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

by Parks, Harold; Musser, Gary; Trimpe, Lynn; Maurer, Vikki; Maurer, Roger

• ISBN13: 9780495010616
• ISBN10: 0495010618
• Edition: 1st
• Format: Hardcover w/ Access Card
• Copyright: 2006-02-10
• Publisher: Cengage Learning

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