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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.
- Sales Rank: #1554686 in Books
- Published on: 2009-05-29
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x 1.08" w x 6.10" l, 1.45 pounds
- Binding: Paperback
- 452 pages
Review
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.
Key features:
*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.
About the Author
Teodora-Liliana Radulescu received her PhD in 2005 from Babes-Bolyai University of Cluj-Napoca, Romania, with a thesis on nonlinear analysis, and she is currently a professor of mathematics at the "Fratii Buzesti" National College in Craiova, Romania. She is a member of the American Mathematical Society and the Romanian Mathematical Society. She is also a reviewer for Mathematical Reviews and Zentralblatt fur Mathematik.
Vicentiu Radulescu received both his PhD and the Habilitation at the Université Pierre et Marie Curie (Paris 6), and he is currently a professor of mathematics at the University of Craiova, Romania and a senior researcher at the Institute of Mathematics "Simion Stoilow" of the Romanian Academy in Bucharest, Romania. He has authored 9 books and over 100 articles.
Titu Andreescu is an associate professor of mathematics at the University of Texas at Dallas. He is also firmly involved in mathematics contests and Olympiads, being the Director of AMC (as appointed by the Mathematical Association of America), Director of MOP, Head Coach of the USA IMO Team and Chairman of the USAMO. He has also authored a large number of books on the topic of problem solving and Olympiad-style mathematics.
Most helpful customer reviews
4 of 6 people found the following review helpful.
A really great book
By ScienceThinker
Around 2000 I had thought that a Real Analysis book should be written in which the various ideas, methods and results could be demonstrated using problems from mathematical competitions. My rationale was that there are many books on real analysis, each with its own characteristics, strengths and weaknesses but, at the end, all of them being very traditional in the core, presenting the material in the same dry way. Unfortunately, soon I stopped thinking about it. That is, until around 2010 when I discovered that a book, as I imagined it, had been published. Obviously, I had missed the opportunity to write such a book first. But I am not sure, even if I had done it, that the result would have been as good as this.
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.
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