Stephen Abbott is currently a member of the Department of Mathematics and Computer Science at Middlebury College. He has held visiting positions at St. Olaf College and the University of Virginia, and in 1998 received the Llewellyn R. Perkins Award at Middlebury for excellence in teaching in the mathematical sciences. His published work includes articles in the areas of operator theory and functional analysis, the algorithmic foundations of robotics, and the plays of Tom Stoppard.
Understanding Analysis
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- Nombre de pages257
- PrésentationRelié
- Poids0.535 kg
- Dimensions16,1 cm × 24,0 cm × 2,1 cm
- ISBN0-387-95060-5
- EAN9780387950600
- Date de parution24/02/2001
- CollectionUndergraduate texts in maths
- ÉditeurSpringer
Résumé
Understanding Analysis outlines on elementary, one-semester course designed to expose students to the rich rewards inherent in taking a mathematically rigorous approach to the study of functions of a real variable. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on the questions that give analysis its inherent fascination. Does the Cantor set contain any irrational numbers? Can the set of points where a function is discontinuous be arbitrary? Are derivatives continuous? Are derivatives integrable? Is an infinitely differentiable function necessarily the limit of its Taylor series? In giving these topics center stage, the hard work of a rigorous study is justified by the fact that they are inaccessible
without it.