
Exercises 6.6
444(1)
Non-Euclidean Geometry
445(15)
The Parallel Postulate
445(1)
Girolamo Saccheri
446(1)
Carl Friedrich Gauss
447(1)
Janos Bolyai
447(1)
Nikolai Lobachevsky
448(1)
Bernhard Riemann
449(1)
Geometric Models
449(2)
A Comparison of Triangles
451(1)
Geometry in Art
452(3)
Exercises 6.7
455(1)
Chapter 6 Review
456(4)
Matrices and Markov Chains
460(59)
Review of Matrices
467(6)
Terminology and Notation
461(1)
Matrix Multiplication
462(3)
Properties of Matrix Multiplication
465(1)
Historical Note: Arthur Cayley and James Joseph Sylvester
466(2)
Identity Matrices
468(1)
Exercises 7.0
469(1)
Matrix Multiplication on a Graphing Calculator
469(4)
Markov Chains
473(14)
Transition Matrices
474(1)
Probability Matrices
475(1)
Using Markov Chains to Predict the Future
476(6)
Historical Note: Andrei Andreevich Markov
482(1)
Exercises 7.1
483(4)
Systems of Linear Equations
487(21)
Linear Equations
487(1)
Systems of Equations
487(3)
Solving Systems: The Elimination Method
490(1)
Solving Systems: The Gauss-Jordan Method
491(8)
Exercises 7.2
499(2)
Technology and the Row Operations
501(1)
The Row Operations on a Graphing Calculator
502
The Row Operations and Amortrix
000(507)
Augmented Identity Matrices
507(1)
Long-Range Predictions with Markov Chains
508(11)
Exercises 7.3
514(3)
Chapter 7 Review
517(2)
Linear Programming
519(61)
Review of Linear Inequalities
521(12)
Systems of Linear Inequalities
524(3)
Finding Corner Points
527(2)
Exercises 8.0
529(1)
Graphing Linear Inequalities on a Graphing Calculator
529(4)
The Geometry of Linear Programming
533(16)
Creating a Model
534(3)
Analyzing the Model
537(2)
Some Graphing Tips
539(1)
Why the Corner Principle Works
539(5)
Historical Note: George Dantzig
544(2)
Exercises 8.1
546(3)
Introduction to the Simplex Method
549(11)
Comparison of the Gauss-Jordan and Simplex Methods
555(1)
Karmarkar's New Method
556(1)
Historical Note: Hindu Mathematics
557(1)
Exercises 8.2
558(2)
The Simplex Method: Complete Problems
560(20)
Pivoting with the Simplex Method
561(2)
When to Stop Pivoting
563(2)
Why the Simplex Method Works
565(6)
Exercises 8.3
571(2)
Technology and the Simplex Method
573(5)
Chapter 8 Review
578(2)
Exponentials and Logarithmic Functions
580(74)
Review of Exponentials and Logarithms
581(10)
Functions
581(1)
Exponential Functions
581(1)
Rational and Irrational Numbers
582(1)
The Natural Exponential Function
583(2)
Logarithms
585(1)
Historical Note; Leonhard Euler
586(1)
Common Logarithms
586(3)
The Natural Logarithm Function
589(2)
Exercises 9.0A
591(1)
Review of Properties of Logarithms
591(13)
The Inverse Properties
591(2)
Solving Exponential Equations
593(2)
The Exponent-Becomes-Multiplier Property
595(1)
Historical Note: John Napier
596(2)
The Division-Becomes-Subtraction Property
598(2)
The Multiplication-Becomes-Addition Property
600(1)
Solving Logarithmic Equations
601(1)
Exercises 9.0B
602(2)
Exponential Growth
604(16)
Delta Notation
604(3)
The Exponential Model
607(6)
Exponential Growth and Compound Interest (for those who have read Chapter 5: Finance)
613(2)
Exercises 9.1
615(5)
Exponential Decay
620(16)
Half-Life
623(3)
Relative Decay Rate
626(3)
Historical Note: Marie Curie
629(1)
Radiocarbon Dating
629(3)
Historical Note: Willard Frank Libby
632(2)
Exercises 9.2
634(2)
Logarithmic Scales
636(18)
Earthquakes
636(3)
The Richter Scale
639(5)
Earthquake Magnitude and Energy
644(1)
The Decibel Scale
645(4)
Historical Note: Alexander Graham Bell
649(1)
Exercises 9.3
650(2)
Chapter 9 Review
652(2)
Calculus
654
Review of Ratios, Parabolas, and Functions
655
Ratios, Proportions, and Rates
655
Delta Notation
656
Similar Triangles
657
Parabolas
660
Secant Lines and Their Slopes
661
Locating the Vertex
662
Functions
664
Exercises 10.0
666
The Antecedents of Calculus
668
Ancient Mathematics
668
Greek Mathematics
669
Hindu Mathematics
671
Arabic Mathematics
672
Historical Note: Arabic Mathematics
676
Mathematics during the Middle Ages
677
Mathematics during the Renaissance
677
Historical Note: Rene Descartes
681
Exercises 10.1
682
Four Problems
684
Find the Distance Traveled by a Falling Object
686
Find the Trajectory of a Cannonball
689
Historical Note: Galileo Galilei
690
Find the Line Tangent to a Given Curve
693
Find the Area of Any Shape
695
Exercises 10.2
697
Newton and Tangent Lines
700
Cauchy's Reformulation of Newton's Method
702
Historical Note: Isaac Newton
705
Exercises 10.3
708
Newton on Falling Objects and the Derivative
709
Average Speed and Instantaneous Speed
709
Newton on Gravity
709
The Derivative
712
Interpreting a Derivative
716
Exercises 10.4
718
The Trajectory of a Cannonball
720
The Motion Due to the Explosion
721
The Motion Due to Gravity
722
The Equation for the Cannonball's Motion
722
The Generalized Equation for the Cannonball's Motion (for those who have read Section 6.5)
728
Exercises 10.5
731
Newton and Areas
734
Find the Area of Any Shape
734
The Area Function A(x)
734
Newton and the Area Function
736
Antiderivatives
737
Antiderivatives and Areas
739
Exercises 10.6
743
Conclusion
744
Rates of Change
744
Sketching Curves
744
Finding Maximum and Minimum Values
746
Motion
747
Areas and Volumes
747
Chapter 10 Review
748
Appendices
Appendix A Using a Scientific Calculator
A-1
The Equals Button
A-1
The Clear Button
A-2
The Subtraction Symbol and the Negative Symbol
A-2
Order of Operations and Use of Parentheses
A-3
The Shift Button
A-6
Memory
A-6
Scientific Notation
A-8
Exercises
A-8
Appendix B Using a Graphing Calculator
A-10
The Enter Button
A-10
The 2nd and Alpha Buttons
A-10
Correcting Typing Errors
A-11
The Subtraction Symbol and the Negative Symbol
A-11
The Multiplication Symbol
A-12
Order of Operations and Use of Parentheses
A-12
Memory
A-15
Scientific Notation
A-17
Exercises
A-18
Appendix C Graphing with a Graphing Calculator
A-20
The Graphing Buttons
A-20
Graphing a Line
A-20
Exercises
A-22
Appendix D Finding Points of Intersection with a Graphing Calculator
A-24
Exercises
A-25
Appendix E Dimensional Analysis
A-26
Exercises
A-28
Appendix F Body Table for the Standard Normal Distribution
A-31
Appendix G Answers to Selected Exercises
A-32
CreditsA-73
IndexA-74

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