Table of Contents

1. Critical Thinking Skills

1.1 Inductive and Deductive Reasoning

1.2 Estimation Techniques

1.3 Problem-Solving Procedures 

2. Sets

2.1 Set Concepts

2.2 Subsets

2.3 Venn Diagrams and Set Operations

2.4 Venn Diagrams with Three Sets and Verification of Equality of Sets

2.5 Applications of Sets

2.6 Infinite Sets 

3. Logic

3.1 Statements and Logical Connectives

3.2 Truth Tables for Negation, Conjunction, and Disjunction

3.3 Truth Tables for the Conditional and Biconditional

3.4 Equivalent Statements

3.5 Symbolic Arguments

3.6 Euler Diagrams and Syllogistic Arguments

3.7 Switching Circuits 

4. Systems of Numeration

4.1 Additive, Multiplicative, and Ciphered Systems of Numeration

4.2 Place-Value or Positional-Value Numeration Systems

4.3 Other Bases

4.4 Perform Computations in Other Bases

4.5 Early Computational Methods 

5. Number Theory and the Real Number System

5.1 Number Theory

5.2 The Integers

5.3 The Rational Numbers

5.4 The Irrational Numbers

5.5 Real Numbers and Their Properties

5.6 Rules of Exponents and Scientific Notation

5.7 Arithmetic and Geometric Sequences

5.8 Fibonacci Sequence 

6. Algebra, Graphs, and Functions

6.1 Order of Operations and Solving Linear Equations

6.2 Formulas

6.3 Applications of Algebra

6.4 Variation

6.5 Solving Linear Inequalities

6.6 Graphing Linear Equations

6.7 Solving Systems of Linear Equations

6.8 Linear Inequalities in Two Variables and Systems of Linear Inequalities

6.9 Solving Quadratic Equations by Using Factoring and by Using the Quadratic Formula

6.10 Functions and Their Graphs 

7. The Metric System

7.1 Basic Terms and Conversions Within the Metric System

7.2 Length, Area, and Volume

7.3 Mass and Temperature

7.4 Dimensional Analysis and Conversions to and from the Metric System 

8. Geometry

8.1 Points, Lines, Planes, and Angles

8.2 Polygons

8.3 Perimeter and Area

8.4 Volume and Surface Area

8.5 Transformational Geometry, Symmetry, and Tessellations

8.6 Topology

8.7 Non-Euclidean Geometry and Fractal Geometry 

9. Mathematical Systems

9.1 Groups

9.2 Finite Mathematical Systems

9.3 Modular Arithmetic

9.4 Matrices 

10. Consumer Mathematics

10.1 Percent

10.2 Personal Loans and Simple Interest

10.3 Compound Interest

10.4 Installment Buying

10.5 Buying a House with a Mortgage

10.6 Ordinary Annuities, Sinking Funds, and Retirement Investments 

11. Probability

11.1 Empirical and Theoretical Probabilities

11.2 Odds

11.3 Expected Value (Expectation)

11.4 Tree Diagrams 678

11.5 OR and AND Problems

11.6 Conditional Probability

11.7 The Fundamental Counting Principle and Permutations

11.8 Combinations

11.9 Solving Probability Problems by Using Combinations

11.10 Binomial Probability Formula 

12. Statistics

12.1 Sampling Techniques and Misuses of Statistics

12.2 Frequency Distributions and Statistical Graphs

12.3 Measures of Central Tendency and Position

12.4 Measures of Dispersion

12.5 The Normal Curve

12.6 Linear Correlation and Regression 

13. Graph Theory

13.1 Graphs, Paths, and Circuits

13.2 Euler Paths and Euler Circuits

13.3 Hamilton Paths and Hamilton Circuits

13.4 Trees 864 14 Voting and Apportionment 

14. Voting and Apportionment

14.1 Voting Methods

14.2 Flaws of the Voting Methods

14.3 Apportionment Methods

14.4 Flaws of the Apportionment Methods