Mathematics Beyond the Numbers

by George T. Gilbert; Rhonda L. Hatcher

• ISBN13: 9780471139348
• ISBN10: 0471139343
• Format: Hardcover
• Copyright: 1999-10-01
• Publisher: Wiley
• More Book Details
• Purchase Benefits

Summary

An applied, interesting approach to one of the most feared subjects around--mathematics! Readers can learn mathematics without intimidation, and the wide variety of applications helps everyone see the critical role mathematics plays in our world.

Table of Contents

Preface	iv
A Note to Students	xi
Voting Methods	2	(68)
Plurality and Runoff Methods	4	(16)
Runoff Elections	8	(3)
Preference Rankings	11	(9)
Borda's Method: A Scoring System	20	(12)
Head-to-Head Comparisons	32	(13)
Single-Peaked Preference Rankings	37	(8)
Approval Voting	45	(13)
The Search for an Ideal Voting System	58	(12)
Writing Exercises	62	(1)
Projects	63	(3)
Key Terms	66	(1)
Review Exercises	66	(2)
Suggested Readings	68	(2)
Apportionment: Sharing What Cannot Be Divided Arbitrarily	70	(56)
Quota Methods	72	(11)
Hamilton's Method	75	(3)
Lowndes' Method	78	(5)
Early Divisor Methods	83	(21)
Jefferson's Method	83	(10)
Webster's Method	93	(11)
Apportionment in Today's House of Representatives	104	(12)
The Hill-Huntington Method	105	(5)
Other Apportionment Methods	110	(6)
The Search for an Ideal Apportionment Method	116	(10)
Writing Exercises	122	(1)
Projects	122	(1)
Key Terms	123	(1)
Review Exercises	123	(2)
Suggested Readings	125	(1)
The Mathematics of Money	126	(58)
Powers, Roots, and Logarithms	128	(5)
Simple Interest	133	(6)
Compound Interest	139	(15)
Inflation	148	(6)
The Rewards of Systematic Savings	154	(9)
Amortized Loans	163	(21)
Finding a Loan Balance	168	(2)
Amortization Schedules	170	(10)
Writing Exercises	180	(1)
Projects	181	(1)
Key Terms	181	(1)
Review Exercises	181	(2)
Suggested Readings	183	(1)
Probability	184	(86)
Elementary Probability	186	(9)
Odds	195	(6)
House Odds and Fair Bets	197	(4)
The Addition Rule	201	(5)
Conditional Probability and the Multiplication Rule	206	(14)
The Multiplication Rule	209	(1)
Independence and the Multiplication Rule	210	(10)
Counting Techniques	220	(15)
Permutations	222	(4)
Combinations	226	(9)
Probability Problems Using Counting Techniques	235	(9)
The Birthday Problem	239	(5)
Expected Value	244	(9)
Genetics	253	(17)
Writing Exercises	263	(1)
Projects	264	(2)
Key Terms	266	(1)
Review Exercises	266	(3)
Suggested Readings	269	(1)
Statistics	270	(92)
Organizing and Presenting Data	272	(19)
Bar Graphs	274	(3)
Histograms	277	(2)
Pie Charts	279	(12)
Typical and Central Values	291	(13)
The Mode	291	(2)
The Median	293	(2)
The Mean	295	(2)
Estimating the Mean of Grouped Data	297	(7)
Measures of Spread	304	(9)
The Range	304	(1)
The Standard Deviation	304	(3)
Estimating the Standard Deviation of Grouped Data	307	(6)
The Normal Distribution	313	(19)
Percentiles	324	(8)
Estimating the Mean	332	(11)
Confidence Intervals	334	(1)
Sample Standard Deviation and Confidence Intervals	335	(8)
Polls and Margin of Error	343	(7)
Garbage In, Garbage Out: A Look at Misleading Uses of Statistics and at Sampling Techniques	350	(12)
The Source of the Data	350	(2)
The Data: Questions and Answers	352	(2)
The Conclusions Drawn from the Data	354	(2)
Writing Exercises	356	(1)
Projects	357	(1)
Key Terms	358	(1)
Review Exercises	358	(3)
Suggested Readings	361	(1)
Paths and Networks	362	(58)
Eulerian Paths and Circuits on Graphs	364	(16)
Eulerization	372	(8)
The Traveling Salesman Problem	380	(23)
The Nearest Neighbor Algorithm	385	(2)
The Greedy Algorithm	387	(16)
Efficient Networking: Minimal Spanning Trees	403	(17)
Prim's Algorithm	405	(9)
Writing Exercises	414	(1)
Projects	415	(1)
Key Terms	416	(1)
Review Exercises	416	(3)
Suggested Readings	419	(1)
Tilings and Polyhedra	420	(46)
Polygons	422	(6)
Tilings	428	(17)
Regular Tilings	429	(1)
Semiregular Tilings	430	(3)
Tilings with Nonregular Polygons	433	(3)
Tilings with Other Shapes	436	(9)
Polyhedra	445	(21)
Regular Polyhedra	448	(4)
Semiregular Polyhedra	452	(8)
Writing Exercises	460	(1)
Projects	460	(1)
Key Terms	461	(1)
Review Exercises	462	(2)
Suggested Readings	464	(2)
Number Theory	466	(74)
Divisibility and Primes	468	(13)
Prime Numbers	469	(4)
The Division Algorithm	473	(3)
The Greatest Common Divisor	476	(5)
Modular Arithmetic	481	(6)
Divisibility Tests	487	(8)
Check Digits	495	(9)
Tournament Scheduling	504	(8)
Introduction to Cryptology	512	(10)
The Caesar Cipher	512	(3)
Affine Ciphers	515	(7)
Advanced Encryption Methods	522	(18)
The Hill Cipher	522	(4)
The RSA Public Key System	526	(8)
Writing Exercises	534	(1)
Projects	534	(1)
Key Terms	535	(1)
Review Exercises	536	(1)
Suggested Readings	537	(3)
Game Theory with an Introduction to Linear Programming	540	(96)
Alternate Move Games	542	(18)
Game Trees	542	(7)
Nim	549	(2)
Playing Against Chance	551	(9)
Simultaneous Move Games and Dominance	560	(16)
Simultaneous Move Games with a Random Component	570	(6)
Zero-Sum Games	576	(8)
Simultaneous Move Games and Mixed Strategies	584	(20)
Playing Against Known Mixed Strategies	585	(3)
Optimal Mixed Strategies for Zero-Sum Games	588	(16)
Mixed Strategies and Linear Programming	604	(9)
Simultaneous Move Games with Communication	613	(23)
Coordination Games and Focal Points	614	(2)
One-Way Communication: Threats	616	(3)
Two-Way Negotiations	619	(8)
Writing Exercises	627	(1)
Projects	628	(2)
Key Terms	630	(1)
Review Exercises	631	(3)
Suggested Readings	634	(2)
Appendix A	636	(1)
Answers to Selected Exercises and Review Exercises	637	(36)
Photo Credits	673	(3)
Sources	676	(5)
Index	681