Mathematical Excursions

Cover
Contents
Preface
AIM for Success
Ch 1: Problem Solving
	1.1 Inductive and Deductive Reasoning
	1.2 Problem Solving with Patterns
	1.3 Problem-Solving Strategies
	Chapter 1 Summary
	Chapter 1 Review Exercises
	Chapter 1 Test
Ch 2: Sets
	2.1 Basic Properties of Sets
	2.2 Complements, Subsets, and Venn Diagrams
	2.3 Set Operations
	2.4 Applications of Sets
	2.5 Infinite Sets
	Chapter 2 Summary
	Chapter 2 Review Exercises
	Chapter 2 Test
Ch 3: Logic
	3.1 Logic Statements and Quantifiers
	3.2 Truth Tables, Equivalent Statements, and Tautologies
	3.3 The Conditional and the Biconditional
	3.4 The Conditional and Related Statements
	3.5 Symbolic Arguments
	3.6 Arguments and Euler Diagrams
	Chapter 3 Summary
	Chapter 3 Review Exercises
	Chapter 3 Test
Ch 4: Apportionment and Voting
	4.1 Introduction to Apportionment
	4.2 Introduction to Voting
	4.3 Weighted Voting Systems
	Chapter 4 Summary
	Chapter 4 Review Exercises
	Chapter 4 Test
Ch 5: The Mathematics of Graphs
	5.1 Graphs and Euler Circuits
	5.2 Weighted Graphs
	5.3 Planarity and Euler's Formula
	5.4 Graph Coloring
	Chapter 5 Summary
	Chapter 5 Review Exercises
	Chapter 5 Test
Ch 6: Numeration Systems and Number Theory
	6.1 Early Numeration Systems
	6.2 Place-Value Systems
	6.3 Different Base Systems
	6.4 Arithmetic in Different Bases
	6.5 Prime Numbers
	6.6 Topics from Number Theory
	Chapter 6 Summary
	Chapter 6 Review Exercises
	Chapter 6 Test
Ch 7: Measurement and Geometry
	7.1 Measurement
	7.2 Basic Concepts of Euclidean Geometry
	7.3 Perimeter and Area of Plane Figures
	7.4 Properties of Triangles
	7.5 Volume and Surface Area
	7.6 Right Triangle Trigonometry
	7.7 Non-Euclidean Geometry
	7.8 Fractals
	Chapter 7 Summary
	Chapter 7 Review Exercises
	Chapter 7 Test
Ch 8: Mathematical Systems
	8.1 Modular Arithmetic
	8.2 Applications of Modular Arithmetic
	8.3 Introduction to Group Theory
	Chapter 8 Summary
	Chapter 8 Review Exercises
	Chapter 8 Test
Ch 9: Applications of Equations
	9.1 First-Degree Equations and Formulas
	9.2 Rate, Ratio, and Proportion
	9.3 Percent
	9.4 Second-Degree Equations
	Chapter 9 Summary
	Chapter 9 Review Exercises
	Chapter 9 Test
Ch 10: Applications of Functions
	10.1 Rectangular Coordinates and Functions
	10.2 Properties of Linear Functions
	10.3 Finding Linear Models
	10.4 Quadratic Functions
	10.5 Exponential Functions
	10.6 Logarithmic Functions
	Chapter 10 Summary
	Chapter 10 Review Exercises
	Chapter 10 Test
Ch 11: The Mathematics of Finance
	11.1 Simple Interest
	11.2 Compound Interest
	11.3 Credit Cards and Consumer Loans
	11.4 Stocks, Bonds, and Mutual Funds
	11.5 Home Ownership
	Chapter 11 Summary
	Chapter 11 Review Exercises
	Chapter 11 Test
Ch 12: Combinatorics and Probability
	12.1 The Counting Principle
	12.2 Permutations and Combinations
	12.3 Probability and Odds
	12.4 Addition and Complement Rules
	12.5 Conditional Probability
	12.6 Expectation
	Chapter 12 Summary
	Chapter 12 Review Exercises
	Chapter 12 Test
Ch 13: Statistics
	13.1 Measures of Central Tendency
	13.2 Measures of Dispersion
	13.3 Measures of Relative Position
	13.4 Normal Distributions
	13.5 Linear Regression and Correlation
	Chapter 13 Summary
	Chapter 13 Review Exercises
	Chapter 13 Test
Solutions to Check Your Progress Problems
Answers to Selected Exercises
Index of Applications
Index