Higher Education

Mathematical Excursions, Enhanced Edition, 3rd Edition

  • Richard N. Aufmann Palomar College
  • Joanne S. Lockwood Nashua Community College
  • Richard D. Nation Palomar College
  • Daniel K. Clegg Palomar College
  • ISBN-10: 1285454227  |  ISBN-13: 9781285454221
  • 1008 Pages
  • Previous Editions: 2013, 2007, 2004
  • © 2015 | Published
  • College Bookstore Wholesale Price = $232.00

About

Overview

MATHEMATICAL EXCURSIONS, Third Edition, teaches you that mathematics is a system of knowing and understanding our surroundings. For example, sending information across the Internet is better understood when you understand prime numbers; the perils of radioactive waste take on new meaning when you understand exponential functions; and the efficiency of the flow of traffic through an intersection is more interesting after seeing the system of traffic lights represented in a mathematical form. You will learn those facets of mathematics that strengthen your quantitative understanding and expand the way you know, perceive, and comprehend your world. We hope you enjoy the journey.

Features and Benefits

  • The Third Edition's table of contents has been reorganized and rearranged to group the chapters by broad topics that you can cover sequentially.
  • In the News exercises, based on media sources, have been added to this edition, providing another way to engage students by demonstrating the contemporary use of mathematics.
  • Chapter Summaries now appear in an easy-to-use grid format organized by section. Each summary point is now paired with the page numbers of an example that illustrates the concept, and exercises that allow students to practice the relevant skill or technique.
  • All application Examples, Exercises, and Excursions have been updated to reflect the most recent data and trends.
  • Definitions are now boxed and highlighted for greater prominence throughout the text, facilitating study and review.
  • All graphing calculator notes have been updated to refer to the TI-84 Plus.
  • In the Answer Section, answers to Chapter Test exercises now include a reference to a similar example in the text, making it easy for students to review relevant material for exercises that they answer incorrectly.
  • Content includes a subsection on Reading and Interpreting Graphs, a section on Right Triangle Trigonometry, and a section on Stocks, Bonds, and Mutual Funds.
  • An online algebra review appendix helps students review prerequisite algebra concepts.
  • An Excursion activity and corresponding Excursion Exercises conclude each section, providing concept reinforcement and opportunities for in-class cooperative work, hands-on learning, and development of critical-thinking skills.
  • Use of the Aufmann Interactive Method ensures that students try concepts and manipulate real-life data as they progress through the material. Every objective contains at least one set of matched-pair examples, the first of which is a completely worked-out example with an annotated solution. Students then actively practice the concept under discussion by trying the second problem, called Check Your Progress, using the example as a model. Each Check Your Progress problem includes a reference to a fully worked-out solution in the back of the text.
  • A section on Problem-Solving Strategies in Chapter 1 introduces students to the inductive and deductive reasoning strategies they will use throughout the text.
  • A Question/Answer feature encourages students to pause and think about the current discussion and to answer the question. For immediate reinforcement, the Answer is provided in a footnote on the same page.
  • Carefully developed exercise sets emphasize skill building, skill maintenance, concepts, and applications. Icons identify various types of exercises, including writing, data analysis, graphing calculator, and web exercises.
  • Extension exercises at the end of each exercise set include Critical Thinking, Cooperative Learning, and Explorations, which may require Internet or library research.
  • The Math Matters feature throughout the text helps to motivate students by containing an interesting sidelight about mathematics, its history, or its applications.
  • Supporting margin notes include Take Note, alerting students to a concept requiring special attention; Point of Interest, offering motivating contextual information; Historical Notes, providing background information or vignettes of individuals responsible for major advancements in their field; and Calculator Notes, providing point-of-use tips.
  • Chapter-ending resources include a Chapter Summary (with Key Words and Essential Concepts), Chapter Review Exercises, and a Chapter Test.

