Table of Contents

Discovering Mathematics concentrates on concepts rather than simple rote understanding. With the Smart Sparrow platform, critical thinking skills are enhanced using adaptive feedback. This process helps boost learning and contextual skills.

The current edition of Discovering Mathematics contains 10 topics typically covered in most liberal arts mathematics courses. Future editions will contain additional topics such as Voting Methods and Fair Sharing.

• 2.1  Basic Properties of Sets

• 2.2  Venn Diagrams and Subsets

• 2.3  Venn Diagrams and Set Operations

• 2.4  Applications of Sets

• 2.5  One-to-One Correspondence and Infinite Sets

Chapter 2  Sets in Practice
Chapter 7  The Dynamics of Probability
Chapter 1  Thinking Critically
Chapter 6  The World of Geometry
Chapter 3  Using Logic
Chapter 8  Statistics and Decision Making

• 1.1  Inductive and Deductive Reasoning

• 1.2  Guesstimates

• 1.3  Polya's Four Principles of Problem Solving

 

• 6.1  Points, Lines, Planes, and Angles

• 6.2  Triangles and Polygons

• 6.3  Pi, Perimeter, Area, and Volume

• 6.4  Coordinate Geometry

• 6.5  Right Triangle Trigonometry

• 6.6  Sine and Cosine

• 3.1  Logic Statements and Their Symbols

• 3.2  The Five Basic Truth Tables

• 3.3  Constructing Truth Tables

• 3.4  Equivalent Statements and De Morgan's Laws

• 3.5  Arguments and Truth Tables

• 3.6  Euler Diagrams and Syllogistic Arguments

• 7.1  The Fundamental Counting Principle

• 7.2  Introduction to Probability

• 7.3  Permutations and Combinations

• 7.4  Probability with Permutations and Combinations

• 7.5  The Addition and Multiplication Rules

• 7.6  Odds and Expected Value

• 7.7  Bayes' Theorem

Chapter 4  Discovering Number Theory
Chapter 9  Buying Power

• 4.1  Divisibility and Prime Numbers

• 4.2  Clock and Modular Arithmetic

• 4.3  Divisibility Testing

• 4.4  Check Digits

• 4.5  Introduction to Cryptography

• 9.1  Consumer Buying

• 9.2  Exponents, Roots, and Logarithms

• 9.3  Simple Interest and Future Value

• 9.4  Compound Interest

• 9.5  Annuities

• 9.6  Open-Ended Credit

Chapter 5  Algebra in Action
Chapter 10  The Influence of Numbers

• 10.1  Math and Design

• 10.2  Math and Music

• 10.3  Math and Sports

• 10.4  Math and the Environment

• 10.5  Math and Health

 

• 5.1  Algebra Expressions and Equations

• 5.2  Solving Linear Equations in One Variable

• 5.3  Graphs and Functions

• 5.4  Linear Functions

• 5.5  Solving Quadratic Equations

 

• 8.1  Sampling and Frequency Distributions

• 8.2  Histograms

• 8.3  Measure of Central Tendency

• 8.4  Measures of Spread

• 8.5  The Normal Distribution

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Copyright © 2018 Stephen G Zuro, Discovering Mathematics

Chapter 10

The Influence of Numbers