- Paperback: 452 pages
- Publisher: Springer; 2009 edition (May 29, 2009)
- Language: English
- ISBN-10: 0387773789
- ISBN-13: 978-0387773780
- Product Dimensions: 6.1 x 1.1 x 9.2 inches
- Shipping Weight: 1.4 pounds (View shipping rates and policies)
- Average Customer Review: 5.0 out of 5 stars See all reviews (1 customer review)
- Amazon Best Sellers Rank: #2,403,762 in Books (See Top 100 in Books)
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Problems in Real Analysis: Advanced Calculus on the Real Axis 2009th Edition
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From the reviews:
"The book … is a problem book in real analysis, chosen mostly from mathematical Olympiads and from problem journals. … The book focuses on analysis on the real line, which is also known as advanced real calculus. … the book under review is a collection of interesting and fresh problems with detailed solutions. The target audience seems to be students preparing for Olympiads and other competitions, but undergraduate students, mathematics teachers and professors of Mathematical Analysis and Calculus courses may also find interesting things here." (Mehdi Hassani, The Mathematical Association of America, August, 2009)
“In this book, the authors intend ‘to build a bridge between ordinary high-school or undergraduate exercises and more difficult and abstract concepts or problems’ in mathematical analysis. … The book may readily be used as a self-study text or … as a classroom text. The introductory material in each section is reasonably self-contained and includes interesting examples and applications. … the collection is a very worth-while contribution and should be included in every high school, college, and university mathematics library collection.” (F. J. Papp, Zentralblatt MATH, Vol. 1209, 2011)
From the Back Cover
Problems in Real Analysis: Advanced Calculus on the Real Axis features a comprehensive collection of challenging problems in mathematical analysis that aim to promote creative, non-standard techniques for solving problems. This self-contained text offers a host of new mathematical tools and strategies which develop a connection between analysis and other mathematical disciplines, such as physics and engineering. A broad view of mathematics is presented throughout; the text is excellent for the classroom or self-study. It is intended for undergraduate and graduate students in mathematics, as well as for researchers engaged in the interplay between applied analysis, mathematical physics, and numerical analysis.
*Uses competition-inspired problems as a platform for training typical inventive skills;
*Develops basic valuable techniques for solving problems in mathematical analysis on the real axis and provides solid preparation for deeper study of real analysis;
*Includes numerous examples and interesting, valuable historical accounts of ideas and methods in analysis;
*Offers a systematic path to organizing a natural transition that bridges elementary problem-solving activity to independent exploration of new results and properties.
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Top Customer Reviews
Indeed, I really like this book. It is a beautiful companion to any standard real analysis text. It will make studying more enjoyable and interesting. And it is not only for those who are learning the topic. Students who know it will also benefit as they can study problems they have not encountered in the traditional curriculum. However, the book cannot be used as a standalone text. Due to the problems from the mathematical competitions and from various professional journals which are used throughout the book and which consume the largest part of the book, the main body of real analysis is presented briefly. At the same time, traditional examples, constructions, etc. which are common to standard texts are omitted. Another issue that potential readers should be aware of is the following: Although the title of the book is Real Analysis, there is no measure theory and no Lebesgue integration in the book. The book goes as far as Riemann integration only. I do not believe that this is a serious flaw but readers who will use it while they are studying these topics will not have the opportunity to study related problems. For the remaining topics there is virtually a corresponding problem for each and every idea and concept.
The authors have place considerable effort and work to make this book as good as possible. So, overall, I strongly recommend this book. I believe it should find its way in every serious mathematician's library.