Excursions in Modern Mathematics, 8th Edition

Excursions in Modern Mathematics introduces you to the beauty of math by exploring applications like social choice and management science, showing that math is more than a set of formulas. Ideal for an applied liberal arts math course, Tannenbaum’s text is known for its clear, accessible writing style and its unique exercise sets that build in complexity from basic to more challenging.

 

The Eighth Edition offers more real data and applications to connect with you, expanded coverage of applications like growth, and revised exercise sets.

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

 

17. The Mathematics of Normality: The Call of the Bell

17.1 Approximately Normal Data Sets

17.2 Normal Curves and Normal Distributions

17.3 Modeling Approximately Normal Distributions

17.4 Normality in Random Events

            Conclusion

            Key Concepts

            Exercises

            Projects and Papers

 

Answers to Selected Exercises

Index

Photo Credits