Math in Society

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.

Applied Mathematics Mathematics

Tác giả: David Lippman
Nhà xuất bản: Pierce College
Nguồn: LibreTexts
Giấy phép: CC BY-SA
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

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Mục lục· 174 mục

01: Problem Solving
1.01: Introduction
1.02: Percents
1.03: Proportions and Rates
1.04: Geometry
1.05: Problem Solving and Estimating
1.06: Exercises
1.07: Extension - Taxes
1.08: Income Taxation
02: Voting Theory
2.01: Introduction
2.02: Preference Schedules
2.03: Plurality
2.04: Whats Wrong with Plurality
2.05: Insincere Voting
2.06: Instant Runoff Voting
2.07: Whats Wrong with IRV
2.08: Borda Count
2.09: Whats Wrong with Borda Count
2.10: Copelands Method (Pairwise Comparisons)
2.11: Whats Wrong with Copelands Method
2.12: So Wheres the Fair Method
2.13: Approval Voting
2.14: Whats Wrong with Approval Voting
2.15: Voting in America
2.16: Exercises
2.17: Concepts
2.18: Exploration
03: Weighted Voting
3.01: Introduction
3.02: Beginnings
3.03: A Look at Power
3.04: Calculating Power- Banzhaf Power Index
3.05: Calculating Power- Shapley-Shubik Power Index
3.06: Exercises(Skills)
3.07: Exercises(Concepts)
3.08: Exercises(Exploration)
04: Apportionment
4.01: Introduction
4.02: Hamiltons Method
4.03: Jeffersons Method
4.04: Websters Method
4.05: Huntington-Hill Method
4.06: Lowndes Method
4.07: Apportionment of Legislative Districts
4.08: Exercises
05: Fair Division
5.01: Introduction
5.02: Divider-Chooser
5.03: How not to divide with 3 parties
5.04: Lone Divider
5.05: Last Diminisher
5.06: Moving Knife
5.07: Sealed Bids Method
5.08: Exercises-1- Skills
5.09: Exercise-2- Exploration
06: Graph Theory
6.01: Introduction
6.02: Graphs
6.03: Shortest Path
6.04: Euler Circuits and the Chinese Postman Problem
6.05: Eulerization and the Chinese Postman Problem
6.06: Hamiltonian Circuits and the Traveling Salesman Problem
6.07: Spanning Trees
6.08: Exercise
07: Scheduling
7.01: Introduction
7.02: Getting Started
7.03: Adding an algorithm
7.04: Choosing a Priority List
7.05: Exercises
08: Growth Models
8.01: Introduction
8.02: Linear (Algebraic) Growth
8.03: When good models go bad
8.04: Exponential (Geometric) Growth
8.05: Solving Exponentials for Time- Logarithms
8.06: Logistic Growth
8.07: Exercises
09: Finance
9.01: Introduction
9.02: Simple Interest
9.03: Compound Interest
9.04: Annuities
9.05: Payout Annuities
9.06: Loans
9.07: Remaining Loan Balance
9.08: Which equation to use
9.09: Solving for time
9.10: Exercises
10: Statistics
10.01: Introduction
10.02: Populations and samples
10.03: Categorizing data
10.04: Sampling methods
10.05: How to mess things up before you start
10.06: Experiments
10.07: Exercise
11: Describing Data
11.02: Presenting Categorical Data Graphically
11.03: Presenting Quantitative Data Graphically
11.04: Numerical Summaries of Data
11.05: Measures of Central Tendency
11.06: Measures of Variation
11.07: Exercises
12: Probability
12.01: Introduction to Probability
12.02: Basic Concepts
12.03: Working with Events
12.04: Bayes Theorem
12.05: Counting
12.06: Expected Value
12.07: Exercises
13: Sets
13.01: Basics of Sets
13.02: Union Intersection and Complement
13.03: Venn Diagrams
13.04: Cardinality
13.05: Exercises
14: Historical Counting Systems
14.01: Introduction and Basic Number and Counting Systems
14.02: The Number and Counting System of the Inca Civilization
14.03: The Hindu-Arabic Number System
14.04: The Development and Use of Different Number Bases
14.05: The Mayan Numeral System
14.06: Exercise
15: Fractals
15.01: Fractals
15.02: Iterated Fractals
15.03: Fractal Dimension
15.04: Complex Numbers
15.05: Complex Recursive Sequences
15.06: Exercises
16: Cryptography
16.01: Cryptography
16.02: Substitution Ciphers
16.03: Transposition Ciphers
16.04: Advanced shared symmetric-key methods
16.05: Public Key Cryptography
16.06: Other Secret Keeping Methods
16.07: The One-Way Function
16.08: The key exchange
17: Logic
17.01: Logic
17.02: Boolean Logic
17.03: Conditional Statements
17.04: Section 4-
17.05: Section 5-
17.06: Section 6-
17.7: De Morgans Laws
17.8: Arguments
17.9: Evaluating Deductive Arguments with Euler Diagrams
17.10: Evaluating Deductive Arguments with Truth Tables
17.11: Forms of Valid Arguments
17.12: Logical Fallacies in Common Language
17.13: Exercises
18: Solutions to Selected Exercises
18.01: Section 1-
18.02: Section 2-
18.03: Section 3-
18.04: Section 4-
18.05: Section 5-
18.06: Section 6-
18.7: Scheduling
18.8: Growth Models
18.9: Finance
18.10: Statistics
18.11: Describing Data
18.12: Probability
18.13: Sets
18.14: Historical Counting
18.15: Fractals
18.16: Cryptography
18.17: Logic