Concepts of Modern Mathematics (eBook)

Ian Stewart (Autor)

eBook Download: EPUB

2012
368 Seiten
Dover Publications (Verlag)
978-0-486-13495-6 (ISBN)

Infos

In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra, and other mathematical subjects. 200 illustrations.

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Some years ago, "e;new math"e; 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 "e;new math"e; 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 "e;new math"e;: 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 "e;new math"e; leads toward a genuine comprehension of the nature of mathematics itself.

Inhalt

Preface to the Dover EditionPreface to the First Edition1. Mathematics in General2. Motion without Movement3. Short Cuts in the Higher Arithmetic4. The Language of Sets5. What is a Function?6. The Beginnings of Abstract Algebra7. Symmetry: The Group Concept8. Axiomatics9. Counting: Finite and Infinite10. Topology11. The Power of Indirect Thinking12. Topological Invariants13. Algebraic Topology14. Into Hyperspace15. Linear Algebra16. Real Analysis17. The Theory of Probability18. Computers and Their Uses19. Applications of Modern Mathematics20. FoundationsAppendixNotesGlossary of SymbolsIndex

Produkt-Details

• Erscheint lt. Verlag: 23.5.2012
• Reihe/Serie: Dover Books on Mathematics
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Maße: 140 x 140 mm
• Themenwelt: Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Schlagworte: abstract algebra • advanced concepts • advanced math • Albert Einstein • Algebraic • Applications • Applied mathematics • arithmetic • books on abstract algebras • books on advanced concepts • books on advanced maths • books on albert einstein • books on applied mathematics • books on central ideas • books on college maths • books on education majors • books on euclidean geometries • books on fundamental concepts • books on graph theories • books on learn maths • books on liberal arts • books on math classes • books on math courses • books on mathematical concepts • books on mathematics degrees • books on odd times • books on projective geometries • books on pure maths • books on school mathematics • books on studying mathematics • books on theory classes • books on undergraduate degrees • Calculus • central ideas • college math • combinatorial • combinatorics • conic • Constructions • Courant • cuts • education majors • Euclid • Euclidean Geometry • Exercises • Functions • fundamental concepts • Geometric • geometries • graph theory • Hilbert • hyperspace • Layman • learning math • learn math • Liberal Arts • math classes • math courses • mathematical background • mathematical concepts • Mathematicians • mathematics degree • Maths • non-mathematician • odd times • one-semester • Partitions • pleasant memories • primitive roots • Projective Geometry • proofs • pure math • Quadratic • riemannian • robbins • school mathematics • studying mathematics • study mathematics • textbooks • Theorems • theory class • Topology • trig • Trigonometry • undergraduate degree • understanding modern • understand modern • wait awhile • waiting awhile
• ISBN-10: 0-486-13495-4 / 0486134954
• ISBN-13: 978-0-486-13495-6 / 9780486134956