Mathematics All Around

by Pirnot, Tom

Edition:

2nd

ISBN13:

9780201795110

ISBN10:

0201795116

Format:

Hardcover

Pub. Date:

1/1/2004

Publisher(s):

Addison Wesley

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Summary

"Tom Pirnot" believes that conceptual understanding is the key to a student' s success in learning mathematics. He focuses on explaining the thinking behind the subject matter, so that students are able to truly understand the material and apply it to their lives. This textbook maintains a conversational tone throughout and focuses on motivating students and the mathematics through current applications. Ultimately, students who use this book will become more educated consumers of the vast amount of technical and mathematical information that they encounter daily, transforming them into mathematically aware citizens.

Set Theory: Using Mathematics to Classify Objects

(67)

Problem Solving

(14)

Estimation

(7)

The Language of Sets

(7)

Comparing Sets

(8)

Set Operations

(12)

Survey Problems

(18)

Chapter Summary

(3)

Chapter Test

(2)

Of Further Interest: Infinite Sets

(5)

Logic: The Study of What's True or False or Somewhere in Between

(72)

Inductive and Deductive Reasoning

(9)

Statements, Connectives, and Quantifiers

(10)

Truth Tables

(12)

The Conditional and Biconditional

100

(10)

Verifying Arguments

110

(9)

Using Euler Diagrams to Verify Syllogisms

119

(21)

Chapter Summary

127

(2)

Chapter Test

129

(3)

Of Further Interest: Fuzzy Logic

132

(8)

Graph Theory: The Mathematics of Relationships

140

(54)

Graphs, Puzzles, and Map Coloring

141

(18)

The Traveling Salesperson Problem

159

(12)

Directed Graphs

171

(23)

Chapter Summary

180

(2)

Chapter Test

182

(2)

Of Further Interest: Scheduling Projects Using PERT

184

(10)

Numeration Systems: Does It Matter How We Name Numbers?

194

(50)

The Evolution of Numeration Systems

195

(11)

Place Value Systems

206

(11)

Calculating in Other Bases

217

(27)

Chapter Summary

230

(2)

Chapter Test

232

(1)

Of Further Interest: Modular Systems

233

(11)

Number Theory and the Real Number System: Understanding the Numbers All Around Us

244

(75)

Number Theory

245

(12)

The Integers

257

(9)

The Rational Numbers

266

(14)

The Real Number System

280

(12)

Exponents and Scientific Notation

292

(27)

Chapter Summary

303

(3)

Chapter Test

306

(1)

Of Further Interest: Sequences

307

(12)

Algebraic Models: How Do We Approximate Reality?

319

(65)

Linear Equations

320

(13)

Modeling with Linear Equations

333

(9)

Modeling with Quadratic Equations

342

(9)

Exponential Equations and Growth

351

(12)

Proportions and Variation

363

(21)

Chapter Summary

371

(3)

Chapter Test

374

(2)

Of Further Interest: Dynamical Systems

376

(8)

Modeling with Systems of Linear Equations and Inequalities: What's the Best Way to Do It?

384

(36)

Systems of Linear Equations

385

(14)

Systems of Linear Inequalities

399

(21)

Chapter Summary

409

(1)

Chapter Test

410

(1)

Of Further Interest: Linear Programming

411

(9)

Geometry: Ancient and Modern Mathematics Embrace

420

(87)

Lines, Angles, and Circles

421

(10)

Polygons

431

(11)

Perimeter and Area

442

(13)

Volume and Surface Area

455

(9)

The Metric System and Dimensional Analysis

464

(12)

Geometric Symmetry and Tessellations

476

(31)

Chapter Summary

491

(4)

Chapter Test

495

(2)

Of Further Interest: Fractals

497

(10)

Apportionment: How Do We Measure Fairness?

507

(59)

Understanding Apportionment

508

(11)

The Huntington--Hill Apportionment Principle

519

(7)

Applications of the Apportionment Principle

526

(9)

Other Paradoxes and Apportionment Methods

535

(31)

Chapter Summary

551

(3)

Chapter Test

554

(2)

Of Further Interest: Fair Division

556

(10)

Voting: Using Mathematics to Make Choices

566

(48)

Voting Methods

567

(12)

Defects in Voting Methods

579

(14)

Weighted Voting Systems

593

(21)

Chapter Summary

602

(2)

Chapter Test

604

(2)

Of Further Interest: The Shapley-Shubik Index

606

(8)

Consumer Mathematics: The Mathematics of Everyday Life

614

(63)

Percent

615

(8)

Interest

623

(14)

Consumer Loans

637

(8)

Annuities

645

(9)

Amortization

654

(23)

Chapter Summary

665

(3)

Chapter Test

668

(2)

Of Further Interest: The Annual Percentage Rate

670

(7)

Counting: Just How Many Are There?

677

(39)

Introduction to Counting Methods

678

(9)

The Fundamental Counting Principle

687

(8)

Permutations and Combinations

695

(21)

Chapter Summary

709

(1)

Chapter Test

710

(1)

Of Further Interest: Counting and Gambling

711

(5)

Probability: What Are the Chances?

716

(59)

The Basics of Probability Theory

717

(18)

Complements and Unions of Events

735

(8)

Conditional Probability and Intersections of Events

743

(14)

Expected Value

757

(18)

Chapter Summary

765

(2)

Chapter Test

767

(1)

Of Further Interest: Binomial Experiments

768

(7)

Descriptive Statistics: What a Data Set Tells Us

775

(74)

Organizing and Visualizing Data

776

(15)

Measures of Central Tendency

791

(15)

Measures of Dispersion

806

(13)

The Normal Distribution

819

(30)

Chapter Summary

834

(2)

Chapter Test

836

(2)

Of Further Interest: Linear Correlation

838

(11)

Answers to Quiz Yourself Problems

849

(10)

Answers to Exercises

859

(46)

Photo Credits

905

Index

Mathematics All Around

9780201795110

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