Problems in Real Analysis 2nd Edition by Charalambos D. Aliprantis (PDF)

Description

A collection of problems and solutions in real analysis based on the major textbook, Principles of Real Analysis (also by Aliprantis and Burkinshaw), Problems in Real Analysis is the ideal companion for senior science and engineering undergraduates and first-year graduate courses in real analysis. It is intended for use as an independent source, and is an invaluable tool for students who wish to develop a deep understanding and proficiency in the use of integration methods.Problems in Real Analysis teaches the basic methods of proof and problem-solving by presenting the complete solutions to over 600 problems that appear in Principles of Real Analysis, Third Edition. The problems are distributed in forty sections, and cover the entire spectrum of difficulty.

User’s Reviews

Editorial Reviews: Review “First published in 1981 as a textbook for undergraduate seniors and first-year graduate students in math, this iteration adds Fourier analysis, a chapter on Hilbert spaces, and about 150 new problems of varying difficulty. Aliprantis (economics and mathematics, Purdue U.) and Burkinshaw (mathematical sciences, Indiana U., Purdue U.) focus on measure theory via the semiring approach and the Lebesgue integral as well as their applications. They also cover topology and continuity, normed spaces, and special topics in integration. A humanistic touch: brief biographies of historical contributors to real analysis are interwoven throughout the text.” –Book News, Inc.®, Portland, OR From the Back Cover Professors Aliprantis and Burkinshaw’s Problems in Real Analysis, 2nd Edition, is designed to equip the reader with the tools to succeed in the real Analysis course. Published as a companion to their successful Principles of Real Analysis, 3rd Edition, this book teaches the basic methods of proof and problem-solving by presenting the complete solutions to over 600 problems that appeal in Principles of Real Analysis. The problem sets cover the entire spectrum of difficulty: some are routine, some require a good grasp of the material involved, and some are exceptionally challenging.This is the first book to offer complete solutions to graduate level problems in real analysis. It is ideal for all under graduate and first-year graduate analysis courses. Students and scholars from all branches of science and engineering will also find this collection of problems an invaluable reference source.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is the younger brother of the authors’s “Principles of Real Analysis”, but it can be used with the first half of Rudin’s “Real and Complex Analysis” or with most boks on the subject, including Apostol and Dieudonné classical MA works (I recently purchased the fantastic Burrill by and Knudsen “Real Variables” and Pugh’s “Real Math. Analysis” and I find that this problem book provides a lot of additional background for them. The scope goes from basic questions on metric spaces to Riesz and Radon-Nikodym paraphernalia. The difficulty is always reasonable. And a lot of detail and attention is provided everywhere. I found the computational exercises on Lebesgue measure and integration particularly interesting (for example, those dealing with improper integrals, where theoretical arguments provide a solid basis for calculus) . The Riemann integral is often used and compared with Lebesgue integral. Maybe, problems Fourier Analysis needed more extension, but nobody is perfect. You can look that in Körner’s problem book on Fourier Analysis.

⭐There is no problem solutions for Real Analysis texts available in U.S. since most of the teachers believe that Math students in grad level should be more creative. However, not all students in Real Analysis are potential mathmatician. If they lost in class and must study by theirselves, they may feel frustrated missing all the stuff contained in problems. The material in “Principles of Real Analysis” may not superior much than other famous text(like Royden, I think Royden is clear enough but too much mysterious things lie in problems.). But use it with this workbook, you will find much comfortable in self study. It helps a lot not only in my homework assignment, but also in my understanding.

⭐great book for school

⭐Love it!!

⭐Excellent book!

⭐perfect!

⭐This book rocks! It covers practically all the major topics of an introductory course in graduate Real Analysis. Excellent solutions that aid in the understanding of the material. This book’s worth is immeasurable, or should I say, non-measurable.

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