Thinking Mathematically

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.  He is most energized by teaching mathematics, and has taught a variety of mathematics courses at Miami-Dade Community College for nearly 30 years.  He has received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College, Teacher of the Year (13 years in a row) and was among the first group of recipients at Miami-Dade Community College for an endowed chair based on excellence in the classroom. In addition to Thinking Mathematically, Bob has written Introductory Algebra for College Students, Intermediate Algebra for College Students, Introductory and Intermediate Algebra for College Students, Algebra for College Students, College Algebra, Algebra and Trigonometry, and Precalculus, all published by Prentice Hall.

Chapter 1. Problem Solving and Critical Thinking

1.1  Inductive and Deductive Reasoning

1.2  Estimation, Graphs, and Mathematical Models

1.3  Problem Solving

 

Chapter 2. 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

 

Chapter 3. 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, Variations of Conditional Statements, and DeMorgan’s Laws

3.6 Arguments and Truth Tables

3.7 Arguments and Euler Diagrams

 

Chapter 4. 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

 

Chapter 5. 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

5.6 Exponents and Scientific Notation

5.7 Arithmetic and Geometric Sequences

 

Chapter 6. Algebra: Equations and Inequalities

6.1 Algebraic Expressions and Formulas

6.2 Linear Equations in One Variable

6.3 Applications of Linear Equations

6.4 Ratio, Proportion, and Variation

6.5 Linear Inequalities in One Variable

6.6 Quadratic Equations

 

Chapter 7. 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 Approximating Reality with Nonlinear Models

 

Chapter 8. Consumer Mathematics and Financial Management

8.1 Percent, Sales Tax, and Income Tax

8.2 Simple Interest

8.3 Compound Interest

8.4 Annuities, Stocks, and Bonds

8.5 Installment Buying

8.6 Amortization and the Cost of Home Ownership

 

Chapter 9. Measurement

9.1 Measuring Length; The Metric System

9.2 Measuring Area and Volume

9.3 Measuring Weight and Temperature

 

Chapter 10. Geometry

10.1 Points, Lines, Planes, and Angles

10.2 Triangles

10.3 Polygons, Perimeter, and Tessellations

10.4 Area and Circumstances

10.5 Volume

10.6 Right Triangle Trigonometry

10.7 Beyond Euclidean Geometry

 

Chapter 11. 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

 

Chapter 12. Statistics

12.1 Sampling, Frequency Distributions, and Graphs

12.2 Measures of Central Tendency

12.3 Measure of Dispersion

12.4 The Normal Distribution

12.5 Scatter Plots, Correlation, and Regression Lines

 

Chapter 13. Mathematical Systems

13.1 Mathematical Systems

13.2 Rotational Symmetry, Groups, and Clock Arithmetic

 

Chapter 14. Voting and Apportionment

14.1 Voting Methods

14.2 Flaws of Voting Methods

14.3 Apportionment Methods

14.4 Flaws of Apportionment Methods

 

Chapter 15. Graph Theory

15.1 Graphs, Paths, and Circuits

15.2 Euler Paths and Euler Circuits

15.3 Hamilton Paths and Hamilton Circuits

15.4 Trees