Table of Contents

1. PROBLEM SOLVING.
Inductive and Deductive Reasoning. Excursion: KenKen Puzzles: An Introduction. Problem Solving with Patterns. Excursion: Polygonal Numbers. Problem-Solving Strategies. Excursion: Routes on a Probability Demonstrator. Chapter 1 Summary. Chapter 1 Review. Chapter 1 Test.
2. SETS.
Basic Properties of Sets. Excursion: Fuzzy Sets. Complements, Subsets, and Venn Diagrams. Excursion: Subsets and Complements of Fuzzy Sets. Set Operations. Excursion: Union and Intersection of Fuzzy Sets. Applications of Sets. Excursion: Voting Systems. Infinite Sets. Excursion: Transfinite Arithmetic. Chapter 2 Summary. Chapter 2 Review Exercises. Chapter 2 Test.
3. LOGIC.
Logic Statements and Quantifiers. Excursion: Switching Networks. Truth Tables, Equivalent Statements, and Tautologies. Excursion: Switching Networks-Part II. The Conditional and the Biconditional. Excursion: Logic Gates. The Conditional and Related Statements. Excursion: Sheffer''s Stroke and the NAND Gate. Symbolic Arguments. Excursion: Fallacies. Arguments and Euler Diagrams. Excursion: Using Logic to Solve Crypterithms. Chapter 3 Summary. Chapter 3 Review Exercises. Chapter 3 Test.
4. APPORTIONMENT AND VOTING.
Introduction to Apportionment. Excursion: Apportioning the 1790 House of Representatives. Introduction to Voting. Excursion: Variations of the Borda Count Method. Weighted Voting Systems. Excursion: Blocking Coalitions and the Banzhaf Power Index. Chapter 4 Summary. Chapter 4 Review Exercises. Chapter 4 Test.
5. THE MATHEMATICS OF GRAPHS.
Graphs and Euler Circuits. Excursion: Pen-Tracing Puzzles. Weighted Graphs. Excursion: Extending the Greedy Algorithm. Planarity and Euler''s Formula. Excursion: The Five Regular Convex Polyhedra. Graph Coloring. Excursion: Modeling Traffic Lights with Graphs. Chapter 5 Summary. Chapter 5 Review Exercises. Chapter 5 Test.
6. NUMERATION SYSTEMS AND NUMBER THEORY.
Early Numeration Systems. Excursion: A Rosetta Tablet for the Traditional Chinese Numeration System. Place-Value Systems. Excursion: Subtraction via the Nines Complement and the End-Around Carry. Different Base Systems. Excursion: Information Retrieval via a Binary Search. Arithmetic in Different Bases. Excursion: Subtraction in Base Two via the Ones Complement and the End-Around Carry. Prime Numbers. Excursion: The Distribution of the Primes. Topics from Number Theory. Excursion: A Sum of the Divisors Formula. Chapter 6 Summary. Chapter 6 Review Exercises. Chapter 6 Test.
7. GEOMETRY.
Basic Concepts of Euclidean Geometry. Excursion: Preparing a Circle Graph. Perimeter and Area of Plane Figures. Excursion: Perimeter and Area of a Rectangle with Changing Dimensions. Properties of Triangles. Excursion: Topology: A Brief Introduction. Volume and Surface Area. Excursion: Water Displacement. Right Triangle Trigonometry. Excursion: Approximating the Value of Trigonometric Ratios. Non-Euclidean Geometry. Excursion: Finding Geodesics. Fractals. Excursion: The Heighway Dragon Fractal. Chapter 7 Summary. Chapter 7 Review Exercises. Chapter 7 Test.
8. MATHEMATICAL SYSTEMS.
Modular Arithmetic. Excursion: Computing the Day of the Week. Applications of Modular Arithmetic. Excursion: Public Key Cryptography. Introduction to Group Theory. Excursion: Wallpaper Groups. Chapter 8 Summary. Chapter 8 Review Exercises. Chapter 8 Test.
9. APPLICATIONS OF EQUATIONS.
First-Degree Equations and Formulas. Excursion: Body Mass Index. Rate, Ratio, and Proportion. Excursion: Earned Run Average. Percent. Excursion: Federal Income Tax. Second-Degree Equations. Excursion: The Sum and Product of the Solutions of a Quadratic Equation. Chapter 9 Summary. Chapter 9 Review Exercises. Chapter 9 Test.
10. APPLICATIONS OF FUNCTIONS.
Rectangular Coordinates and Functions. Excursion: Dilations of a Geometric Figure. Properties of Linear Functions. Excursion: Negative Velocity. Finding Linear Models. Excursion: A Linear Business Model. Quadratic Functions. Excursion: Reflective Properties of a Parabola. Exponential Functions. Excursion: Chess and Exponential Functions. Logarithmic Functions. Excursion: Benford''s Law. Chapter 10 Summary. Chapter 10 Review Exercises. Chapter 10 Test.
11. THE MATHEMATICS OF FINANCE.
Simple Interest. Excursion: Day-of-the-Year Table. Compound Interest. Excursion: Consumer Price Index. Credit Cards and Consumer Loans. Excursion: Car Leases. Stocks, Bonds, and Mutual Funds. Excursion: Treasury Bills. Home Ownership. Excursion: Home Ownership Issues. Chapter 11 Summary. Chapter 11 Review Exercises. Chapter 11 Test.
12. COMBINATORICS AND PROBABILITY.
The Counting Principle. Excursion: Decision Trees. Permutations and Combinations. Excursion: Choosing Numbers in Keno. Probability and Odds. Excursion: The Value of Pi by Simulation. Addition and Complement Rules. Excursion: Keno Revisited. Conditional Probability. Excursion: Sharing Birthdays. 12.6 Expectation. Excursion: Chuck-a-luck. Chapter 12 Summary. Chapter 12 Review Exercises. Chapter 12 Test.
13. STATISTICS.
Measures of Central Tendency. Excursion: Linear Interpolation and Animation. Measures of Dispersion. Excursion: Geometric View of Variance and Standard Deviation. Measures of Relative Position. Excursion: Stem-and-Leaf Diagrams. Normal Distribution. Excursion: Cut-Off Scores. Linear Regression and Correlation. Excursion: An Application of Linear Regression. Chapter 13 Summary. Chapter 13 Review Exercises. Chapter 13 Test.

