Concepts of Modern Mathematics

Ian Stewart

Publié par Dover, le 01 février 1995

340 pages

Résumé

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 authors lucid and thought-provoking discussions of such topics as functions, symmetry, axiomatics, counting, topology, hyperspace, linear algebra, real analysis, probability, computers, applications of modem mathematics and much more. By the time readers have finished this book, they'll have a much clearer grasp of how modem 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.