Thinking Mathematically

1. Problem Solving and Critical Thinking

1.1 Inductive and Deductive Reasoning

1.2 Estimation, Graphs, and Mathematical Models

1.3 Problem Solving

 

2. Set Theory

2.1 Basic Set Concepts

2.2 Subsets

2.3 Venn Diagrams and Set Operations

2.4 Set Operations and Venn Diagrams with Three Sets

2.5 Survey Problems

 

3. Logic

3.1 Statements, Negations, and Quantified Statements

3.2 Compound Statements and Connectives

3.3 Truth Tables for Negations, Conjunction, and Disjunction

3.4 Truth Tables for the Conditional and the Biconditional

3.5 Equivalent Statements and Variations of Conditional Statements

3.6 Negations of Conditional Statements and De Morgan's Laws

3.7 Arguments and Truth Tables

3.8 Arguments and Euler Diagrams

 

4. Number Representation and Calculation

4.1 Our Hindu-Arabic System and Early Positional Systems

4.2 Number Bases in Positional Systems

4.3 Computation in Positional Systems

4.4 Looking Back at Early Numeration Systems

 

5. Number Theory and the Real Number System

5.1 Number Theory, Prime and Composite Numbers

5.2 The Integers; Order of Operations

5.3 The Rational Numbers

5.4 The Irrational Numbers

5.5 Real Numbers and Their Properties

5.6 Exponents and Scientific Notation

5.7 Arithmetic and Geometric Sequences

 

6. Algebra: Equations and Inequalities

6.1 Algebraic Expressions and Formulas

6.2 Linear Equations in One Variable and Proportions

6.3 Applications of Linear Equations

6.4 Linear Inequalities in One Variable

6.5 Quadratic Equations

 

7. Algebra: Graphs, Functions, and Linear Systems

7.1 Graphing and Functions

7.2 Linear Functions and Their Graphs

7.3 Systems of Linear Equations in Two Variables

7.4 Linear Inequalities in Two Variables

7.5 Linear Programming

7.6 Modeling Data: Exponential, Logarithmic, and Quadratic Functions

 

8. Consumer Mathematics and Financial Management

8.1 Percent, Sales Tax, and Income Tax

8.2 Simple Interest

8.3 Compound Interest

8.4 Annuities, Stocks, and Bonds

8.5 Installment Loans, Amortization, and Credit Cards

 

9. Measurement

9.1 Measuring Length; The Metric System

9.2 Measuring Area and Volume

9.3 Measuring Weight and Temperature

 

10. Geometry

10.1 Points, Lines, Planes, and Angles

10.2 Triangles

10.3 Polygons, Perimeter, and Tessellations

10.4 Area and Circumference

10.5 Volume

10.6 Right Triangle Trigonometry

10.7 Beyond Euclidean Geometry

 

11. Counting Methods and Probability Theory

11.1 The Fundamental Counting Principle

11.2 Permutations

11.3 Combinations

11.4 Fundamentals of Probability

11.5 Probability with the Fundamental Counting principle, Permutations, and Combinations

11.6 Events Involving Not and Or; Odds

11.7 Events Involving And; Conditional Probability

11.8 Expected Value

 

12. Statistics

12.1 Sampling, Frequency Distributions, and Graphs

12.2 Measures of Central Tendency

12.3 Measures of Dispersion

12.4 The Normal Distribution

12.5 Problem Solving with the Normal Distribution

12.6 Scatter Plots, Correlation, and Regression Lines

 

13. Mathematical Systems

13.1 Mathematical Systems

13.2 Rotational Symmetry, Groups, and Clock Arithmetic

 

14. Voting and Apportionment

14.1 Voting Methods

14.2 Flaws of Voting Methods

14.3 Apportionment Methods

14.4 Flaws of Apportionment Methods