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Full Description
"Mathematical Excursions," 5th Edition, will help you develop mathematical and analytical thinking skills for wherever your own excursions may lead. The authors prepare you for success with study strategies and an introduction to problem solving at the start and then help you discover key mathematical concepts and why they matter. This new edition focuses on what you need to know for your life and career. The coverage will help you make more informed decisions, including financial decisions as well as quick decisions in a variety of contexts. Relatable applications include social media, streaming services, wind energy and hybrid vehicles. We hope you enjoy the journey!
Contents
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. THE MATHEMATICS OF FINANCE. Simple Interest. Excursion: Interest on a Car Loan. Compound
