David Lippman
Math in Society
Free
Description
Contents
Reviews

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

Language
English
ISBN
Unknown
FrontMatter
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
Choosing a priority list
Decreasing time algorithm
Critical path algorithm
Exercises
Skills
Concepts
Exploration
GrowthModels
Growth Models
Linear (Algebraic) Growth
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
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
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
The book hasn't received reviews yet.