Understanding Analysis

Description

Introduction to the Problems in Analysis outlines an elementary, one semester course which exposes students to both the process of rigor, and the rewards inherent in taking an axiomatic 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 questions which 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? Can the rational numbers be written as a countable intersection of open sets? Is an infinitely differentiable function necessarily the limit of its Taylor series? Giving these topics center stage, the motivation for a rigorous approach is justified by the fact that they are inaccessible without it.

First Sentence

Toward the end of his distinguished career, the renowned British mathematician G.H. Hardy eloquently laid out a justification for a life of studying mathematics in A Mathematician's Apology, an essay first published in 1940.

Subjects

Other Editions

• Understanding AnalysisSpringer2002-07-12
• Understanding AnalysisIsland Press2001-01-01
• Understanding AnalysisSpringer2010-01-01
• Understanding AnalysisSpringer London, Limited2015-01-01
• Understanding AnalysisSpringer New York2016-01-01
• Understanding AnalysisHardcoverimusti2016-08-22