Free

# Math in Society

By David Lippman
Free
Book Description

A survey of mathematics for the liberal arts major

Math in Society is a free, open textbook. This book is a survey of contemporary mathematical topics, most non-algebraic, appropriate for a college-level quantitative literacy topics course for liberal arts majors. The text is designed so that most chapters are independent, allowing the instructor to choose a selection of topics to be covered. Emphasis is placed on the applicability of the mathematics. Core material for each topic is covered in the main text, with additional depth available through exploration exercises appropriate for in-class, group, or individual investigation. This book is appropriate for Washington State Community Colleges' Math 107.

In September 2012, am Edition 2 of the book was posted, followed by a few typo revisions. The current version is 2.4. Additional material and print editions available at opentextbookstore.com

• 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
• 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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