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Nature of Mathematics, 13th Edition

Karl Smith

  • Copyright 2017
  • {{checkPublicationMessage('Published', '2016-01-01T00:00:00+0000')}}
Starting At £36.00 See pricing and ISBN options
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Nature of Mathematics 13th Edition by Karl Smith
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Overview

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 complete 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.

Instructors and students benefit from WebAssign content updates without having to transition to a new edition, including new problem types such as Responsive Labs, a new Activities Booklet, and more.

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Meet the Authors

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Karl Smith

Karl Smith is professor emeritus at Santa Rosa Junior College in Santa Rosa, California. He has written more than 36 mathematics textbooks. He firmly 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. More than one million students have successful learned mathematics from Karl Smith's textbooks.

Features

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  • JUST IN TIME SUPPORT built into questions contains direct links to the eTextbook (Read It) and videos (Watch It).
  • EXPANDED PROBLEMS include intermediary steps to guide students to the final answer.
  • MASTER IT TUTORIALS break problems down into steps to help guide students through the mathematical process.
  • 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.
  • 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.
  • 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.
  • 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.
  • HISTORICAL QUEST PROBLEMS are designed to involve students in the historical development of the great ideas in mathematical history.
  • 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.
  • INDEPENDENT CHAPTERS allow for maximum teaching flexibility.
  • PROBLEM LEVELS 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.
  • 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.
  • 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 RESEARCH PROJECTS require collaborative research work and are suitable for larger-scale class projects.

Table of Contents

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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.

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Each WebAssign online product offers the full textbook combined with a flexible and fully customizable online instructional assignments and tools.

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  • ISBN-10: 1337879681
  • ISBN-13: 9781337879682
  • RETAIL £36.00
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  • ISBN-10: 0357540239
  • ISBN-13: 9780357540237
  • RETAIL £53.00

  • ISBN-10: 1133947255
  • ISBN-13: 9781133947257
  • RETAIL £88.99
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Supplements

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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.

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WebAssign Instant Access for Smith's Nature of Mathematics, Multi-Term

ISBN: 9781337879682
WebAssign for Nature of Mathematics is a flexible and fully customizable online instructional solution that puts powerful tools in the hands of instructors, enabling you to deploy assignments, instantly assess individual student and class performance and help your students master the course concepts. Enrich the teaching and learning experience with the superior content within the powerful digital platform of WebAssign. Tailor your course with a wide range of assignment settings, the ability to add your own questions and content, analytics at the individual and course level and student/teacher communication tools.