Excursions in Modern Mathematics: Pearson New International Edition


8e édition

VitalSource eBook (VitalBook) - En anglais 63,00 € DRM

Spécifications


Éditeur
Pearson Education
Édition
8
Auteur
Peter Tannenbaum,
Langue
anglais
BISAC Subject Heading
MAT000000 MATHEMATICS
BIC subject category (UK)
PB Mathematics
Code publique Onix
05 College/higher education
Date de première publication du titre
01 novembre 2013
Subject Scheme Identifier Code
Classification thématique Thema: Mathématiques

VitalSource eBook


Date de publication
01 novembre 2013
ISBN-13
9781292035253
Ampleur
Nombre de pages de contenu principal : 544
Code interne
1292035250
Protection technique e-livre
DRM

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Sommaire


PART 1. SOCIAL CHOICE

 

1. The Mathematics of Elections: The Paradoxes of Democracy

1.1 The Basic Elements of an Election

1.2 The Plurality Method

1.3 The Borda Count Method

1.4 The Plurality-with-Elimination Method

1.5 The Method of Pairwise Comparisons

1.6 Fairness Criteria and Arrow’s Impossibility Theorem

   Conclusion

   Key Concepts

   Exercises

   Projects and Papers

 

2. The Mathematics of Power: Weighted Voting

2.1 An Introduction to Weighted Voting

2.2 Banzhaf Power

2.3 Shapley-Shubik Power

2.4 Subsets and Permutations

   Conclusion

   Key Concepts

   Exercises

   Projects and Papers

 

3. The Mathematics of Sharing: Fair-Division Games

3.1 Fair-Division Games

3.2 The Divider-Chooser Method

3.3 The Lone-Divider Method

3.4 The Lone-Chooser Method

3.5 The Method of Sealed Bids

3.6 The Method of Markers

   Conclusion

   Key Concepts

   Exercises

   Projects and Papers

 

4. The Mathematics of Apportionment: Making the Rounds

4.1 Apportionment Problems and Apportionment Methods

4.2 Hamilton’s Method

4.3 Jefferson’s Method

4.4 Adams’s and Webster’s Methods

4.5 The Huntington-Hill Method

4.6 The Quota Rule and Apportionment Paradoxes

   Conclusion

   Key Concepts

   Exercises

   Projects and Papers

 

PART 2. MANAGEMENT SCIENCE

 

5. The Mathematics of Getting Around: Euler Paths and Circuits

5.1 Street-Routing Problems

5.2 An Introduction to Graphs

5.3 Euler’s Theorems and Fleury’s Algorithm

5.4 Eulerizing and Semi-Eulerizing Graphs

   Conclusion

   Key Concepts

   Exercises

   Projects and Papers

 

6. The Mathematics of Touring: Traveling Salesman Problems

6.1 What Is a Traveling Salesman Problem?

6.2 Hamilton Paths and Circuits

6.3 The Brute-Force Algorithm

6.4 The Nearest-Neighbor and Repetitive Nearest-Neighbor Algorithms

6.5 The Cheapest-Link Algorithm

   Conclusion

   Key Concepts

   Exercises

   Projects and Papers

   The Mathematics of Networks

 

7. The Cost of Being Connected

7.1 Networks and Trees

7.2 Spanning Trees, MST’s, and MaxST’s

7.3 Kruskal’s Algorithm

   Conclusion

   Key Concepts

   Exercises

   Projects and Papers

 

8. The Mathematics of Scheduling: Chasing the Critical Path

8.1 An Introduction to Scheduling

8.4 Directed Graphs

8.3 Priority-List Scheduling

8.4 The Decreasing-Time Algorithm

8.5 Critical Paths and the Critical-Path Algorithm

   Conclusion

   Key Concepts

   Exercises

   Projects and Papers

 

PART 3. GROWTH

 

9. Population Growth Models: There Is Strength in Numbers

9.1 Sequences and Population Sequences

9.2 The Linear Growth Model

9.3 The Exponential Growth Model

9.4 The Logistic Growth Model

   Conclusion

   Key Concepts

   Exercises

   Projects and Papers

 

10. Financial Mathematics: Money Matters

10.1 Percentages

10.2 Simple Interest

10.3 Compound Interest

10.4 Consumer Debt

   Conclusion

   Key Concepts

   Exercises

   Projects and Papers

 

PART 4. SHAPE AND FORM

 

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 Symmetries and Symmetry Types

11.7 Patterns

   Conclusion

   Key Concepts

   Exercises

   Projects and Papers

 

12. Fractal Geometry: The Kinky Nature of Nature

12.1 The Koch Snowflake and Self-Similarity

12.2 The Sierpinski Gasket and the Chaos Game

12.3 The Twisted Sierpinski Gasket

13.4 The Mandelbrot Set

   Conclusion

   Key Concepts

   Exercises

   Projects and Papers

 

13. Fibonacci Numbers and the Golden Ratio: Tales of Rabbits and Gnomons

13.1 Fibonacci Numbers

13.2 The Golden Ratio

13.3 Gnomons

13.4 Spiral Growth in Nature

   Conclusion

   Key Concepts

   Exercises

   Projects and Papers

 

PART 5. STATISTICS

 

14. Censuses, Surveys, Polls, and Studies: The Joys of Collecting Data

14.1 Enumeration

14.2 Measurement

14.3 Cause and Effect

   Conclusion

   Key Concepts

   Exercises

   Projects and Papers

 

15. Graphs, Charts, and Numbers: The Data Show and Tell

15.1 Graphs and Charts

15.2 Means, Medians, and Percentiles

15.3 Ranges and Standard Deviations

   Conclusion

   Key Concepts

   Exercises

   Projects and Papers

 

16. Probabilities, Odds, and Expectations: Measuring Uncertainty and Risk

16.1 Sample Spaces and Events

16.2 The Multiplication Rule, Permutations, and Combinations

16.3 Probabilities and Odds

16.4 Expectations

16.5 Measuring Risk

   Conclusion

   Key Concepts

   Exercises

   Projects and Papers

 

Answers to Selected Exercises

Index

Photo Credits

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