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.
The current version is 2.6, released July 2022.
Conditions of Use
This book is licensed under a Creative Commons License (CC BY-NC-SA). You can download the ebook Math in Society for free.
- Title
- Math in Society
- Publisher
- OpenTextbookStore
- Author(s)
- David Lippman
- Published
- 2022-07-01
- Edition
- 1
- Format
- eBook (pdf, epub, mobi)
- Pages
- 476
- Language
- English
- ISBN-10
- 1479276537
- ISBN-13
- 9781479276530
- License
- CC BY-NC-SA
- Book Homepage
- Free eBook, Errata, Code, Solutions, etc.
About the Author/Editor Acknowledgements Preface New in This Edition Supplements 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. 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 Weighted Voting Beginnings A Look at Power Calculating Power: Banzhaf Power Index Calculating Power: Shapley-Shubik Power Index Exercises Skills Concepts Exploration Apportionment Hamilton’s Method Jefferson’s Method Webster’s Method Huntington-Hill Method Lowndes’ Method Apportionment of Legislative Districts Exercises Fair Division Divider-Chooser How not to divide with 3 parties Lone Divider Last Diminisher Moving Knife Sealed Bids Method Exercises Skills Exploration 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 Getting Started Adding an algorithm Choosing a priority list Decreasing time algorithm Critical path algorithm Exercises Skills Concepts Exploration 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 Simple Interest Compound Interest Annuities Payout Annuities Loans Remaining Loan Balance Which equation to use? Solving for time Exercises Skills Concepts Exploration Statistics Populations and samples Categorizing data Sampling methods How to mess things up before you start Experiments Exercises Skills Concepts Exploration 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 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 Basics Union, Intersection, and Complement Venn Diagrams Cardinality Exercises 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 Iterated Fractals Fractal Dimension Complex Numbers Arithmetic on Complex Numbers Complex Recursive Sequences Mandelbrot Set Additional Resources Exercises Iterated Fractals Fractal Dimension Complex Numbers Recursive Sequences Exploration 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 Logic Boolean Logic Conditional Statements Quantified Statements Truth Tables: Conjunction (and), Disjunction (or), Negation (not) Truth Tables: Conditional, Biconditional De Morgan’s Laws Arguments Evaluating Deductive Arguments with Euler Diagrams Evaluating Deductive Arguments with Truth Tables Forms of Valid Arguments Logical Fallacies in Common Language Exercises 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 Logic
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