What's New

  • New! Interactive Excursions are now available through Enhanced WebAssign. These activities with assignable questions are based on the Excursions found in the textbook. Through these activities, students can become more openly engaged as they explore the Excursions in a newly enriched, media-enhanced environment.
  • New! A comprehensive skills-review is now available through Enhanced WebAssign. This preloaded and assignable review presents students with questions that focus on prerequisite skills. The review will help students refresh their knowledge and fill in any gaps so they may advance more smoothly through new concepts or topics.

Learning Resource Bundles

Choose the textbook packaged with the resources that best meet your course and student needs. Contact your Learning Consultant for more information.

Printed Text + Enhanced WebAssign Instant Access for Liberal Arts Math & Teacher Math, Single-Term Courses

ISBN-10: 1337068292 | ISBN-13: 9781337068291

List Price = $314.95  | College Bookstore Wholesale Price = $237.00

This Bundle Includes:

  • Enhanced WebAssign Instant Access for Liberal Arts Math & Teacher Math, Single-Term Courses
    List Price = $94.00  | CengageBrain Price = $94.00  | College Bookstore Wholesale Price = $94.00
  • Mathematical Excursions, Enhanced Edition
    List Price = $308.95  | CengageBrain Price = $308.95  | College Bookstore Wholesale Price = $232.00


Supplements

All supplements have been updated in coordination with the main title. Select the main title's "About" tab, then select "What's New" for updates specific to title's edition.

For more information about these supplements, or to obtain them, contact your Learning Consultant.

Instructor Supplements

Mathematical Excursions, 3rd: Instructor's Solutions Manual  (ISBN-10: 113311220X | ISBN-13: 9781133112204)

This manual contains complete solutions to all the problems in the text.

Mathematical Excursions, 3rd: PowerLecture CD-ROM with ExamView Test Generator  (ISBN-10: 1133112188 | ISBN-13: 9781133112181)

PowerLecture™ instructor resources are a collection of book-specific lecture and class tools on either CD or DVD. The fastest and easiest way to build powerful, customized media-rich lectures, PowerLecture includes chapter-specific PowerPoint® presentations, images, animations and video, instructor manuals, test banks, useful web links and more. New for this edition, the PowerLecture features a Syllabus Creator. This allows you to create your new syllabus in six easy steps: select the required course objectives, add your contact information, course information, student expectations, the grading policy, dates and location, and your course outline. And now you have your syllabus! PowerLecture media-teaching tools are an effective way to enhance the educational experience.

Student Solutions Manual  (ISBN-10: 1133112218 | ISBN-13: 9781133112211)

Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.

