General and Finite Mathematics: Liberal Arts Mathematics I & II

PART ONE—LIBERAL ARTS MATH I

CHAPTER 1 SET THEORY 1
1.1 Basic Concepts in Set Theory
1.2 Subsets
1.3 Set Operations and Venn Diagrams with One or Two Sets
1.4 Set Operations and Venn Diagrams with Three Sets
1.5 Survey Problems

CHAPTER 2 LOGIC
2.1 Statements, Negations, and Quantified Statements
2.2 Compound Statements and Connectives
2.3 Truth Tables: Negation, Conjunction, and Disjunction
2.4 Truth Tables: Conditional and Biconditional
2.5 Equivalent Statements and Conditional Statement Variations
2.6 Negations of Conditional Statement and De Morgan’s Laws
2.7 Arguments and Truth Tables
2.8 Arguments and Euler Diagrams

CHAPTER 3 GEOMETRY
3.1 Points, Lines, Planes, and Angles
3.2 Triangles
3.3 Polygons and Tessellations
3.4 Area and Circumference
3.5 Volume and Surface Area

CHAPTER 4 PROBABILITY AND COMBINATORICS
4.1 The Fundamental Counting Principle
4.2 Permutations
4.3 Combinations
4.4 Probability with the Fundamental Counting Principle, Permutations, and Combinations
4.5 Events Involving Not and Or; Odds
4.6 Events Involving And; Conditional Probability

CHAPTER 5 STATISTICS
5.1 Sampling, Frequency Distributions, and Graphs
5.2 Measures of Central Tendency
5.3 Measures of Dispersion

PART TWO—LIBERAL ARTS MATH II

CHAPTER 6 NUMBER SYSTEMS AND NUMBER THEORY
6.1 Our Hindu–Arabic System and Early Positional Systems
6.2 Number Bases in Positional Systems
6.3 Computation in Positional Systems
6.4 Ancient and Classical Numeration Systems
6.5 Number Theory: Prime and Composite Numbers

CHAPTER 7 EQUATIONS AND FUNCTIONS
7.1 Functions and Graphing
7.2 Linear Functions and Their Graphs
7.3 Exponential, Logarithmic, and Quadratic Functions

CHAPTER 8 PERSONAL FINANCE
8.1 Percents and Their Basic Applications
8.2 Income Tax
8.3 Simple Interest
8.4 Compound Interest
8.5 Annuities, Saving Methods, and Investments
8.6 Car Finance
8.7 Home Ownership Finance
8.8 Credit Card Finance

CHAPTER 9 VOTING METHODS
9.1 Voting Methods
9.2 Flaws of Voting Methods

CHAPTER 10 GRAPH THEORY
10.1 Graphs, Paths, and Circuits
10.2 Euler Paths and Euler Circuits