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Written for liberal arts students and based on the belief that learning to solve problems is the principal reason for studying mathematics, Karl Smith introduces students to Polya’s problem-solving techniques and shows them how to use these techniques to solve unfamiliar problems that they encounter in their own lives. Through the emphasis on problem solving and estimation, along with numerous in-text study aids, students are assisted in understanding the concepts and mastering the techniques. In addition to the problem-solving emphasis, THE NATURE OF MATHEMATICS is renowned for its clear writing, coverage of historical topics, selection of topics, level, and excellent applications problems. Smith includes material on such practical real-world topics as finances (e.g. amortization, installment buying, annuities) and voting and apportionment. With the help of this text, thousands of students have "experienced" mathematics rather than just do problems--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.
- The examples throughout the book have been redesigned to more effectively engage students. Each now includes a title and is presented in a fresh, easy-to-read format.
- "Historical Quest" problems, an overwhelming success in the previous edition, appear more frequently in the thirteenth edition. These problems are designed to involve students in the historical development of the great ideas in mathematical history.
- Website: The text-specific website (www.mathnature.com) provides homework hints, a listing of essential ideas, projects, a list of important terms and types of problems (including section references), and links to related information on the Web.
- Real-World Problem-Solving Emphasis: Polya’s method of problem solving is used throughout the text. Students learn how to apply these techniques to solve problems they encounter in their everyday lives in such areas as finance (installment buying, amortization, annuities) and voting and apportionment.
- WEBASSIGN: NATURE OF MATHEMATICS, 13th 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..
- Flexibility: The chapters are independent of one another and allow maximum teaching flexibility.
- Learning Aids: The book offers a variety of interesting and helpful learning aids. Icons, like "Caution" and "Stop," guide students through concepts. "Historical Notes" place students’ view of mathematics in a historical perspective and include a category of related problems entitled "Historical Quest." "Chapter Summaries" include chapter review exercises, group research projects, and individual research projects. Additionally, a list of important terms and types of problems, including section references, is available to students at www.mathnature.com.
- Exercise Sets: Problems range from easy to challenging and are clearly marked by type. "Level 1" problems are mechanical or drill. "Level 2" problems require the understanding of concepts. "Level 3" problems require problem-solving skills or original thinking.
- Communication Skills: "In Your Own Words" problems provide students with practice in communicating the concepts they’ve learned. These problems are especially helpful for education majors who will go on to teach in secondary schools.
- Research: "Individual Research Projects" help students apply what they are learning to familiar situations. These projects require research or library work, further reinforcing for students the value of mathematical concepts in a variety of fields.
- Group Work: "Group Research Projects" require collaborative research work and are suitable for larger-scale class projects.
1. THE NATURE OF PROBLEM SOLVING.
The Nature of Problem Solving. Problem Solving. Inductive and Deductive Reasoning. Scientific Notation and Estimation. Summary.
2. THE NATURE OF SETS.
Sets, Subsets, and Venn Diagrams. Operations with Sets. Applications of Sets. Finite and Infinite Sets. Summary.
3. THE NATURE OF LOGIC.
Deductive Reasoning. Truth Tables and the Conditional. Operators and Laws of Logic. The Nature of Proof. Problem Solving Using Logic. Logic Circuits (Optional). Summary.
4. THE NATURE OF NUMERATION SYSTEMS.
Early Numeration Systems. Hindu-Arabic Numeration System. Different Numeration Systems. Binary Numeration System. History of Calculating Devices (Optional). Summary.
5. THE NATURE OF NUMBERS.
Natural Numbers. Prime Numbers. Integers. Rational Numbers. Irrational Numbers. Groups, Fields, and Real Numbers. Discrete Mathematics. Cryptography (Optional). Summary.
6. THE NATURE OF ALGEBRA.
Polynomials. Factoring. Evaluation, Applications, and Spreadsheets. Equations. Inequalities. Algebra in Problem Solving. Ratios, Proportions, and Problem Solving.
Percents. Modeling Uncategorized Problems. Summary.
7. THE NATURE OF GEOMETRY.
Geometry. Polygons and Angles. Triangles. Similar Triangles. Right Triangle Trigonometry (Optional). Mathematics, Art, and Non-Euclidean Geometries (Optional Sections). Summary.
8. THE NATURE OF MEASUREMENT.
Perimeter. Area. Surface Area, Volume and Capacity. Miscellaneous Measurements (Optional). U.S.-Metric Conversions. Summary.
9. THE NATURE OF NETWORKS AND GRAPH THEORY.
Euler Circuits and Hamiltonian Cycles. Trees and Minimum Spanning Trees. Topology and Fractals. Guest Essay: “What Good Are Fractals?” . Summary.
10. THE NATURE OF GROWTH.
Exponential Equations. Logarithmic Equations. Applications of Growth and Decay. Summary.
11. THE NATURE OF SEQUENCES, SERIES, AND FINANCIAL MANAGEMENT.
Interest. Installment Buying. Sequences. Series. Annuities. Amortization. Summary of Financial Formulas. Summary.
12. THE NATURE OF COUNTING.
Permutations. Combinations. Counting without Counting. Rubik’s Cube and Instant Insanity (Optional). Summary.
13. THE NATURE OF PROBABILITY.
Introduction to Probability. Mathematical Expectation. Probability Models. Calculated Probabilities. GUEST ESSAY: "EXTRASENSORY PERCEPTION". "Bayes'' Theorem". The
Binomial Distribution (Optional). Summary.
14. THE NATURE OF STATISTICS.
Frequency Distributions and Graphs. Descriptive Statistics. The Normal Curve. Correlation and Regression. Sampling (Optional). Summary.
15. THE NATURE OF GRAPHS AND FUNCTIONS.
Cartesian Coordinates and Graphing Lines. Graphing Half-Planes. Graphing Curves. Conic Sections.Functions. Summary.
16. THE NATURE OF MATHEMATICAL SYSTEMS.
Systems of Linear Equations. Problem Solving with Systems. Matrix Solution of a System of Equations. Inverse Matrices. Modeling with Linear Programming (Optional). Summary.
17. THE NATURE OF VOTING AND APPORTIONMENT.
Voting. Voting Dilemmas. Apportionment. Apportionment Flaws. Summary.
18. THE NATURE OF CALCULUS (OPTIONAL).
What Is Calculus? Limits. Derivatives. Integrals. Summary.
Epilogue: Why Not Math? Mathematics in the Natural Sciences, Social Sciences, and in the Humanities.
B. Selected Answers.
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.
Written by author Karl Smith, the Instructor's Manual provides worked-out solutions to all of the problems in the text. For instructors only.
This CD-ROM provides the instructor with dynamic media tools for teaching. Create, deliver, and customize tests (both print and online) in minutes with ExamView® Computerized Testing Featuring Algorithmic Equations. Easily build solution sets for homework or exams using Solution Builder's online solutions manual. Microsoft® PowerPoint® lecture slides and figures from the book are also included on this CD-ROM.
Annotated Instructor's Edition
The Annotated Instructor's Edition features an appendix containing the answers to all problems in the book as well as icons denoting which problems can be found in Enhanced WebAssign.
Student Survival and Solutions Manual
The Student Survival and Solutions Manual provides helpful study aids and fully worked-out solutions to all of the odd-numbered exercises in the text. It's a great way to check your answers and ensure that you took the correct steps to arrive at an answer.