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A Mathematical View of Our World (with CD-ROM and iLrn™ Student, and Personal Tutor Printed Access Card),9780495010616
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A Mathematical View of Our World (with CD-ROM and iLrn™ Student, and Personal Tutor Printed Access Card)

by ; ; ; ;
Edition:
1st
ISBN13:

9780495010616

ISBN10:
0495010618
Format:
Hardcover
Pub. Date:
2/10/2006
Publisher(s):
Brooks Cole
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Summary

Harness the power of mathematics in school and your future career with A MATHEMATICAL VIEW OF OUR WORLD. This liberal arts textbook helps you see the beauty and power of mathematics as it is applied to the world around you. You will recognize the connections, patterns, and significance of the mathematics you study, and see that mathematics has a meaningful place in your life. Included with your purchase is access to the CengageNOW, 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.

Table of Contents

Numbers in Our Lives
1(1)
Chapter Opener: The Evolution of the Braille Reading Code
1(58)
The Human Side of Mathematics
2(1)
Herman Hollerith
George J. Laurer
Identification Numbers and Check Digits
3(1)
Social Security Numbers
3(2)
General Identification Numbers
5(1)
Transmission Errors
6(1)
Check Digits
6(3)
Universal Product Codes
9(9)
Modular Arithmetic and Check-Digit Schemes
18(19)
The Division Algorithm
19(2)
The Division Algorithm for Integers
21(2)
Congruence Modulo m
23(1)
Modular Arithmetic
24(2)
Modular Check-Digit Schemes
26(4)
Summary of Common Check-Digit Schemes
30(7)
Encoding Data
37(22)
Binary Codes
37(3)
UPC Bar Codes
40(4)
Manufacturer Numbers and Product Numbers in UPC Bar Codes
44(1)
UPC Codes on Retail Items
44(2)
Other Binary Codes
46(10)
Chapter Review
56(1)
Chapter Review Problems
57(2)
Shapes in Our Lives
59(82)
Chapter Opener: Can a Soccer Ball Glow?
59(1)
The Human Side of Mathematics
60(1)
Marjorie Rice
R. Buckminster Fuller
Tilings
61(25)
Polygons and Tilings
62(3)
Regular Polygons
65(1)
Regular Tilings
66(2)
Semiregular Tilings
68(4)
Miscellaneous Tilings
72(3)
The Pythagorean Theorem
75(11)
Symmetry, Rigid Motions, and Escher Patterns
86(26)
Strip Patterns and Symmetry
86(2)
Two-Dimensional Patterns and Symmetry
88(2)
Definitions of Rigid Motions
90(7)
Rigid Motions and the Basic Strip Patterns
97(2)
Escher Patterns
99(13)
Fibonacci Numbers and the Golden Mean---Shapes in Nature
112(29)
Fibonacci Numbers
112(3)
Recursion
115(2)
Fibonacci Numbers in Nature
117(1)
Geometric Recursion
118(2)
The Golden Ratio
120(1)
Golden Rectangles and the Golden Ratio
121(2)
A Final Look at Fibonacci Sequences
123(12)
Chapter Review
135(2)
Chapter Review Problems
137(4)
Voting and Elections
141(64)
Chapter Opener: Coach Decides It's Best Not to Win
141(1)
The Human Side of Mathematics
142(1)
Marquis de Condorcet
Kenneth J. Arrow
Voting Systems
143(20)
Plurality Method
144(1)
Borda Count Method
145(1)
Plurality with Elimination Method
146(3)
Pairwise Comparison Method
149(3)
Tie Breaking
152(11)
Flaws of the Voting Systems
163(20)
The Majority Criterion
163(2)
The Head-to-Head Criterion
165(1)
The Monotonicity Criterion
166(2)
The Irrelevant-Alternatives Criterion
168(2)
Summary of the Criteria and Various Voting Methods
170(1)
Approval Voting
171(12)
Weighted Voting Systems
183(22)
Weighted Voting Systems
183(2)
Coalitions
185(2)
Dictators, Dummies, and Voters with Veto Power
187(1)
Critical Voters
188(1)
The Banzhaf Power Index
189(12)
Chapter Review
201(1)
Chapter Review Problems
202(3)
Fair Division
205(80)
Chapter Opener: Legislator Wants State to Get Bigger Cut of Video Poker Profit
205(1)
The Human Side of Mathematics
206(1)
John H. Conway
Hugo Steinhaus
Divide and Choose Methods
207(28)
Fair-Division Problems: Definitions and Assumptions
207(2)