List Price = $106.95  | CengageBrain Price = $106.95  | College Bookstore Wholesale Price = $80.25

Enhanced WebAssign - Start Smart Guide for Students  (ISBN-10: 0495384798 | ISBN-13: 9780495384793)

This guide helps students navigate Enhanced WebAssign. It includes instructions on how to use the Assignment page and its Summary, tips on using MathPad for providing easy input of math notation and symbols, an overview of the Graphing Utility's drawing tools for completing graphing assignments, and information on how to access grades and scores summary.

List Price = $50.95  | CengageBrain Price = $50.95  | College Bookstore Wholesale Price = $38.25

Enhanced WebAssign Instant Access for Liberal Arts Math & Teacher Math, Single-Term Courses  (ISBN-10: 1285858034 | ISBN-13: 9781285858036)

IMPORTANT: When purchasing this instant access code for Liberal Arts Math & Teacher Math, ensure that you are using it in one of the following courses: Mathematical Excursions, Topics in Contemporary Mathematics, Elementary Technical Mathematics, Mathematics for Teachers or Math for Liberal Arts. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If your students need to retake the course and you are using the same book AND edition then they will not need to buy a new code. This instant access code will be delivered via email when purchased. If you are not certain this is the correct access code for your course, please contact your Cengage Learning Consultant.

List Price = $94.00  | CengageBrain Price = $94.00  | College Bookstore Wholesale Price = $94.00

Mathematical Excursions, 3rd: Instructor's Annotated Edition  (ISBN-10: 1111579024 | ISBN-13: 9781111579029)

Enhanced WebAssign® International Instant Access Code Homework with e-Book  (ISBN-10: 133729697X | ISBN-13: 9781337296977)

Exclusively from Cengage Learning, Enhanced WebAssign® combines the exceptional mathematics content in this text with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive eBook, helping students to develop a deeper conceptual understanding of their subject matter. Online assignments can be built by selecting from thousands of text-specific problems, supplemented if you wish with problems from any Cengage Learning textbook.

List Price = $125.00  | College Bookstore Wholesale Price = $125.00

Enhanced WebAssign® International Instant Access Code Homework Only  (ISBN-10: 133729926X | ISBN-13: 9781337299268)

Exclusively from Cengage Learning, Enhanced WebAssign® combines the exceptional mathematics content in this text with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback and rich tutorial content, helping students to develop a deeper conceptual understanding of their subject matter. Online assignments can be built by selecting from thousands of text-specific problems, supplemented if you wish with problems from any Cengage Learning textbook.

List Price = $125.00  | College Bookstore Wholesale Price = $125.00

Enhanced WebAssign® International Printed Access Card Homework with e-Book  (ISBN-10: 1337296961 | ISBN-13: 9781337296960)

Exclusively from Cengage Learning, Enhanced WebAssign® combines the exceptional mathematics content in this text with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive eBook, helping students to develop a deeper conceptual understanding of their subject matter. Online assignments can be built by selecting from thousands of text-specific problems, supplemented if you wish with problems from any Cengage Learning textbook.

List Price = $125.00  | College Bookstore Wholesale Price = $93.75

Enhanced WebAssign® International Printed Access Card Homework Only  (ISBN-10: 1337299251 | ISBN-13: 9781337299251)

Exclusively from Cengage Learning, Enhanced WebAssign® combines the exceptional mathematics content in this text with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback and rich tutorial content, helping students to develop a deeper conceptual understanding of their subject matter. Online assignments can be built by selecting from thousands of text-specific problems, supplemented if you wish with problems from any Cengage Learning textbook.

List Price = $125.00  | College Bookstore Wholesale Price = $93.75

Student Supplements

Student Solutions Manual  (ISBN-10: 1133112218 | ISBN-13: 9781133112211)

Go beyond the answers--see what it takes to get there and improve your grade! This manual provides worked-out, step-by-step solutions to the odd-numbered problems in the text. You'll have the information you need to truly understand how these problems are solved.

List Price = $106.95  | CengageBrain Price = $106.95  | College Bookstore Wholesale Price = $80.25

Enhanced WebAssign - Start Smart Guide for Students  (ISBN-10: 0495384798 | ISBN-13: 9780495384793)

If your instructor has chosen to package Enhanced WebAssign with your text, this manual will help you get up and running quickly with the Enhanced WebAssign system so you can study smarter and improve your performance in class.

