Excursions in Modern Mathematics
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Excursions in Modern Mathematics: United States Edition

Excursions in Modern Mathematics: United States Edition


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About the Book

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.

Table of Contents:
Part 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 Plurality-with-Elimination 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 Shapely-Shubik Power Index 2.5 Applications of the Shapely-Shubik Power Index             Profile: Lloyd S. Shapely             Key Concepts             Exercises             Projects and Papers             References and Further Readings   3. The Mathematics of Sharing: Fair-Division Games 3.1 Fair-Division Games 3.2 Two Players: The Divider-Chooser Method 3.3 The Lone-Divider Method 3.4 The Lone-Chooser Method 3.5 The Last-Diminisher 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   Mini-Excursion 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 Brute-Force and Nearest-Neighbor Algorithms 6.6 Approximate Algorithms 6.7 The Repetitive Nearest-Neighbor 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 Decreasing-Time Algorithm 8.5 Critical Paths 8.6 The Critical-Path Algorithm 8.7 Scheduling with Independent Tasks             Profile: Ronald L. Graham             Key Concepts             Exercises             Projects and Papers             References and Further Readings   Mini-Excursion 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   Mini-Excursion 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 Capture-Recapture 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 68-95-99.7 Rule 16.5 Normal Curves as Models of Real-Life 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   Mini-Excursion 4: The Mathematics of Managing Risk

About the Author :
Peter 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).


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Product Details
  • ISBN-13: 9780321568038
  • Publisher: Pearson Education (US)
  • Publisher Imprint: Pearson
  • Height: 254 mm
  • No of Pages: 704
  • Weight: 1197 gr
  • ISBN-10: 0321568036
  • Publisher Date: 13 Feb 2009
  • Binding: Hardback
  • Language: English
  • Sub Title: United States Edition
  • Width: 202 mm


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