Fair Division for Two Players
209(4)
Fair Division for Three Players
213(3)
Fair Division for Three or More Players
216(19)
Discrete and Mixed Division Problems
235(21)
The Method of Sealed Bids---Discrete Fair Division
235(3)
The Method of Points---Discrete Division
238(6)
The Adjusted-Winner Procedure---Mixed Fair Division
244(12)
Envy-Free Division
256(29)
Envy-Free Division
256(25)
Chapter Review
281(1)
Chapter Review Problems
282(3)
Apportionment
285(54)
Chapter Opener: Some Think It's the Pits at High-Tech Heaven
285(1)
The Human Side of Mathematics
286(1)
Michel L. Balinski
H. Peyton Young
The Apportionment Problem---Quota Methods
287(19)
Apportionment
288(1)
The Standard Divisor and The Standard Quota
288(3)
Hamilton's Method
291(2)
Quota Rule and Quota Method
293(1)
Lowndes' Method
293(13)
The Apportionment Problem---Divisor Methods
306(16)
Jefferson's Method
307(3)
Webster's Method
310(12)
Flaws of the Apportionment Methods
322(17)
The Quota Rule
322(1)
The Alabama Paradox
323(2)
Population Paradox
325(1)
New-States Paradox
326(2)
Seeking a Perfect Apportionment Method
328(7)
Chapter Review
335(1)
Chapter Review Problems
336(3)
Routes and Networks
339(70)
Chapter Opener: Internet Fashion Show Swamps Network
339(1)
The Human Side of Mathematics
340(1)
Leonhard Euler
William Rowan Hamilton
Routing Problems
341(19)
Graphs, Vertices, and Edges
341(3)
Paths and Circuits
344(2)
Connected Graphs
346(2)
Euler's Theorem
348(1)
Fleury's Algorithm
349(11)
Network Problems
360(18)
Weighted Graphs
361(1)
Subgraphs
362(2)
Trees
364(1)
Minimal Spanning Trees
365(13)
The Traveling-Salesperson Problem
378(31)
Hamiltonian Paths and Circuits
378(2)
Complete Graphs
380(3)
The Traveling-Salesperson Problem
383(3)
Approximation Algorithms
386(18)
Chapter Review
404(1)
Chapter Review Problems
405(4)
Scheduling
409(66)
Chapter Opener: Emergency Bridge Repair Speeded by Good Planning and Scheduling
409(1)
The Human Side of Mathematics
410(1)
W. Edward Deming
Sigrid Knust
Basic Concepts of Scheduling
411(21)
Projects, Tasks, and Precedence Relations
411(3)
Digraphs
414(2)
Paths
416(4)
Weighted Digraphs
420(1)
Finishing Time of a Project
421(11)
The List-Processing Algorithm and the Decreasing-Time Algorithm
432(20)
Priority Lists
432(3)
Gantt Charts
435(1)
The List-Processing Scheduling Algorithm
435(7)
Optimal Schedules
442(10)
The Critical-Path Algorithm
452(23)
Finishing Times and Critical Paths
452(3)
Critical-Path Priority Lists
455(5)
The Critical-Path Scheduling Algorithm
460(11)
Chapter Review
471(1)
Chapter Review Problems
472(3)
Descriptive Statistics---Data and Patterns
475(88)
Chapter Opener: Action Proposed to Fight the Bloated Budget
475(1)
The Human Side of Mathematics
476(1)
William Playfair
John Wilder Tukey
Organizing and Picturing Data
477(26)
Obtaining Data
477(1)
Dot Plots
478(1)
Stem-and-Leaf Plots
479(1)
Histograms
480(3)
Bar Graphs
483(3)
Line Graphs
486(1)
Pie Charts
487(1)
Choosing an Appropriate Graph
487(16)
Comparisons
503(24)
Double Stem-and-Leaf plots
503(1)
Comparison Histograms
504(1)
Multiple-Bar Graphs
505(1)
Multiple-Line Graphs
506(1)
Multiple Pie Charts
507(2)
Proportional Bar Graphs
509(1)
Choosing an Appropriate Graph
509(18)
Enhancement, Distraction, and Distortion
527(36)
Scaling and Axis Manipulation
528(4)
Line Graphs and Cropping
532(2)
Three-Dimensional Effects
534(2)
Pictographs
536(5)
Pie Charts
541(1)
Graphical Maps
542(12)
Chapter Review
554(1)
Chapter Review Problems
555(8)
Collecting and Interpreting Data
563(68)
Chapter Opener: Literary Digest Poll Shows Landslide Victory for Landon over Roosevelt
563(1)
The Human Side of Mathematics
564(1)
George Gallup
Elmo Roper
Populations, Samples, and Data
565(13)
Populations and Samples
565(2)
Data and Bias
567(2)
Simple Random Samples
569(9)
Survey Sampling Methods
578(16)
Independent Sampling
578(2)
Systematic Sampling
580(1)
