Mathematical Excursions

  • AUTHORS: Richard N. Aufmann; Joanne S. Lockwood; Richard D. Nation; Daniel K. Clegg
  • ISBN-13: 9781111578497 
  • Grade(s): 9 | 10 | 11 | 12
  • 1008 Pages  Hardcover 
  • 3rd Edition  |  Previous Editions: 2007, 2004
  • ©2013     Published
  • Prices are valid only in the respective region

Overview

About The Product

MATHEMATICAL EXCURSIONS, Third Edition, teaches students that mathematics is a system of knowing and understanding our surroundings. For example, sending information across the Internet is better understood when one understands prime numbers; the perils of radioactive waste take on new meaning when one understands 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. Students will learn those facets of mathematics that strengthen their quantitative understanding and expand the way they know, perceive, and comprehend their world. We hope you enjoy the journey.

Features

  • 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.

About the Contributor

AUTHORS
  • 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.

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.

New to this Edition

  • 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.

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  • 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.
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