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More copies of this ISBNThis title in other editionsStudent Resource Guide for Excursions in Modern Mathematicsby Peter Tannenbaum
Synopses & ReviewsPublisher Comments:Excursions in Modern Mathematics, Seventh Edition, shows readers that math is a lively, interesting, useful, and surprisingly rich subject. With a new chapter on financial math and an improved supplements package, this book helps students appreciate that math is more than just a set of classroom theories: math can enrich the life of any one who appreciates and knows how to use it.
The Mathematics of Social Choice; The Mathematics of Voting: The Paradox of Democracy; The Mathematics of Power: Weighted Voting ; The Mathematics of Sharing: FairDivision Games; The Mathematics of Apportionment: Making the Rounds; Apportionment Today; Management Science; The Mathematics of Getting Around: Euler Paths and Circuits; The Mathematics of Touring: The Traveling Salesman Problem; The Mathematics of Networks: The Cost of Being Connected; The Mathematics of Scheduling: Chasing the Critical Path; Growth And Symmetry; The Mathematics of Spiral Growth in Nature: Fibonacci Numbers and the Golden Ratio; The Mathematics of Money: Spending it, Saving It, and Growing It; The Mathematics of Symmetry: Beyond Reflection; The Geometry of Fractal Shapes: Naturally Irregular; The Mathematics of Population Growth: There is Strength in Numbers; Statistics; Collecting Statistical Data: Censuses, Surveys, and Clinical Studies; Descriptive Statistics: Graphing and Summarizing Data; Chances, Probabilities, and Odds: Measuring Uncertainty; The Mathematics of Normal Distributions: The Call of the Bell
For all readers interested in a survey of mathematics. Synopsis:Excursions in Modern Mathematics, Seventh Edition, shows readers that math is a lively, interesting, useful, and surprisingly rich subject. With a new chapter on financial math and an improved supplements package, this book helps students appreciate that math is more than just a set of classroom theories: math can enrich the life of any one who appreciates and knows how to use it.
About the AuthorPeter Tannenbaum has bachelor's degrees in Mathematics and Political Science and a Ph. D. in Mathematics, all from the University of California, Santa Barbara. He has held faculty positions at the University of Arizona, Universidad Simon Bolivar (Venezuela), and is currently professor of mathematics at the California State University, Fresno. His current research interests are in the interface between mathematics, politics and behavioral economics. He is also involved in mathematics curriculum reform and teacher preparation. His hobbies are travel, foreign languages and sports. He is married to Sally Tannenbaum, a professor of communication at CSU Fresno, and is the father of three (twin sons and a daughter).
Table of ContentsPart 1. The Mathematics of Social Choice
1. The Mathematics of Voting: The Paradox of Democracy 1.1 Preference Ballots and Preference Schedules 1.2 The Plurality Method 1.3 The Borda Count Method 1.4 The PluralitywithElimination Method (Instant Runoff Voting) 1.5 The Method of Piecewise Comparisons 1.6 Rankings Profile: Kenneth J. Arrow Key Concepts Exercises Projects and Papers References and Further Readings
2. The Mathematics of Power: Weighted Voting 2.1 An Introduction to Weighted Voting 2.2 The Banzhaf Power Index 2.3 Applications of the Banzhaf Power Index 2.4 The ShapelyShubik Power Index 2.5 Applications of the ShapelyShubik Power Index Profile: Lloyd S. Shapely Key Concepts Exercises Projects and Papers References and Further Readings
3. The Mathematics of Sharing: FairDivision Games 3.1 FairDivision Games 3.2 Two Players: The DividerChooser Method 3.3 The LoneDivider Method 3.4 The LoneChooser Method 3.5 The LastDiminisher Method 3.6 The Method of Sealed Bids 3.7 The Method of Markers Profile: Hugo Steinhaus Key Concepts Exercises Projects and Papers References and Further Readings
4. The Mathematics of Apportionment: Making the Rounds 4.1 Apportionment Problems 4.2 Hamilton's Method and the Quota Rule 4.3 The Alabama and Other Paradoxes 4.4 Jefferson's Method 4.5 Adams's Method 4.6 Webster's Method Historical Note: A Brief History of Apportionment in the United States Key Concepts Exercises Projects and Papers References and Further Readings
