Authors:
- Contains exercises ranging from easy to difficult, with level of difficulty designated
- Features an encyclopedic volume of exercises in five core topics of mathematical analysis
- Prepares students well for qualifying exams and tests their depth of understanding of the material
- Includes supplementary material: sn.pub/extras
Part of the book series: Problem Books in Mathematics (PBM)
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Table of contents (5 chapters)
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Front Matter
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Back Matter
About this book
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.
Reviews
“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)
Authors and Affiliations
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Faculty of Mathematics and Computer Science, Jagiellonian University, Krakow, Poland
Leszek Gasińksi
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Department of Mathematics, National Technical University, Athens, Greece
Nikolaos S. Papageorgiou
About the authors
Bibliographic Information
Book Title: Exercises in Analysis
Book Subtitle: Part 1
Authors: Leszek Gasińksi, Nikolaos S. Papageorgiou
Series Title: Problem Books in Mathematics
DOI: https://doi.org/10.1007/978-3-319-06176-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2014
Hardcover ISBN: 978-3-319-06175-7Published: 07 August 2014
Softcover ISBN: 978-3-319-35535-1Published: 17 September 2016
eBook ISBN: 978-3-319-06176-4Published: 26 July 2014
Series ISSN: 0941-3502
Series E-ISSN: 2197-8506
Edition Number: 1
Number of Pages: X, 1037
Number of Illustrations: 5 b/w illustrations, 112 illustrations in colour
Topics: Functional Analysis, Measure and Integration, Probability Theory and Stochastic Processes, Topology
Industry Sectors: IT & Software