Authors:
- Brings carefully selected, challenging problems in mathematical analysis
- Explores the standard topics of mathematical analysis in ways not seen in regular textbooks
- Offers original problems of mathematical analysis called gems, scattered throughout the text, that stimulate the reader who enjoy creativity and discovery in mathematics
- Useful for students seeking to strengthen their skills in analysis, to prepare for math contests, instructors and connoisseurs of ingenious computations
Part of the book series: Problem Books in Mathematics (PBM)
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Table of contents (15 chapters)
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Front Matter
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Back Matter
About this book
The sets of problems are comprised in Part I. The exercises are arranged on topics, many of them being preceded by supporting theory. Content starts with limits, series of real numbers and power series, extending to derivatives and their applications, partial derivatives and implicit functions. Difficult problems have been structured in parts, helping the reader to find a solution. Challenges and open problems are scattered throughout the text, being an invitation to discover new original methodsfor proving known results and establishing new ones. The final two chapters offer ambitious readers splendid problems and two new proofs of a famous quadratic series involving harmonic numbers. In Part II, the reader will find solutions to the proposed exercises.
Undergraduate students in mathematics, physics and engineering, seeking to strengthen their skills in analysis, will most benefit from this work, along with instructors involved in math contests, individuals who want to enrich and test their knowledge in analysis, and anyone willing to explore the standard topics of mathematical analysis in ways that aren’t commonly seen in regular textbooks.
Reviews
"It should be of use to a variety of readers including, those teaching Calculus sequence, researchers who routinely deal with series, and mathematical laypeople who wish to enjoy some punchy, beautiful identities and revel at some mathematical jokes. ... the solutions are frequently high-quality step-by-step derivations. The book is more than a collection of problems." (Russel Jay, Hendel, MAA Reviews, May 23, 2022)
“Think of competition level problems like those of the Putnam competition or the Mathematical Olympaids like SEEMOUS. This book can be used to prepare for such contests both by potential participants as well as by those that have to set up the questions. … This is a challenging, surprising, and interesting way to explore the classical topics in analysis clearly intended for the those who want to excel in mathematics.” (Adhemar Bultheel, zbMATH1482.00001, 2022)
Authors and Affiliations
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Department of Mathematics, Technical University of Cluj-Napoca, Cluj-Napoca, Romania
Alina Sîntămărian, Ovidiu Furdui
About the authors
Ovidiu Furdui is an Associate Professor of Mathematics at Technical University of Cluj-Napoca, Romania. He has published more than 500 problems in journals, with a problem column, from all over the world and he is the author of Limits, Series, and Fractional Part Integrals and has co-authored Square Matrices of Order 2, both published by Springer.
Bibliographic Information
Book Title: Sharpening Mathematical Analysis Skills
Authors: Alina Sîntămărian, Ovidiu Furdui
Series Title: Problem Books in Mathematics
DOI: https://doi.org/10.1007/978-3-030-77139-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-77138-6Published: 26 October 2021
Softcover ISBN: 978-3-030-77141-6Published: 27 October 2022
eBook ISBN: 978-3-030-77139-3Published: 25 October 2021
Series ISSN: 0941-3502
Series E-ISSN: 2197-8506
Edition Number: 1
Number of Pages: XX, 536
Number of Illustrations: 1 b/w illustrations, 10 illustrations in colour
Topics: Analysis, Real Functions, Sequences, Series, Summability