# Thinking Mathematically

**by**Blitzer, Robert F.

### 9780321645852

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## Summary

**Blitzer** continues to raise the bar with his engaging applications developed to motivate students from diverse majors and backgrounds. **Thinking Mathematically, Fifth Edition**, draws from the author's unique background in art, psychology, and math to present math in the context of real-world applications.

Students in this course are not math majors, and they may never take a subsequent math course, so they are often nervous about taking the class. **Blitzer** understands those students' needs and provides helpful tools in every chapter to help them master the material. Voice balloons appear right when students need them, showing what an instructor would say when leading a student through the problem. Study tips, chapter review grids, **Chapter Tests**, and abundant exercises provide ample review and practice.

**The Fifth Edition's MyMathLab** course boasts more than 2,000 assignable exercises, plus a new question type for applications-driven questions that correlate to every section of the textbook. **Chapter Test Prep Videos** show students how to work out solutions to the **Chapter Tests**; the videos are available in **MyMathLab** and on **YouTubetrade**.

## Author Biography

**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 introductory algebra, college algebra, algebra and trigonometry, and precalculus, all published by Prentice Hall. When not secluded in his Northern California writer’s cabin, Bob can be found hiking the beaches and trails of Point Reyes National Seashore, and tending to the chores required by his beloved entourage of horses, chickens, and irritable roosters.

## Table of Contents

**1. Problem Solving and Critical Thinking**

1.1 Inductive and Deductive Reasoning

1.2 Estimation, Graphs, and Mathematical Models

1.3 Problem Solving

**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

**3. Logic**

3.1 Statements, Negations, and Quantified Statements

3.2 Compound Statements and Connectives

3.3 Truth Tables for Negations, 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

**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

**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

**6. 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

**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 Modeling Data: Exponential, Logarithmic, and Quadratic Functions

**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 Loans, Amortization, and Credit Cards

**9. Measurement**

9.1 Measuring Length; The Metric System

9.2 Measuring Area and Volume

9.3 Measuring Weight and Temperature

**10. 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

10.6 Right Triangle Trigonometry

10.7 Beyond Euclidean Geometry

**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

**12. 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

**13. Mathematical Systems**

13.1 Mathematical Systems

13.2 Rotational Symmetry, Groups, and Clock Arithmetic

**14. Voting and Apportionment**

14.1 Voting Methods

14.2 Flaws of Voting Methods

14.3 Apportionment Methods

14.4 Flaws of Apportionment Methods

**15. Graph Theory**

15.5 Graphs, Paths, and Circuits

15.2 Euler Paths and Euler Circuits

15.3 Hamilton Paths and Hamilton Circuits

15.4 Trees