Excursions in Modern Mathematics
Excursions in Modern Mathematics
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The excursions are organized into four independent parts: The Mathematics of Social Choice, Management Science, Growth and Symmetry, and Statistics. Each part consists of four chapters plus a mini-excursion (new feature in 6/e). The book is written in an informal, very readable style, with pedagogical features that make the material both interesting and clear. The presentation is centered on an assortment of real-world examples and applications specifically chosen to illustrate the usefulness, relevance, and beauty of liberal arts mathematics.
Contents: (Note: Each chapter includes a Chapter Opener that includes an outline of the chapter, a Conclusion, a list of Key Terms, , Exercises, a Biographical Note, and References and Further Readings.) PART I.THE MATHEMATICS OF SOCIAL CHOICE. 1. The Mathematics of Voting: The Paradoxes of Democracy. 2. Weighted Voting Systems: The Power Game. 3. Fair Division: The Mathematics of Sharing. 4. The Mathematics of Apportionment: Making the Rounds. Mini-Excursion 1. Apportionment Today: The Huntington-Hill Method.II. MANAGEMENT SCIENCE. 5. Euler Circuits: The Circuit Comes to Town. 6. The Traveling-Salesman Problem: Hamilton Joins the Circuit. 7. The Mathematics of Networks: The Cost of Being Connected. 8. The Mathematics of Scheduling: Directed Graphs and Critical Paths. Mini-Excursion 2. A Touch of Color: Graph Coloring and Matching. III. GROWTH AND SYMMETRY. 9. Spiral Growth in Nature: Fibonacci Numbers and the Golden Ratio. 10. The Mathematics of Population Growth: There is Strength in Numbers. 11. Symmetry: Mirror, Mirror, off the Wall... 12. Fractal Geometry: Fractally Speaking. Mini-Excursion 3. The Time Value of Money: Annuities. IV. STATISTICS. 13. Collecting Statistical Data: Censuses, Surveys, and Studies. 14. Descriptive Statistics: Graphing and Summarizing Data. 15. Chances, Probability, and Odds: Measuring Uncertainty. 16. Normal Distributions: Everything is Back to Normal(Almost). Mini-Excursion 4. The Cost of Risk-Taking: Expected Value. Answers to Selected Problems
Contents: (Note: Each chapter includes a Chapter Opener that includes an outline of the chapter, a Conclusion, a list of Key Terms, , Exercises, a Biographical Note, and References and Further Readings.) PART I.THE MATHEMATICS OF SOCIAL CHOICE. 1. The Mathematics of Voting: The Paradoxes of Democracy. 2. Weighted Voting Systems: The Power Game. 3. Fair Division: The Mathematics of Sharing. 4. The Mathematics of Apportionment: Making the Rounds. Mini-Excursion 1. Apportionment Today: The Huntington-Hill Method.II. MANAGEMENT SCIENCE. 5. Euler Circuits: The Circuit Comes to Town. 6. The Traveling-Salesman Problem: Hamilton Joins the Circuit. 7. The Mathematics of Networks: The Cost of Being Connected. 8. The Mathematics of Scheduling: Directed Graphs and Critical Paths. Mini-Excursion 2. A Touch of Color: Graph Coloring and Matching. III. GROWTH AND SYMMETRY. 9. Spiral Growth in Nature: Fibonacci Numbers and the Golden Ratio. 10. The Mathematics of Population Growth: There is Strength in Numbers. 11. Symmetry: Mirror, Mirror, off the Wall... 12. Fractal Geometry: Fractally Speaking. Mini-Excursion 3. The Time Value of Money: Annuities. IV. STATISTICS. 13. Collecting Statistical Data: Censuses, Surveys, and Studies. 14. Descriptive Statistics: Graphing and Summarizing Data. 15. Chances, Probability, and Odds: Measuring Uncertainty. 16. Normal Distributions: Everything is Back to Normal(Almost). Mini-Excursion 4. The Cost of Risk-Taking: Expected Value. Answers to Selected Problems
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