Mathematics Old and New by Stahl, Saul -- Read -- Imperial Library of Trantor

Index

Cover Title Page Copyright Page Contents Preface 1. Probability

1.1 The Quantification of Likelihood 1.2 Galileo Galilei (A Historical Interlude)* 1.3 Binomial Processes 1.4 The Normal Approximation 1.5 Activities/Websites

2. Statistics

2.1 Summarizing Data 2.2 Totaling Measurement Errors 2.3 Least Squares and Regression 2.4 Normally Distributed Data 2.5 Statistical Inference 2.6 The Central Limit Theorem 2.7 Activities/Websites

3. Voting Systems

3.1 Introduction 3.2 Mathematical Concepts 3.3 The Plurality Problem 3.4 Rank-order Voting: The Borda Count 3.5 Sequential Pairwise Comparisons 3.6 Condorcet Methods: The Round Robin Tournament 3.7 Single Vote Systems: Cousins of Plurality and Majority Rule 3.8 Conclusion

4. Game Theory

4.1 Introduction to Games 4.2 Formal Zero-Sum Games 4.3 Pure Strategies for Nonzero-Sum Games 4.4 Mixed Strategies for Nonzero-Sum Games 4.5 The Solution of Zero-Sum Games 4.6 Activities/Websites

5. Linear Programming

5.1 Graphing Inequalities 5.2 Optimization

6. Planar Symmetries

6.1 Introduction 6.2 Rigid Motions of the Plane 6.3 Symmetries of Polygons 6.4 Frieze Patterns 6.5 Wallpaper Designs

7. Spatial Symmetries

7.1 Regular and Semiregular Solids 7.2 Symmetries of Regular Solids 7.3 Monstrous Moonshine 7.4 Activities/Websites

8. The Bell-Shaped Curve

8.1 An Approximation Tool 8.2 The Search for an Error Curve 8.3 The Proof 8.4 Beyond Errors 8.5 Why Normal?

9. Map Colorings

9.1 Heawood’s Conjecture 9.2 Heffter’s Contributions 9.3 The Resolution of Heawood’s Conjecture 9.4 Coloring Maps on Other Surfaces

Appendix A Sopra Le Scoperte Dei Dadi Table A Cumulative Normal Probabilities Table B Cumulative Binomial Probabilities Appendix B References and Further Readings Appendix C Solutions Index