MiniExcursion 1: Apportionment Today
Part 2. Management Science
5. The Mathematics of Getting Around: Euler Paths and Circuits 5.1 Euler Circuit Problems 5.2 What is a Graph? 5.3 Graph Concepts and Terminology 5.4 Graph Models 5.5 Euler's Theorems 5.6 Fleury's Algorithm 5.7 Eulerizing Graphs Profile: Leonard Euler Key Concepts Exercises Projects and Papers References and Further Readings
6. The Mathematics of Touring: The Traveling Salesman Problem 6.1 Hamilton Circuits and Hamilton Paths 6.2 Complete Graphs 6.3 Traveling Salesman Problems 6.4 Simple Strategies for Solving TSPs 6.5 The BruteForce and NearestNeighbor Algorithms 6.6 Approximate Algorithms 6.7 The Repetitive NearestNeighbor Algorithm 6.8 The Cheapest Link Algorithm Profile: Sir William Rowan Hamilton Key Concepts Exercises Projects and Papers References and Further Readings
7. The Mathematics of Networks: The Cost of Being Connected 7.1 Trees 7.2 Spanning Trees 7.3 Kruskal's Algorithm 7.4 The Shortest Network Connecting Three Points 7.5 Shortest Networks for Four or More Points Profile: Evangelista Torricelli Key Concepts Exercises Projects and Papers References and Further Readings
8. The Mathematics of Scheduling: Chasing the Critical Path 8.1 The Basic Elements of Scheduling 8.2 Directed Graphs (Digraphs) 8.3 Scheduling with Priority Lists 8.4 The DecreasingTime Algorithm 8.5 Critical Paths 8.6 The CriticalPath Algorithm 8.7 Scheduling with Independent Tasks Profile: Ronald L. Graham Key Concepts Exercises Projects and Papers References and Further Readings
MiniExcursion 2: A Touch of Color
Part 3. Growth And Symmetry
9. The Mathematics of Spiral Growth: Fibonacci Numbers and the Golden Ratio 9.1 Fibonacci's Rabbits 9.2 Fibonacci Numbers 9.3 The Golden Ratio 9.4 Gnomons 9.5 Spiral Growth in Nature Profile: Leonardo Fibonacci Key Concepts Exercises Projects and Papers References and Further Readings
10. The Mathematics of Money: Spending it, Saving It, and Growing It 10.1 Percentages 10.2 Simple Interest 10.3 Compound Interest 10.4 Geometric Sequences 10.5 Deferred Annuities: Planned Savings for the Future Key Concepts Exercises Projects and Papers References and Further Readings
11. The Mathematics of Symmetry: Beyond Reflection 11.1 Rigid Motions 11.2 Reflections 11.3 Rotations 11.4 Translations 11.5 Glide Reflections 11.6 Symmetry as a Rigid Motion 11.7 Patterns Profile: Sir Roger Penrose Key Concepts Exercises Projects and Papers References and Further Readings
12. The Geometry of Fractal Shapes: Naturally Irregular 12.1 The Koch Snowflake 12.2 The Sierpinski Gasket 12.3 The Chaos Game 12.4 The Twisted Sierpinski Gasket 12.5 The Mandelbrot Set Profile: Benoit Mandelbrot Key Concepts Exercises Projects and Papers References and Further Readings
MiniExcursion 3: The Mathematics of Population Growth: There is Strength in Numbers
Part 4. Statistics
13. Collecting Statistical Data: Censuses, Surveys, and Clinical Studies 13.1 The Population 13.2 Sampling 13.3 Random Sampling 13.4 Sampling: Terminology and Key Concepts 13.5 The CaptureRecapture Method 13.6 Clinical Studies Profile: George Gallup Key Concepts Exercises Projects and Papers References and Further Readings
14. Descriptive Statistics: Graphing and Summarizing Data 14.1 Graphical Descriptions of Data 14.2 Variables 14.3 Numerical Summaries of Data 14.4 Measures of Spread Profile: W. Edwards Deming Key Concepts Exercises Projects and Papers References and Further Readings
15. Chances, Probabilities, and Odds: Measuring Uncertainty 15.1 Random Experiments and Sample Spaces 15.2 Counting Outcomes in Sample Spaces 15.3 Permutations and Combinations 15.4 Probability Spaces 15.5 Equiprobable Spaces 15.6 Odds Profile: Persi Diaconis Key Concepts Exercises Projects and Papers References and Further Readings
16. The Mathematics of Normal Distributions: The Call of the Bell 16.1 Approximately Normal Distributions of Data 16.2 Normal Curves and Normal Distributions 16.3 Standardizing Normal Data 16.4 The 689599.7 Rule 16.5 Normal Curves as Models of RealLife Data Sets 16.6 Distributions of Random Events 16.7 Statistical Inference Profile: Carl Friedrich Gauss Key Concepts Exercises Projects and Papers References and Further Readings MiniExcursion 4: The Mathematics of Managing Risk What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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