Be An Expert in Mathematics Calculations: Shortcuts & Tricks

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. 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. 'an Unabridged, Slightly Corrected Republication Of The 1981 Edition Of The Work First Published By Penguin Books, Harmondsworth, Middlesex, England, 1975. The Author Has Written A New Preface And Some Notes Especially For This Edition'--t.p. Verso. Includes Bibliographical References (p.p. [322]-334) And Index. -- 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 Indirecting 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 Ian Stewart. An Unabridged, Slightly Corrected Republication Of The 1981 Edition Of The Work First Published By Penguin Books, Harmondsworth, Middlesex, England, 1975. The Author Has Written A New Preface And Some Notes Especially For This Edition--t.p. Verso. Includes Bibliographical References (p. [322]-334) And Index. 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 other subjects. No advanced mathematical background is needed to follow thought-provoking discussions of such topics as functions, symmetry, axiomatics, counting, topology, hyperspace, linear algebra, and more. 200 illustrations.