MFP

 

1.  You do not have to do any work in the chapters listed below other than read the chapters and respond to the forum. 

A.  For EACH CHAPTER listed below, post a response to prompt:  What ideas interested, surprised, or confused you, and why so.  Please make your posts meaningful and sufficiently complete to verify that you read the chapter.  

B.  For AT LEAST SIX ideas in the chapters (hopefully ideas in different chapters), post a response to the prompt:  Many of you have hobbies, interests, recreations, or particular careers in mind that involve greater or lesser amounts of mathematics.  While our textbook has many examples of real-life applications of the respective mathematical topics, those applications still may not address some of your individual interests, hobbies, recreations, careers, concerns, or life situations.  Rather than asking "How does this math affect my life?" I want you to tell us so.  Select six topics from these chapters and tell the class how each of those topics applies to your life in ways that we may not know.  Do your best to be creative, honest, and detailed.  DO NOT USE AN APPLICATION MENTIONED IN THE BOOK.  

CHAPTER CONTENTS:

PART I Management Science:

Chapter 1 Urban Services: 1.1 Euler Circuits; 1.2 Finding Euler Circuits; 1.3 Beyond Euler Circuits; 1.4 Urban Graph Traversal Problems

Chapter 2 Business Efficiency: 2.1 Hamiltonian Circuits; 2.2 Traveling Salesman Problem; 2.3 Helping Traveling Salesmen; 2.4 Minimum-Cost Spanning Trees; 2.5 Critical-Path Analysis

Chapter 3 Planning and Scheduling: 3.1 Scheduling Tasks; 3.2 Critical-Path Schedules; 3.3 Independent Tasks; 3.4 Bin Packing; 3.5 Resolving Conflict via Coloring

Chapter 4 Mathematics in Your Daily Life: Linear Programming: 4.1 From Graph Theory to Linear and Integer Programming; 4.2 Linear Programming and Mixture Problems: Combining Resources to Maximize Profit; 4.3 Finding the Optimal Production Policy; 4.4 Why the Corner Point Principle Works; 4.5 Linear Programming: Life Is Complicated

PART II Statistics: The Science of Data

Chapter 6 Exploring Data: Relationships: 6.1 Displaying Relationships: Scatterplot; 6.2 Making Predictions: Regression Line; 6.3 Correlation; 6.4 Least-Squares Regression; 6.5 Interpreting Correlation and Regression

Chapter 9 Social Choice: 9.1 Electoral Systems and Majority Rule; 9.2 Plurality and Runoff Elections; 9.3 Condorcet and Borda; 9.4 Pairing Agendas; 9.5 Irrelevant Alternatives and Strategic Voting; 9.6 Cardinal Electoral Systems; 9.7 Multimember Districts

Chapter 10 Weighted Voting Systems: 10.1 How Weighted Voting Works; 10.2 The Shapley–Shubik Model; 10.3 Critical Voters and the Banzhaf Index; 10.4 Calculating the Banzhaf Index with Combinations

Chapter 11 From Primaries to Presidency: 11.1 Narrowing the Field Through the Primary Process; 11.2 How to Appeal to Voters to Win an Election; 11.3 Winning More Than One State and the Electoral College; 11.4 Proposed Changes to the Electoral College and Gerrymandering

PART IV Fairness and Game Theory

Chapter 12 Fair Division: 12.1 Taking Turns; 12.2 The Adjusted Winner Procedure; 12.3 The Knaster Inheritance Procedure; 12.4 Bankruptcy Rules; 12.5 Divide-and-Choose

Chapter 13 Apportionment: 13.1 The Apportionment Problem; 13.2 The Hamilton Method; 13.3 Divisor Methods; 13.4 A Controversy; 13.5 Gerrymandering; 13.6 Party List Proportional Representation

Chapter 14 Game Theory: The Mathematics of Competition: 14.1 Making Moves: Sequentially Playing Games; 14.2 Simultaneous-Move Games for Two Players; 14.3 A Stable of Two-Player, Two-Strategy Games; 14.4 Using Game Theory; 14.5 Mechanism Design: Designing Games to Have a Particular Outcome

PART V On Size and Growth

Chapter 15 Growth and Form: 15.1 Geometric Similarity; 15.2 How Much Is That In . . . ?; 15.3 Big Stuff; 15.4 Dimension Tension; 15.5 How We Grow

Chapter 16 Symmetry and Pattern: 16.1 Fibonacci Numbers and the Golden Ratio; 16.2 Rosette, Strip, and Wallpaper Patterns; 16.3 Symmetry Groups; 16.4 Fractal Patterns and Chaos

Chapter 17 Tilings: 17.1 Tilings with Regular Polygons; 17.2 Tilings with Irregular Polygons; 17.3 Using Translations; 17.4 Using Translations plus Half-Turns; 17.5 Nonperiodic Tilings