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Exercises in Analysis: Part 1 (Problem Books in Mathematics), by Leszek Gasiński, Nikolaos S. Papageorgiou
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Exercises in Analysis will be published in two volumes. This first volume covers problems in five core topics of mathematical analysis: metric spaces; topological spaces; measure, integration and Martingales; measure and topology and functional analysis. Each of five topics correspond to a different chapter with inclusion of the basic theory and accompanying main definitions and results, followed by suitable comments and remarks for better understanding of the material. At least 170 exercises/problems are presented for each topic, with solutions available at the end of each chapter. The entire collection of exercises offers a balanced and useful picture for the application surrounding each topic.
This nearly encyclopedic coverage of exercises in mathematical analysis is the first of its kind and is accessible to a wide readership. Graduate students will find the collection of problems valuable in preparation for their preliminary or qualifying exams as well as for testing their deeper understanding of the material. Exercises are denoted by degree of difficulty. Instructors teaching courses that include one or all of the above-mentioned topics will find the exercises of great help in course preparation. Researchers in analysis may find this Work useful as a summary of analytic theories published in one accessible volume.
- Sales Rank: #359675 in Books
- Published on: 2014-07-27
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x 2.13" w x 6.14" l, .0 pounds
- Binding: Hardcover
- 1037 pages
Review
“The book presents most standard theorems in real analysis, topology and functional analysis as well as a variety of problems with their solutions. … The presentation is lucid and elegant. The notations are standard throughout the text. … useful to graduate students and faculty whose interests are in probability, finance, measure theory, topology, partial differential equations and operator theory … . Such a book certainly must live in every library where other mathematics books in the similar topics reside.” (Dhruba Adhikari, MAA Reviews, maa.org, December, 2015)
“The topics covered will carry almost any serious student from advanced undergraduate mathematics all the way through graduate qualifying examinations … . Summing Up: Recommended. Upper-division undergraduates and graduate students.” (D. V. Feldman, Choice, Vol. 52 (9), May, 2015)
“This volume is a collection of interesting problems in real analysis and functional analysis. It is addressed to advanced undergraduate and graduate students as well as to researchers in pure and applied analysis. … The entire collection of exercises offers a balanced and useful picture for the application surrounding each topic. The reviewer highly recommends this book to all mathematical libraries.” (Vicenţiu D. Rădulescu, zbMATH, Vol. 1298, 2014)
From the Back Cover
Exercises in Analysis will be published in two volumes. This first volume covers problems in five core topics of mathematical analysis: metric spaces; topological spaces; measure, integration, and Martingales; measure and topology; and functional analysis. Each of five topics correspond to a different chapter with inclusion of the basic theory and accompanying main definitions and results, followed by suitable comments and remarks for better understanding of the material. At least 170 exercises/problems are presented for each topic, with solutions available at the end of each chapter. The entire collection of exercises offers a balanced and useful picture for the application surrounding each topic.
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This nearly encyclopedic coverage of exercises in mathematical analysis is the first of its kind and is accessible to a wide readership. Graduate students will find the collection of problems valuable in preparation for their preliminary or qualifying exams as well as for testing their deeper understanding of the material. Exercises are denoted by degree of difficulty. Instructors teaching courses that include one or all of the above-mentioned topics will find the exercises of great help in course preparation. Researchers in analysis may find this Work useful as a summary of analytic theories published in one accessible volume.
About the Author
Leszek Gasińksi is the Chair of Optimization and Control Theory in the Institute of Computer Science at Jagiellonian University in Krakow, Poland. He is the co-author, along with Nikolaos S. Papageorgiou, of "Nonlinear Analysis" (CRC 2005) and "Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems" (CRC 2006). Nikolaos S. Papageorgiou is a Professor of Mathematics in the School of Applied Mathematical and Physical Sciences at National Technical University in Athens, Greece. He is the co-author, along with Leszek Gasińksi, of "Nonlinear Analysis" (CRC 2005) and "Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems" (CRC 2006).
Most helpful customer reviews
4 of 4 people found the following review helpful.
