Mathematical Excursions,
4th Edition

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 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.

• Richard N. Aufmann

  Richard Aufmann is the lead author of two best-selling Developmental Math series and a best-selling College Algebra and Trigonometry series, as well as several derivative Math texts. 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. He holds a Bachelor of Arts in Mathematics from the University of California, Irvine, and a Master of Arts degree in Mathematics from California State University, Long Beach.

• Joanne 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. Clegg co-authored BRIEF APPLIED CALCULUS with James Stewart and also assisted Stewart with various aspects of his calculus texts and ancillaries for almost 20 years.

• JUST IN TIME SUPPORT built into questions contains direct links to the eTextbook (Read It) and videos (Watch It).

• MASTER IT TUTORIALS break problems down into steps to help guide students through the mathematical process.

• VIDEO EXAMPLES provide embedded videos paired with follow-up questions to ensure student understanding.

• COURSE PACKS are modifiable, ready-to-use assignments built by subject matter experts to help save time.

• CLASS INSIGHTS provide understanding of student knowledge gaps.

• RESPONSIVE LABS are multi-step projects (Labs) that provide an authentic and personalized application problem that gives learners the skills to think about and use the mathematics they are learning in various ways outside the classroom.

• STUDENT ACTIVITIES BOOKLET includes crowd-sourced projects contributed by instructors that give students in-depth practice either with a group or on their own.

• COREQUISITE VERSION AVAILABLE to provide the flexibility to match any corequisite implementation model and to empower you to deliver high quality content at the right time for your students at an affordable price.

• ANSWER SECTION provides answers to Chapter Test Exercises that 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.

• 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

• AUFMANN INTERACTIVE METHODensures 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.

• PROBLEM-SOLVING STRATEGIES section in Chapter 1 introduces students to the inductive and deductive reasoning strategies they will use throughout the text.

• MATH MATTERS features throughout the text help to motivate students by containing an interesting sidelight about mathematics, its history, or its applications.

• 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.

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