List Price = $50.95  | CengageBrain Price = $50.95  | College Bookstore Wholesale Price = $38.25

Enhanced WebAssign Instant Access for Liberal Arts Math & Teacher Math, Single-Term Courses  (ISBN-10: 1285858034 | ISBN-13: 9781285858036)

IMPORTANT: When purchasing this instant access code for Liberal Arts Math & Teacher Math, ensure that you are using it in one of the following courses: Mathematical Excursions, Topics in Contemporary Mathematics, Elementary Technical Mathematics, Mathematics for Teachers or Math for Liberal Arts. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If you need to retake the course and your instructor is using the same book AND edition then you will not need to buy a new code. This instant access code will be delivered via email when purchased. If you are not certain this is the correct access code for your course, please contact your instructor.

List Price = $94.00  | CengageBrain Price = $94.00  | College Bookstore Wholesale Price = $94.00

Enhanced WebAssign® International Instant Access Code Homework with e-Book  (ISBN-10: 133729697X | ISBN-13: 9781337296977)

Enhanced WebAssign® engages you with immediate feedback, rich tutorial content, and an interactive eBook, helping you to develop a deeper conceptual understanding of your subject matter.

List Price = $125.00  | College Bookstore Wholesale Price = $125.00

Enhanced WebAssign® International Instant Access Code Homework Only  (ISBN-10: 133729926X | ISBN-13: 9781337299268)

Enhanced WebAssign® engages you with immediate feedback and rich tutorial content, helping you to develop a deeper conceptual understanding of your subject matter.

List Price = $125.00  | College Bookstore Wholesale Price = $125.00

Enhanced WebAssign® International Printed Access Card Homework with e-Book  (ISBN-10: 1337296961 | ISBN-13: 9781337296960)

Enhanced WebAssign® engages you with immediate feedback, rich tutorial content, and an interactive eBook, helping you to develop a deeper conceptual understanding of your subject matter.

List Price = $125.00  | College Bookstore Wholesale Price = $93.75

Enhanced WebAssign® International Printed Access Card Homework Only  (ISBN-10: 1337299251 | ISBN-13: 9781337299251)

Enhanced WebAssign® engages you with immediate feedback and rich tutorial content, helping you to develop a deeper conceptual understanding of your subject matter.

List Price = $125.00  | College Bookstore Wholesale Price = $93.75

Meet the Author

Author Bio

Richard N. Aufmann

Richard Aufmann is the lead author of two bestselling developmental math series and a bestselling college algebra and trigonometry series, as well as several derivative math texts. He received a BA in mathematics from the University of California, Irvine, and an MA in mathematics from California State University, Long Beach. Mr. Aufmann taught math, computer science, and physics at Palomar College in California, where he was on the faculty for 28 years. His textbooks are highly recognized and respected among college mathematics professors. Today, Mr. Aufmann's professional interests include quantitative literacy, the developmental math curriculum, and the impact of technology on curriculum development.

Joanne S. Lockwood

Joanne Lockwood received a BA in English Literature from St. Lawrence University and both an MBA and a BA in mathematics from Plymouth State University. Ms. Lockwood taught at Plymouth State University and Nashua Community College in New Hampshire, and has over 20 years' experience teaching mathematics at the high school and college level. Ms. Lockwood has co-authored two bestselling developmental math series, as well as numerous derivative math texts and ancillaries. Ms. Lockwood's primary interest today is helping developmental math students overcome their challenges in learning math.

Richard D. Nation

Richard Nation received a B.A. in mathematics from Morningside College and a M.S. degree in mathematics from the University of South Dakota. Mr. Nation also attended a National Science Foundation academic year institute in mathematics at San Diego State University. Mr. Nation taught math at Palomar College in California, where he was on the faculty for 20 years. He has over 38 years’ experience teaching mathematics at the high school and college levels. He is the co-author of several Aufmann titles. Today, Mr. Nation’s professional interests include the impact of technology on curriculum development and on the teaching of mathematics at the precalculus level.

Daniel K. Clegg

Daniel Clegg received his B.A. in Mathematics from California State University, Fullerton and his M.A. in Mathematics from UCLA. He is currently a professor of mathematics at Palomar College near San Diego, California, where he has taught for more than 20 years. In addition to writing with the Aufmann team, he co-authored “Brief Applied Calculus” with James Stewart. He has also assisted James Stewart with various aspects of his calculus texts and ancillaries for almost 20 years.