Problems in Real Analysis: Advanced Calculus on the Real Axis

This carefully written book presents an extremely motivating and original approach, by means of problem-solving, to calculus on the real line, and as such, serves as a perfect introduction to real analysis. To achieve their goal, the authors have care­fully selected problems that cover an impressive range of topics, all at the core of the subject. Some problems are genuinely difficult, but solving them will be highly rewarding, since each problem opens a new vista in the understanding of mathematics. This book is also perfect for self-study, since solutions are provided.

I like the care with which the authors intersperse their text with careful reviews of the background material needed in each chapter, thought-provoking quotations, and highly interesting and well-documented historical notes. In short, this book also makes very pleasant reading, and I am confident that each of its readers will enjoy reading it as much as I did. The charm and never-ending beauty of mathematics pervade all its pages.

In addition, this little gem illustrates the idea that one cannot learn mathematics without solving difficult problems. It is a world apart from the “computer addiction” that we are unfortunately witnessing among the younger generations of would-be mathematicians, who use too much ready-made software instead or their brains, or who stand in awe in front of computer-generated images, as if they had become the essence of mathematics. As such, it carries a very useful message.

One cannot help comparing this book to a “great ancestor,” the famed Problems and Theorems in Analysis, by Polya and Szego, a text that has strongly influenced generations of analysts. I am confident that this book will have a similar impact.

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