Description
Book SynopsisAbout our author
Bob Blitzer is a native of Manhattan and received a Bachelor of Arts degree with dual majors in mathematics and psychology (minor: English literature) from the City College of New York. His unusual combination of academic interests led him toward a Master of Arts in mathematics from the University of Miami and a doctorate in behavioral sciences from Nova University. Bob's love for teaching mathematics was nourished for nearly 30 years at Miami Dade College, where he received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College and an endowed chair based on excellence in the classroom. In addition to Thinking Mathematically, Bob has written textbooks covering developmental mathematics, algebra & trigonometry, trigonometry, college algebra, and precalculus, all published by Pearson. When not secluded in his Northern California writer's cabin, Bob can be found hikin
Table of Contents
Table of Contents
(NOTE: Each chapter concludes with a Chapter Summary, Review, and Test, and a comprehensive Chapter Test.)
- Problem Solving and Critical Thinking
- 1.1 Inductive and Deductive Reasoning
- 1.2 Estimation, Graphs, and Mathematical Models
- 1.3 Problem Solving
- 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
- Logic
- 3.1 Statements, Negations, and Quantified Statements
- 3.2 Compound Statements and Connectives
- 3.3 Truth Tables for Negation, 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
- 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
- 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; Clock Addition
- 5.6 Exponents and Scientific Notation
- 5.7 Arithmetic and Geometric Sequences
- 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
- 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
- Personal Finance
- 8.1 Percent, Sales Tax, and Discounts
- 8.2 Income Tax
- 8.3 Simple Interest
- 8.4 Compound Interest
- 8.5 Annuities, Methods of Saving, and Investments
- 8.6 Cars
- 8.7 The Cost of Home Ownership
- 8.8 Credit Cards
- Measurement
- 9.1 Measuring Length; The Metric System
- 9.2 Measuring Area and Volume
- 9.3 Measuring Weight and Temperature
- 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 and Surface Area
- 10.6 Right Triangle Trigonometry
- 10.7 Beyond Euclidean Geometry
- 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
- 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
- Voting and Apportionment
- 13.1 Voting Methods
- 13.2 Flaws of Voting Methods
- 13.3 Apportionment Methods
- 13.4 Flaws of Apportionment Methods
- Graph Theory
- 14.1 Graphs, Paths, and Circuits
- 14.2 Euler Paths and Euler Circuits
- 14.3 Hamilton Paths and Hamilton Circuits
- 14.4 Trees
Answers to Selected Exercises Credits Subject Index
