Addison-Wesley / Prentice Hall

Mathematics

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Thinking Mathematically, 4/E
Robert F. Blitzer, Miami-Dade Community College

ISBN-10: 0131752049
ISBN-13: 9780131752047

Publisher: Prentice Hall
Copyright: 2008
Format: Cloth; 900 pp
Published: 12/21/2006

Suggested retail price: $130.67
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For a one- or two-term course in Liberal Arts Mathematics, Survey of Mathematics, Finite Mathematics, and Mathematics for education majors.

 

This general survey of mathematical topics helps diverse students, with different backgrounds and career plans, to succeed in mathematics. Blitzer provides the applications and technology students need to gain an appreciation of mathematics through their college careers and beyond. His goal is to demonstrate how mathematics can be applied to students’ lives in interesting, enjoyable, and meaningful ways.

  • Flexible organization – The book’s variety of topics and flexibility of sequence make it appropriate for a one- or two-term course in liberal arts mathematics, quantitative reasoning, finite mathematics, mathematics for education majors, and courses specifically designed to meet state-mandated requirements in mathematics.
  • Abundant step-by-step, annotated Examples – Give students a problem-solving approach to reach the solution. This helps students through "sticking points" that can cause their enthusiasm to wane during assignments and study. Annotations are conversational in tone, explaining key steps and ideas as the problem is solved.
  • Check Point Examples – Each worked example is followed by a similar matched example offering students the opportunity to test their understanding of the example. The answers to the Check Points are provided in the answer section.
  • Extensive, well-organized exercise sets that precisely parallel Examples at the end of each section:
    • Organized into six categories for instructor flexibility: Practice Exercises, Application Exercises, Writing in Mathematics, Technology Exercises, Critical Thinking Exercises, Group Activity Exercises.
    • The order of the practice exercises is exactly the same order as the order of the section's illustrative examples.
    • The parallel order enables students to refer to the titled examples and their detailed explanations to achieve success working the practice exercises.
  • Unique Chapter- and Section-Opening Vignettes–Begin each section with a compelling vignette highlighting an every day scenario, posing a question about it, and exploring how the chapter section subject can be applied to answer the question. These scenarios are revisited in the course of the chapter or section example, discussion or exercise.
  • Explanatory Voice Balloons– Used in a variety of ways to demystify mathematics. They:
    • Translate mathematical ideas into plain English
    • Help clarify problem-solving procedures
    • Present alternative ways of understanding concepts
    • Connect complex problems to the basic concepts students have already learned.
  • Clearly stated Section Objectives–Help students recognize and focus on the most important ideas, and appear in the margin at their point of use.
  • Chapter Tests – Enable students to assess their understanding of the contents from the chapter.

  • Practice Plus Exercises  – More challenging practice exercises that often require students to combine several skills or concepts have been added to the exercise sets. The 442 Practice Plus Exercises in the Fourth Edition provide instructors with the option of creating assignments that take practice exercises to a more challenging level than in the previous edition.
  • New Applications and Real-World Data – Contains more new, innovative applications (supported by data that extend as far up to the present as possible) than in earlier revisions.
    • Includes 453 new exercises in the application category of the exercise sets, as well as 54 titled, worked-out examples that are based on new applications.
  • Over 1400 new examples and exercises – Contains more than 500 new exercises in the practice category of the exercise sets, in addition to the 442 Practice Plus Exercises and the 507 new application examples and exercises.
  • Integration of graphs and mathematical models:
    • Introduces mathematical modeling in Chapter 1
    • Provides integrated use of graphs so that students can interpret and reason with information involving numbers and mathematical ideas.
  • More Study Tip Boxes – Offer suggestions for problem solving, point out common errors to avoid, and provide informal hints and suggestions.
  • New, optional Enrichment Essays (“Blitzer Bonuses”).
  • Chapter Test Prep Video CD – Gives students step-by-step solutions for each of the exercises in the book’s check points and chapter tests. Packaged at the back of the text.

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

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.

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