Nelson Higher Education

Higher Education

Nature of Mathematics, 13th Edition

  • Karl Smith
  • ISBN-10: 1133947255
  • ISBN-13: 9781133947257
  • 1024 Pages | Hardcover
  • Previous Editions: 2012, 2007, 2004
  • COPYRIGHT: 2017 Published
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Overview

About the Product

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.

Features

  • 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.

  • 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.

About the Author

Karl Smith

Karl Smith is professor emeritus at Santa Rosa Junior College in Santa Rosa, California. He has written over 36 mathematics textbooks and believes that students can learn mathematics if it is presented to them through the use of concrete examples designed to develop original thinking, abstraction, and problem-solving skills. Over one million students have learned mathematics from Karl Smith's textbooks.

Table of Contents

Prologue: Why Math? A Historical Overview.
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.
Appendices.
A. Glossary.
B. Selected Answers.
C. Index.

New to this edition

  • NOTE: This title is also available in WebAssign with Corequisite Support that provides the flexibility to match any corequisite implementation model and empowers you to deliver high quality content at the right time for your students at an affordable price.
  • "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.
  • 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.

Supplements

All supplements have been updated in coordination with the Main title.
Please see Main title page for new to this edition information.

Instructor Supplements

WebAssign ePin, Single-Term  (ISBN-10: 1337652172 | ISBN-13: 9781337652179)

WebAssign for Smith's Nature of Mathematics, 13th edition is a flexible and fully customizable online instructional solution that puts powerful tools in the hands of instructors, enabling you deploy assignments, instantly assess individual student and class performance, and help your students master the course concepts. With WebAssign’s powerful digital platform and [title] specific content, you can tailor your course with a wide range of assignment settings, add your own questions and content, and access student and course analytics and communication tools.

Student Supplements

Activities Booklet for Liberal Arts Mathematics and Quantitative Reasoning Courses  (ISBN-10: 0357025628 | ISBN-13: 9780357025628)

This ancillary includes real-world/applied projects that can be used in a variety of ways that supplements what is in the textbook. It can be used as single or group collaborative activities in a variety of classrooms styles (such as traditional or active learning).

WebAssign ePin, Single-Term  (ISBN-10: 1337652172 | ISBN-13: 9781337652179)

IMPORTANT: This instant access code includes access to WebAssign for only one term. When purchasing please ensure that you are using it for ONLY ONE TERM of the following course areas: Calculus, Physics or Chemistry. Use with a different course may cause complications with access. This code will NOT allow access beyond one semester. WebAssign engages you with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping you to develop a deeper conceptual understanding of the subject matter. This instant access code will be delivered via email when purchased. If you are not certain this is the correct access code for your course, please contact your instructor.

WebAssign, Single-Term Instant Access  (ISBN-10: 1337879681 | ISBN-13: 9781337879682)

WebAssign for Nature of Mathematics helps you prepare for class with confidence. Its online learning platform for your math, statistics and science courses helps you practice and absorb what you learn. Videos and tutorials walk you through concepts when you're stuck, and instant feedback and grading let you know where you stand--so you can focus your study time and perform better on in-class assignments. Study smarter with WebAssign!