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## Overview

MATHEMATICAL EXCURSIONS, Fourth Edition, teaches students that mathematics is a system of knowing and understanding our surroundings, and explores a selection of topics from various areas in mathematics. The topics were chosen to exemplify the power and diversity of mathematics and to connect math concepts to contemporary applications. 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. WebAssign is a flexible and fully customizable online instructional solution that puts powerful tools in your hands, enabling you to deploy assignments, add your own content, instantly assess individual student and class performance, and help your students master course concepts.

- A new section on Measurement was added to Chapter 7.
- New or updated Excursions have been added.
- Updated exercise sets provide students with ample opportunities to practice.

- In the Answer Section, answers to Chapter Test Exercises 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 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 section 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.
- 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.
- Chapter Summaries are arranged 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.
- WEBASSIGN: MATHEMATICAL EXCURSIONS, Fourth Edition, is the powerful online homework and course management system that engages students in learning the math. WebAssign includes new end-of-chapter exercises and pre-built assignments vetted by trusted subject matter experts along with robust course, section, assignment, and question settings and online testing to help instructors foster a deeper understanding of course concepts.
- The Fourth Edition's table of contents has been organized to group the chapters by broad topics that you can cover sequentially.
- All application Examples, Exercises, and Excursions have been updated to reflect the most recent data and trends.
- Definitions are boxed and highlighted for greater prominence throughout the text, facilitating study and review.
- All graphing calculator notes refer to the TI-84 Plus.

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 Cryptarithms. 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. MEASUREMENT AND GEOMETRY.

Measurement. Excursion: Drawing with a Straightedge and a Compass. 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: Interest on a Car Loan. 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. 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: Exponential Regression. An Application of Linear Regression. Chapter 13 Summary. Chapter 13 Review Exercises. Chapter 13 Test.

"The Excursion/application topics are interesting and creative."

"All of the examples are clear and provide enough detail for less-prepared students to follow. The language used is generally understandable for students, even if they are not experts at reading in English."

"I think the Finance unit is important. It involves such real-life application and it's important that students have financial literacy. So many students are ignorant about saving money and how much interest accumulates on loans. It's a real eye opening unit!"

Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.

### FOR INSTRUCTORS

#### Mathematical Excursions, 3rd: Instructor's Solutions Manual

ISBN: 9781133112204

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

#### Mathematical Excursions, 3rd: PowerLecture CD-ROM with ExamView Test Generator

ISBN: 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: 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.

#### Mathematical Excursions, 3rd: Instructor's Annotated Edition

ISBN: 9781111579029

### FOR STUDENTS

#### Student Solutions Manual

ISBN: 9781133112211