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Home > Mathematics and Science Textbooks > Mathematics > Calculus and mathematical analysis > Real analysis, real variables > A Guide to Advanced Real Analysis: (Dolciani Mathematical Expositions)
A Guide to Advanced Real Analysis: (Dolciani Mathematical Expositions)

A Guide to Advanced Real Analysis: (Dolciani Mathematical Expositions)


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About the Book

This concise guide to real analysis covers the core material of a graduate level real analysis course. On the abstract level, it covers the theory of measure and integration and the basics of point set topology, functional analysis, and the most important types of function spaces. On the more concrete level, it also deals with the applications of these general theories to analysis on Euclidean space: the Lebesgue integral, Hausdorff measure, convolutions, Fourier series and transforms, and distributions. The relevant definitions and major theorems are stated in detail. Proofs, however, are generally presented only as sketches, in such a way that the key ideas are explained but the technical details are omitted. In this way a large amount of material is presented in a concise and readable form. The prerequisite is a familiarity with classical real-variable theory.

Table of Contents:
Preface; Prologue: notation, terminology, and set theory; Numbers; sets and mappings; Zorn's lemma; 1. Topology; 2. Measure and integration: general theory; 3. Measure and integration; 4. Rudiments of functional analysis; 5. Function spaces; 6. Topics in analysis on Euclidean space; Bibliography; Index.

About the Author :
Gerald B. Folland was born and raised in Salt Lake City, Utah. He received his bachelor's degree from Harvard University in 1968 and his doctorate from Princeton University in 1971. After two years at the Courant Institute, he moved to the University of Washington, where he is now professor of mathematics. He is the author of ten textbooks and research monographs in the areas of real analysis, harmonic analysis, partial differential equations, and mathematical physics.

Review :
This work serves as a Baedeker to the more accessible parts of the terrain of advanced real analysis, providing an overview for those less familiar, a refresher for those more so, and a key to the features of that terrain, including what high points and cultural monuments to visit if planning to explore the subject more seriously. Intended as a guide for grduate students preparing for qualifying exams." - F. E. J. Linton, Choice "The book covers material that is standardly taught at universities in graduate courses of real analysis and measure theory, plus some extra material from point-set topology and functional analysis, including some basic facts from the theory of function spaces. On the one hand it is written in a very skillful manner in a brief and concise reader-friendly way, but, on the other hand, the text is surprisingly comprehensive. … The book is a wonderful example of how much can be achieved in a relatively small space." - Lubos Pick, Mathematical Reviews


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Product Details
  • ISBN-13: 9780883853436
  • Publisher: Mathematical Association of America
  • Publisher Imprint: Mathematical Association of America
  • Height: 236 mm
  • No of Pages: 110
  • Series Title: Dolciani Mathematical Expositions
  • Weight: 280 gr
  • ISBN-10: 0883853434
  • Publisher Date: 30 Nov 2009
  • Binding: Hardback
  • Language: English
  • Returnable: N
  • Spine Width: 11 mm
  • Width: 157 mm


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