The Nature of Problem Solving in Algebra : A Liberal Arts Approach (with BCA/iLrn' Tutorial and InfoTrac (R))
A liberal arts approach (with bca/ilrn tutorial and infotrac)
Published on 9. September 2003
Book
Hardback
592 pages
978-0-534-42147-2 (ISBN)
Description
Liberal Arts mathematics books often cover much more material than can be addressed in a one-semester course. Karl Smith has created a solution to this problem with his new book: THE NATURE OF PROBLEM SOLVING IN ALGEBRA. Loyal customers of Karl Smith's books laud his clear writing, coverage of historical topics, selection of topics, and emphasis on problem solving. Based on the successful NATURE OF MATHEMATICS text, this new book is designed to give you only the chapters and information you need, when you need it. Smith takes great care to provide insight into precisely what mathematics is--the nature of mathematics--what it can accomplish, and how it is pursued as a human enterprise. At the same time, Smith emphasizes Polya's problem-solving method throughout the text so students can take from the course an ability to estimate, calculate, and solve problems outside the classroom. Moreover, Smith's writing style gives students the confidence and ability to function mathematically in their everyday lives.
This new text emphasizes problem solving and estimation, which, along with numerous in-text study aids, encourage students to understand the concepts as well as mastering techniques.
This new text emphasizes problem solving and estimation, which, along with numerous in-text study aids, encourage students to understand the concepts as well as mastering techniques.
Reviews / Votes
Prologue--Why Math? An Historical Overview. 1. THE NATURE OF PROBLEM SOLVING. Problem Solving. Inductive and Deductive Reasoning. Scientific Notation and Estimation. Finite and Infinite. 2. THE NATURE OF NUMERATION SYSTEMS. Early Numeration Systems. Hindu-Arabic Numeration Systems. Different Numeration Systems. Binary Numeration Systems. History of Calculating Devices. 3. THE NATURE OF NUMBERS. Natural Numbers. Prime Numbers. Integers. Rational Numbers. Irrational Numbers. Groups, Fields, and Real Numbers. Discrete Mathematics. Cryptography. 4. 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. 5. THE NATURE OF GROWTH. Logarithms and Exponents. Exponential Equations. Logarithmic Equations. Applications of Growth and Decay. 6. THE NATURE OF SEQUENCES, SERIES AND FINANCIAL MANAGEMENT. Interest. Installment Buying. Sequences. Series. Annuities. Amortization. Summary of Financial Formulas. 7. THE NATURE OF GRAPHS AND FUNCTIONS. Cartesian Coordinates and Graphing Lines. Graphing Half-Planes. Graphing Curves. Conic Sections. Functions. 8. THE NATURE OF MATHEMATICAL SYSTEMS. Systems of Linear Equations. Problem Solving with Systems. Matrix Solution of a System of Equations. Inverse Matrices. Systems of Inequalities. Modeling with Linear Programming. 9. THE NATURE OF NETWORKS AND GRAPH THEORY. Euler Circuits and Hamiltonian Cycles. Trees and Minimum Spanning Trees. Topology and Fractals. Guest Essay: Chaos. 10. THE NATURE OF VOTING AND APPORTIONMENT. Voting. Voting Dilemmas. Apportionment. Apportionment Flaws. Epilogue--Why Not Math? Mathematics In The Natural Sciences, Social Sciences, And In The Humanities. Appendices: A. Glossary. B. Selected Answers. C. Credits. D. Index.More details
Edition
New edition
Language
English
Place of publication
CA
United States
Publishing group
Cengage Learning, Inc
Target group
College/higher education
Professional and scholarly
Edition type
New edition
ISBN-13
978-0-534-42147-2 (9780534421472)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
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.
Content
Prologue--Why Math? An Historical Overview. 1. THE NATURE OF PROBLEM SOLVING. Problem Solving. Inductive and Deductive Reasoning. Scientific Notation and Estimation. Finite and Infinite. 2. THE NATURE OF NUMERATION SYSTEMS. Early Numeration Systems. Hindu-Arabic Numeration Systems. Different Numeration Systems. Binary Numeration Systems. History of Calculating Devices. 3. THE NATURE OF NUMBERS. Natural Numbers. Prime Numbers. Integers. Rational Numbers. Irrational Numbers. Groups, Fields, and Real Numbers. Discrete Mathematics. Cryptography. 4. 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. 5. THE NATURE OF GROWTH. Logarithms and Exponents. Exponential Equations. Logarithmic Equations. Applications of Growth and Decay. 6. THE NATURE OF SEQUENCES, SERIES AND FINANCIAL MANAGEMENT. Interest. Installment Buying. Sequences. Series. Annuities. Amortization. Summary of Financial Formulas. 7. THE NATURE OF GRAPHS AND FUNCTIONS. Cartesian Coordinates and Graphing Lines. Graphing Half-Planes. Graphing Curves. Conic Sections. Functions. 8. THE NATURE OF MATHEMATICAL SYSTEMS. Systems of Linear Equations. Problem Solving with Systems. Matrix Solution of a System of Equations. Inverse Matrices. Systems of Inequalities. Modeling with Linear Programming. 9. THE NATURE OF NETWORKS AND GRAPH THEORY. Euler Circuits and Hamiltonian Cycles. Trees and Minimum Spanning Trees. Topology and Fractals. Guest Essay: Chaos. 10. THE NATURE OF VOTING AND APPORTIONMENT. Voting. Voting Dilemmas. Apportionment. Apportionment Flaws. Epilogue--Why Not Math? Mathematics In The Natural Sciences, Social Sciences, And In The Humanities. Appendices: A. Glossary. B. Selected Answers. C. Credits. D. Index.