Short description:

This book gathers together a novel collection of problems in mathematical analysis that are challenging and worth studying. They cover most of the classical topics of a course in mathematical analysis, and include challenges presented with an increasing level of difficulty. Problems are designed to encourage creativity, and some of them were especially crafted to lead to open problems which might be of interest for students seeking motivation to get a start in research.

Long description:

This book gathers together a novel collection of problems in mathematical analysis that are challenging and worth studying. They cover most of the classical topics of a course in mathematical analysis, and include challenges presented with an increasing level of difficulty. Problems are designed to encourage creativity, and some of them were especially crafted to lead to open problems which might be of interest for students seeking motivation to get a start in research.

"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)

Table of Contents:

Preface.- Notations.- Sequences of Real Numbers.- Series of Real Numbers.- Power Series.- Derivatives and Applications.- Partial Derivatives and Applications.- Implicit Functions.- Challenges, Gems, and Mathematical Beauties.- An Artistry of Quadratic Series. Two New Proofs of Sandham-Yeung Series.- Solutions.- References.- Index.