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.

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· 110 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: Geometry
2.01: Basic Geometric Concepts and Figures
2.02: Perimeter Circumference and Area
2.03: Volume of Geometric Solids
2.04: Exercises
03: Historical Counting Systems
3.01: The Evolution of Numeration Systems
3.02: The Number and Counting System of the Inca Civilization
3.03: The Hindu-Arabic Number System
3.04: The Development and Use of Different Number Bases
3.05: The Mayan Numeral System
3.06: Exercise
04: Saving
4.01: Introduction
4.02: Simple Interest
4.03: Compound Interest
05: Annuities and Loans
5.01: Annuities
5.02: Payout Annuities
5.03: Loans
5.04: Remaining Loan Balance
5.05: Which equation to use
5.06: Solving for time
5.07: Exercises
06: Logic
6.01: Statements Connectives and Quantifiers
6.02: Truth Tables- Conjunction (and) Disjunction (or) Negation (not)
6.03: Truth Tables- Conditional Biconditional
6.04: Verifying Arguments
07: Sets and Venn Diagrams
7.01: Basics of Sets
7.02: Union Intersection and Complement
7.03: Venn Diagrams
7.04: Cardinality
7.05: Exercises
08: Counting
8.01: The Fundamental Counting Principle
8.02: Permutations and Combinations
09: Probability
9.01: Introduction to Probability
9.02: Basic Concepts
9.03: Working with Events
9.04: Bayes Theorem
9.05: Counting
9.06: Expected Value
9.07: Exercises
10: Descriptive 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
10.08: Presenting Categorical Data Graphically
10.09: Presenting Quantitative Data Graphically
10.10: Numerical Summaries of Data
10.11: Measures of Central Tendency
10.12: Measures of Variation
10.13: Exercises
11: Normal Distribution
11.01: The Standard Normal Probability Distribution
11.02: The Density Curve of a Normal Distribution
11.03: Application of Normal Distributions
11.04: The Central Limit Theorem
11.05: Exercises
12: Confidence Intervals and Hypothesis Tests
12.01: Confidence Intervals
12.02: Confidence Intervals and Sample Size for Proportions
12.03: Steps in Hypothesis Testing
12.3.01: Null and Alternative Hypotheses
12.3.02: Outcomes and the Type I and Type II Errors
12.3.03: Distribution Needed for Hypothesis Testing
12.3.04: Rare Events the Sample Decision and Conclusion
12.3.05: Additional Information on Hypothesis Tests
12.04: Hypothesis Test Examples for Proportions
12.E: Confidence Intervals (Optional Exercises)
1.E: Confidence Intervals for the Mean with Known Standard Deviation (Optional Exercises)
1.E: Hypothesis Testing (Optional Exercises)
13: Graph Theory
13.01: Introduction
13.02: Graphs
13.03: Shortest Path
13.04: Euler Circuits and the Chinese Postman Problem
13.05: Eulerization and the Chinese Postman Problem
13.06: Hamiltonian Circuits and the Traveling Salesman Problem
13.07: Spanning Trees
13.08: Exercise
14: Solutions to Selected Exercises
14.01: Problem Solving
14.02: Geometry
14.03: Historical Counting
14.04: Sets
14.05: Probability
14.06: Statistics
14.6.01: Describing Data
14.07: Saving
14.08: Annuities and Loans
14.09: Confidence Intervals and Hypothesis Tests
14.10: Graph Theory
14.11: Normal