Quota Sampling
581(1)
Stratified Sampling
582(1)
Cluster Sampling
583(2)
Summary
585(9)
Measures of Central Tendency and Variability
594(37)
Measures of Central Tendency
595(8)
Measures of Variability
603(5)
Variance and Standard Deviation
608(17)
Chapter Review
625(2)
Chapter Review Problems
627(4)
Probability
631(68)
Chapter Opener: Run That Ball!
631(1)
The Human Side of Mathematics
632(1)
David Blackwell
Marilyn vos Savant
Computing Probabilities in Simple Experiments
633(19)
Interpreting Probability
633(1)
Sample Spaces and Events
634(1)
Experimental Probability
635(1)
Theoretical Probability
636(3)
Mutually Exclusive Events
639(1)
Complement of an Event
640(2)
Properties of Probability
642(10)
Computing Probabilities in Multistage Experiments
652(21)
Tree Diagrams
652(1)
Fundamental Counting Principle
653(3)
Probability Tree Diagrams and Their Properties
656(6)
Applying Properties of Probability Tree Diagrams
662(11)
Conditional Probability, Expected Value, and Odds
673(26)
Conditional Probability
674(6)
Independent Events
680(2)
Expected Value
682(2)
Odds
684(10)
Chapter Review
694(1)
Chapter Review Problems
695(4)
Inferential Statistics
699(52)
Chapter Opener: P&G to Cut Spending on Local Television Advertising
699(1)
The Human Side of Mathematics
700(1)
William Sealy Gossett
Ronald A. Fisher
Normal Distributions
701(14)
Distributions of Large Data Sets
701(2)
Normal Distributions
703(1)
The Standard Normal Distribution
704(2)
Areas under the Standard Normal Distribution Curve
706(2)
Symmetry and Tables for the Normal Distribution
708(7)
Applications of Normal Distributions
715(14)
The Relationship among Normal Distributions
715(2)
The 68-95-99.7 Rule for Normal Distributions
717(2)
Population z-scores
719(2)
Computing with Normal Distributions
721(8)
Confidence Intervals and Reliable Estimation
729(22)
Sample Proportion
729(1)
Distribution of Sample Proportions
730(3)
The Standard Error
733(1)
Confidence Intervals and the Margin of Error
734(3)
Confidence Intervals and Quality Control
737(9)
Chapter Review
746(1)
Chapter Review Problems
747(4)
Growth and Decay
751(48)
Chapter Opener: Growing Enrollment at White Oaks Elementary School Outstrips Budget
751(1)
The Human Side of Mathematics
752(1)
Thomas Robert Malthus
Lise Meitner
Malthusian Population Growth
753(16)
Population Growth
753(4)
Population Growth Rate
757(3)
Ponzi Schemes
760(2)
Chain Letters
762(7)
Population Decrease, Radioactive Decay
769(11)
Population Decline
769(1)
Radioactive Decay
770(1)
Half-Life of a Radioactive Substance
771(4)
Carbon-14 Dating
775(5)
Logistic Population Models
780(19)
Logistic Population Models
781(3)
Steady-State Population
784(2)
Verhulst's Equation
786(10)
Chapter Review
796(1)
Chapter Review Problems
797(2)
Consumer Mathematics---Buying and Saving
799(52)
Chapter Opener: Analyst Predicts Stock Market Perfectly
799(1)
The Human Side of Mathematics
800(1)
Charles Dow
Amadeo Peter Giannini
Simple and Compound Interest
801(16)
Simple Interest
801(1)
Future Value
802(2)
Ordinary Interest
804(1)
Compound Interest
804(2)
Formula for Compound Interest
806(3)
Effective Annual Rate---The Effect of the Compounding Period
809(8)
Loans
817(18)
Simple-Interest Loans
817(3)
Amortized Loans
820(1)
Charting the History of an Amortized Loan
820(1)
Calculating the Monthly Payment for an Amortized Loan
821(1)
Using an Amortization Table
822(3)
Using a Formula
825(1)
Using Financial Software for Online Calculator
826(1)
The Rent-to-Own Option
826(9)
Buying a House
835(16)
Affordability Guidelines
835(1)
The Mortgage
836(1)
Points and Closing Costs
837(1)
Annual Percentage Rate
838(3)
The Down Payment
841(6)
Chapter Review
847(2)
Chapter Review Problems
849(2)
Appendices 851(12)
Answers to Odd-Numbered Problems and Chapter Review Problems 863(78)
Index 941


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