Nothing Quite Like it Since REA Problem Solvers
By Let's Compare Options Preptorial
Mathematicians, Physicists, STEM teachers and students, as well as older Engineers like me, who grew up with the 1,000 page plus REA Problem Solvers series (eg: Finite and Discrete Math Problem Solver (Problem Solvers Solution Guides)), will be overjoyed at this new series.
There are two senses in which it is a wonderful new approach-- first, it is one of a kind in topic (analysis, as you know touches thousands of subjects in and out of math), and second, it is completely focused on problem solving, as in advanced exam prep. I'm a quantitative/ math volunteer at preptorial dot org and our lives there are about the best test prep tools available. Today, this is a tough job because many text authors (or more specifically their publishers) love "splitting" their work into a series of expensive instructor and student student manuals, to make even more money after gouging students with the primary text.
Not so this text! All questions and answers are given in the text, and the focus is on problem solving-- giving exercises relevant to the material, then giving problems marked by difficulty level with fully explained solutions. Note that this material is clearly graduate level, or very bright ready for grad undergrad math majors. Even the "easier" problems are professional exam level.
The text is the most up to date analysis text out, regardless of format. I review hundreds of these for preptorial and none comes even close if your objective is problem solving or exam prep. In fact, going back even 10 years, the only series that even comes close is the outstanding MIT/China PhD series of test prep, and they are not nearly as comprehensive or up to date at this volume (example: Problems and Solutions on Thermodynamics and Statistical Mechanics (Major American Universities Ph.D. Qualifying Questions and Solutions) published by World Scientific Pub Co Inc (1990)).
In today's desktop supercomputing, Matlab, Mathcad, GNU Octave, NumPy worlds, "analysis" can be limited to formula application in some narrow definitions. That runs counter to the real world problems today that involve all four tools-- analysis, qualitative, numeric and stochastic. Amazingly, even with the analysis title, the problem set up and definition techniques are just like the exams-- and I see the real ones every day-- and DO NOT shy away from all three other techniques.
The price at $70 US from Springer is a shocker-- 1,000 page technical books from this publisher, especially with good journal references, are normally $300 plus and often don't even have websites or solution manuals, let alone complete solutions IN the text.
Given the formula formats, with thick graduate level notation on every page, I'd be extremely suspicious of a Kindle version if we get one, and also, there is an e-book version on Springer dot com but it costs $70 US anyway!
Although there is no "look inside" (Springer: please?), the Springer site has a brief shot of metric spaces that isn't helpful as it doesn't let you know that the "easy" problems are still grad level! Here is the missing table of contents:
1. Metric Spaces.- 2. Topological Spaces.- 3. Measure, Integral, and Martingales.- 4. Measures and Topology.- 5. Functional Analysis.- Other Problem Books.- List of Symbols.- Index
Highly recommended for all fields involving analysis, especially functional analysis, but also the numerous applications of stochastic techniques like Martingales, as long as you bear in mind the quick/graduate level of the material. Even the hints, explanations and "easy" problems assume you've completed grad level analysis courses and are ready to "learn by doing" problems and solutions you'll encounter in interviews, real life applications, and advanced professional and academic exams.
Every time I make that comment in a review, a smart undergrad emails to say they even find the hard problems easy, but I'd rather take that risk than have you pay this much only to find you're lost even in the "easy" problems. You have to learn this by doing, and the undergrads I teach, even in the advanced MIT and Coursera online courses FOR grads in topics like advanced quantum computing, are sometimes lost with real number/set mapping notation without review. And with today's numeric techniques and algorithms lurking beneath every function, even in analysis, you HAVE to know your matrix manipulations. That's not to take away at all from the execution of this volume, bravo Dr. Gasinski and Springer for contributing to the problem/solution field in so fine a fashion.
Emailer answer: Self teaching? Yes and no. Due to the fine explanations, this would be great for test prep without an instructor, BUT you might also have a lot of questions that you'd have to look up as you go along in other analysis texts or online. The bibs are excellent, and sites like preptorial dot org and textextras dot com are preparing adjuncts and online ponies for these volumes right now.
0 of 1 people found the following review helpful.
Deep and beautiful
By Olga Kharitonova
This book is for serious readers and I confirm it is deep and beautiful.
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