Mathematical Excursions

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 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 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 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.

• 1. PROBLEM SOLVING.Inductive and Deductive Reasoning. Excursion: The Monty Hall Problem. Estimation and Graphs. Excursion: Scientific Notation. Problem Solving with Patterns. Excursion: Polygonal Numbers. Problem-Solving Strategies. Excursion: Routes on a Probability Demonstrator.Chapter 1 Summary.Chapter 1 Review Exercises.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: Minimal Spanning Trees. 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: Lines of Symmetry. Perimeter and Area of Plane Figures. Excursion: Tessellations. Properties of Triangles. Excursion: Topology: A Brief Introduction. Volume and Surface Area. Excursion: Water Displacement. Right Triangle Trigonometry. Excursion: Approximating the Value of a Trigonometric Ratio. 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 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. Systems of Linear Equations in Two Variables. Excursion: Rate-of-Wind and Rate-of-Current Problems. Quadratic Functions. Excursion: Reflective Properties of a Parabola. Exponential Functions. Excursion: Chess and Exponential Functions. Logarithmic Functions. Excursion: Benford's Law.Chapter 9 Summary.Chapter 9 Review Exercises.Chapter 9 Test.10.