Some years ago, "new math" took the country's classrooms by storm. Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts. The result, at least at first, was a great deal of confusion among teachers, students, and parents. Since then, the negative aspects of "new math" have been eliminated and its positive elements assimilated into classroom instruction. In this charming volume, a noted English mathematician ... Read More
Some years ago, "new math" took the country's classrooms by storm. Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts. The result, at least at first, was a great deal of confusion among teachers, students, and parents. Since then, the negative aspects of "new math" have been eliminated and its positive elements assimilated into classroom instruction. In this charming volume, a noted English mathematician ... Read More
Description
Some years ago, "new math" took the country's classrooms by storm. Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts. The result, at least at first, was a great deal of confusion among teachers, students, and parents. Since then, the negative aspects of "new math" have been eliminated and its positive elements assimilated into classroom instruction. In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math": groups, sets, subsets, topology, Boolean algebra, and more. According to Professor Stewart, an understanding of these concepts offers the best route to grasping the true nature of mathematics, in particular the power, beauty, and utility of pure mathematics. No advanced mathematical background is needed (a smattering of algebra, geometry, and trigonometry is helpful) to follow the author's lucid and thought-provoking discussions of such topics as functions, symmetry, axiomatics, counting, topology, hyperspace, linear algebra, real analysis, probability, computers, applications of modern mathematics, and much more. By the time readers have finished this book, they'll have a much clearer grasp of how modern mathematicians look at figures, functions, and formulas and how a firm grasp of the ideas underlying "new math" leads toward a genuine comprehension of the nature of mathematics itself.
Reprint of the Penguin Books, Harmondsworth, Middlesex, England, 1981 edition.
Details
Price: $16.95
Pages: 368
Publisher: Dover Publications
Imprint: Dover Publications
Series: Dover Books on Mathematics
Publication Date: 1st February 1995
Trim Size: 5.5 x 8.5 in
ISBN: 9780486284248
Format: Paperback
BISACs: MATHEMATICS / Recreations & Games MATHEMATICS / History & Philosophy MATHEMATICS / General
Author Bio
Ian Stewart, an active popularizer of mathematics, is Professor of Mathematics at England's University of Warwick and a former columnist for Scientific American's "Mathematical Games" column. In 1995, he won math's version of the Nobel Prize, the Michael Faraday Medal.
Martin Golubitsky is Distinguished Professor of Mathematics and Physical Sciences at Ohio State University, where he serves as Director of the Mathematical Biosciences Institute.
Ian Stewart: Winner of the Michael Faraday Medal Professor Emeritus at Britain's University of Warwick, and Fellow of the Royal Society, Ian Stewart has entertained and instructed readers with a few dozen books, five of which have found their way to Dover: Catastrophe Theory and Its Applications (with Tim Poston, 1996); Concepts of Modern Mathematics, (1995); Another Fine Math You've Got Me Into (2003); Game, Set and Math (2007); and Fearful Symmetry (with Martin Golubitsky, 2011).
His overall output has been wide and various with books on 'straight' mathematics, mathematics teaching, science fiction, as well as a very popular three-volume series, The Science of Discworld, with Terry Pratchett and Jack Cohen.
In the Author's Own Words: "By the 18th century science had been so successful in laying bare the laws of nature that many thought there was nothing left to discover. Immutable laws prescribed the motion of every particle in the universe, exactly and forever: the task of the scientist was to elucidate the implications of those laws for any particular phenomenon of interest. Chaos gave way to a clockwork world. But the world moved on. . . . Today even our clocks are not made of clockwork. . . . With the advent of quantum mechanics, the clockwork world has become a lottery. Fundamental events, such as the decay of a radioactive atom, are held to be determined by chance, not law." — Ian Stewart Critical Acclaim for Fearful Symmetry: "This book's central theme involves two remarkably nonintuitive facts. First, a completely symmetric plane looks the same at every point and from every angle. We find this uninteresting and pay it no heed. Thus, what we detect as symmetry is, in fact, those symmetries that remain after the greater symmetry has been broken. Second, the study of symmetry is really the study of groups of transformations. Stewart and Golubitsky show how these modern mathematical concepts can be used to describe many of the most interesting features of the physical and biological world. This is not an easy book but well worth the effort." — Library Journal
Table of Contents
Preface to the Dover Edition Preface to the First Edition 1. Mathematics in General 2. Motion without Movement 3. Short Cuts in the Higher Arithmetic 4. The Language of Sets 5. What is a Function? 6. The Beginnings of Abstract Algebra 7. Symmetry: The Group Concept 8. Axiomatics 9. Counting: Finite and Infinite 10. Topology 11. The Power of Indirect Thinking 12. Topological Invariants 13. Algebraic Topology 14. Into Hyperspace 15. Linear Algebra 16. Real Analysis 17. The Theory of Probability 18. Computers and Their Uses 19. Applications of Modern Mathematics 20. Foundations Appendix Notes Glossary of Symbols Index
Some years ago, "new math" took the country's classrooms by storm. Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts. The result, at least at first, was a great deal of confusion among teachers, students, and parents. Since then, the negative aspects of "new math" have been eliminated and its positive elements assimilated into classroom instruction. In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math": groups, sets, subsets, topology, Boolean algebra, and more. According to Professor Stewart, an understanding of these concepts offers the best route to grasping the true nature of mathematics, in particular the power, beauty, and utility of pure mathematics. No advanced mathematical background is needed (a smattering of algebra, geometry, and trigonometry is helpful) to follow the author's lucid and thought-provoking discussions of such topics as functions, symmetry, axiomatics, counting, topology, hyperspace, linear algebra, real analysis, probability, computers, applications of modern mathematics, and much more. By the time readers have finished this book, they'll have a much clearer grasp of how modern mathematicians look at figures, functions, and formulas and how a firm grasp of the ideas underlying "new math" leads toward a genuine comprehension of the nature of mathematics itself.
