Problem Books in Mathematics

Exercises in Analysis

Part 1

Authors: Gasiński, Leszek, Papageorgiou, Nikolaos S.

  • 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
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eBook $69.99
price for USA (gross)
  • ISBN 978-3-319-06176-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA
  • ISBN 978-3-319-06175-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.99
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: November 4, 2016
  • ISBN 978-3-319-35535-1
  • Free shipping for individuals worldwide
About this Textbook

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.

About the authors

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).

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)


Table of contents (5 chapters)

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-319-06176-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA
  • ISBN 978-3-319-06175-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.99
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: November 4, 2016
  • ISBN 978-3-319-35535-1
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Exercises in Analysis
Book Subtitle
Part 1
Authors
Series Title
Problem Books in Mathematics
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
Distribution Rights
Distribution rights for India: Researchco Book Centre, New Delhi, India
eBook ISBN
978-3-319-06176-4
DOI
10.1007/978-3-319-06176-4
Hardcover ISBN
978-3-319-06175-7
Softcover ISBN
978-3-319-35535-1
Series ISSN
0941-3502
Edition Number
1
Number of Pages
X, 1037
Number of Illustrations and Tables
5 b/w illustrations, 112 illustrations in colour
Topics