Chapter 1: Critical Thinking Skills
1.1 Inductive and Deductive Reasoning
1.2 Estimation Techniques
1.3 Problem-Solving Procedures
Chapter 2: Sets
2.1 Set Concepts
2.2 Subsets
2.3 Venn Diagrams, Set Operations, and Data Representation
2.4 Venn Diagrams with Three Sets and Verification of Equality of Sets
2.5 Set Applications and Survey Data Analysis
2.6 Infinite Sets
Chapter 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
Chapter 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
Chapter 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 The Fibonacci Sequence and The Golden Ratio
Chapter 6: Algebra, Graphs, and Functions
6.1 Order of Operations and Solving Linear Equations
6.2 Formulas and Modeling
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
Chapter 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
Chapter 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
Chapter 9: Mathematical Systems
9.1 Groups
9.2 Finite Mathematical Systems
9.3 Modular Arithmetic
9.4 Matrices
Chapter 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
Chapter 11: Probability
11.1 Empirical and Theoretical Probabilities
11.2 Odds
11.3 Expected Value (Expectation)
11.4 Tree Diagrams
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
Chapter 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
Chapter 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
Chapter 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
