Math in Society

Free

Description

Contents

Reviews

Language

English

ISBN

Unknown

FrontMatter

About the Author/Editor

Acknowledgements

Preface

New in This Edition

Supplements

ProblemSolving

Problem Solving

Percents

Proportions and Rates

Geometry

Problem Solving and Estimating

Exercises

Extension: Taxes

Income Taxation

Project 1: Flat tax, Modified Flat Tax, and Progressive Tax.

Project 2: Calculating Taxes.

VotingTheory

Voting Theory

Preference Schedules

Plurality

What’s Wrong with Plurality?

Insincere Voting

Instant Runoff Voting

What’s Wrong with IRV?

Borda Count

What’s Wrong with Borda Count?

Copeland’s Method (Pairwise Comparisons)

What’s Wrong with Copeland’s Method?

So Where’s the Fair Method?

Approval Voting

What’s Wrong with Approval Voting?

Voting in America

Exercises

Skills

Concepts

Exploration

WeightedVoting

Weighted Voting

Beginnings

A Look at Power

Calculating Power: Banzhaf Power Index

Calculating Power: Shapley-Shubik Power Index

Exercises

Skills

Concepts

Exploration

Apportionment

Apportionment

Hamilton’s Method

Jefferson’s Method

Webster’s Method

Huntington-Hill Method

Lowndes’ Method

Apportionment of Legislative Districts

Exercises

FairDivision

Fair Division

Divider-Chooser

How not to divide with 3 parties

Lone Divider

Last Diminisher

Moving Knife

Sealed Bids Method

Exercises

Skills

Exploration

GraphTheory

Graph Theory and Network Flows

Graphs

Drawing Graphs

Definitions

Shortest Path

Euler Circuits and the Chinese Postman Problem

Eulerization and the Chinese Postman Problem

Hamiltonian Circuits and the Traveling Salesman Problem

Spanning Trees

Exercises

Skills

Concepts

Explorations

Scheduling

Scheduling

Getting Started

Adding an algorithm

Choosing a priority list

Decreasing time algorithm

Critical path algorithm

Exercises

Skills

Concepts

Exploration

GrowthModels

Growth Models

Linear (Algebraic) Growth

When good models go bad

Exponential (Geometric) Growth

Solving Exponentials for Time: Logarithms

Logistic Growth

Exercises

Skills

Concepts

Exploration

Finance

Finance

Simple Interest

Compound Interest

Annuities

Payout Annuities

Loans

Remaining Loan Balance

Which equation to use?

Solving for time

Exercises

Skills

Concepts

Exploration

Statistics

Statistics

Populations and samples

Categorizing data

Sampling methods

How to mess things up before you start

Experiments

Exercises

Skills

Concepts

Exploration

DescribingData

Describing Data

Presenting Categorical Data Graphically

Presenting Quantitative Data Graphically

Numerical Summaries of Data

Measures of Central Tendency

Measures of Variation

Exercises

Skills

Concepts

Exploration

Probability

Probability

Introduction

Basic Concepts

Working with Events

Complementary Events

Probability of two independent events

Conditional Probability

Bayes Theorem

Counting

Basic Counting

Permutations

Combinations

Probability using Permutations and Combinations

Birthday Problem

Expected Value

Exercises

Exploration

Sets

Sets

Basics

Union, Intersection, and Complement

Venn Diagrams

Cardinality

Exercises

HistoricalCounting

Historical Counting Systems

Introduction and Basic Number and Counting Systems

Introduction

Recognition of More vs. Less

The Need for Simple Counting

Spoken Words

Written Numbers

The Number and Counting System of the Inca Civilization

Background

Counting Boards

The Quipu

The Hindu – Arabic Number System

The Evolution of a System

The Positional System

Transmission to Europe

The Development and Use of Different Number Bases

Introduction and Basics

Other Bases

Converting from Base 10 to Other Bases

Another Method For Converting From Base 10 to Other Bases

The Mayan Numeral System

Background

The Mayan Number System

Adding Mayan Numbers

Conclusion

Exercises

Skills

Exploration

Endnotes

Fractals

Fractals

Iterated Fractals

Fractal Dimension

Complex Numbers7F

Arithmetic on Complex Numbers

Complex Recursive Sequences

Mandelbrot Set

Additional Resources

Exercises

Iterated Fractals

Fractal Dimension

Complex Numbers

Recursive Sequences

Exploration

Cryptography

Cryptography

Substitution Ciphers

Transposition Ciphers

Advanced shared symmetric-key methods

Public Key Cryptography

Modular arithmetic

The one-way function

The key exchange

RSA

Other secret keeping methods

Resources

Exercises

SolutionstoSelectedExercises

Solutions to Selected Exercises

Problem Solving

Voting Theory

Weighted Voting

Fair Division

Apportionment

Graph Theory

Scheduling

Growth Models

Finance

Statistics

Describing Data

Probability

Sets

Historical Counting

Fractals

Cryptography

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