Experience mathematics--and develop problem-solving skills that will benefit you throughout your life--with THE NATURE OF MATHEMATICS and its accompanying online learning tools. Karl Smith introduces you to proven problem-solving techniques and shows you how to use these techniques to solve unfamiliar problems. You’ll also find coverage of interesting historical topics, and practical applications to settings and situations that you encounter in your day-to-day world, such as finance (amortization, installment buying, annuities) and voting. With this book’s guidance, you’ll both understand mathematical concepts and master the techniques.
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.
-
Karl J. 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.
-
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.
-
Communication Skills: "In Your Own Words" problems provide you with practice in communicating the concepts you’ve learned. These problems are especially helpful for education majors who will go on to teach in secondary schools.
-
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.
Cengage Testing, powered by Cognero® for Smith’s Nature of Mathematics, Instant Access
9781305657830
Cengage Testing, powered by Cognero® for Smith's Nature of Mathematics
9781305657823
Instructor's Web Site with Complete Solutions Manual for Smith's Nature of Mathematics, 13th
9781305657779
Online PowerPoint® for Smith's Nature of Mathematics, 13th
9781305657816