Reprint of the Penguin Books, Harmondsworth, Middlesex, England, 1981 edition.
Price: $16.95
Pages: 368
Publisher: Dover Publications
Imprint: Dover Publications
Series: Dover Books on Mathematics
Publication Date: 1st February 1995
Trim Size: 5.5 x 8.5 in
ISBN: 9780486284248
Format: Paperback
BISACs: MATHEMATICS / Recreations & Games MATHEMATICS / History & Philosophy MATHEMATICS / General
Ian Stewart, an active popularizer of mathematics, is Professor of Mathematics at England's University of Warwick and a former columnist for Scientific American's "Mathematical Games" column. In 1995, he won math's version of the Nobel Prize, the Michael Faraday Medal.
Martin Golubitsky is Distinguished Professor of Mathematics and Physical Sciences at Ohio State University, where he serves as Director of the Mathematical Biosciences Institute.
Ian Stewart: Winner of the Michael Faraday Medal Professor Emeritus at Britain's University of Warwick, and Fellow of the Royal Society, Ian Stewart has entertained and instructed readers with a few dozen books, five of which have found their way to Dover: Catastrophe Theory and Its Applications (with Tim Poston, 1996); Concepts of Modern Mathematics, (1995); Another Fine Math You've Got Me Into (2003); Game, Set and Math (2007); and Fearful Symmetry (with Martin Golubitsky, 2011).
His overall output has been wide and various with books on 'straight' mathematics, mathematics teaching, science fiction, as well as a very popular three-volume series, The Science of Discworld, with Terry Pratchett and Jack Cohen.
In the Author's Own Words: "By the 18th century science had been so successful in laying bare the laws of nature that many thought there was nothing left to discover. Immutable laws prescribed the motion of every particle in the universe, exactly and forever: the task of the scientist was to elucidate the implications of those laws for any particular phenomenon of interest. Chaos gave way to a clockwork world. But the world moved on. . . . Today even our clocks are not made of clockwork. . . . With the advent of quantum mechanics, the clockwork world has become a lottery. Fundamental events, such as the decay of a radioactive atom, are held to be determined by chance, not law." — Ian Stewart Critical Acclaim for Fearful Symmetry: "This book's central theme involves two remarkably nonintuitive facts. First, a completely symmetric plane looks the same at every point and from every angle. We find this uninteresting and pay it no heed. Thus, what we detect as symmetry is, in fact, those symmetries that remain after the greater symmetry has been broken. Second, the study of symmetry is really the study of groups of transformations. Stewart and Golubitsky show how these modern mathematical concepts can be used to describe many of the most interesting features of the physical and biological world. This is not an easy book but well worth the effort." — Library Journal
Preface to the Dover Edition Preface to the First Edition 1. Mathematics in General 2. Motion without Movement 3. Short Cuts in the Higher Arithmetic 4. The Language of Sets 5. What is a Function? 6. The Beginnings of Abstract Algebra 7. Symmetry: The Group Concept 8. Axiomatics 9. Counting: Finite and Infinite 10. Topology 11. The Power of Indirect Thinking 12. Topological Invariants 13. Algebraic Topology 14. Into Hyperspace 15. Linear Algebra 16. Real Analysis 17. The Theory of Probability 18. Computers and Their Uses 19. Applications of Modern Mathematics 20. Foundations Appendix Notes Glossary of Symbols Index