A Problem Book in Real Analysis

ISBN-13: 9781493951093 / Angielski / Miękka / 2016 / 254 str.

Asuman G. Aksoy; Mohamed A. Khamsi

Opis

This book systematically solves the problems related to the core concepts of most analysis courses. The wide variety of exercises presented in this book range from the computational to the more conceptual and vary in difficulty.

Recenzje

From the reviews:

"Spread out over 11 chapters, this is a collection of 319 problems in what used to be called Advanced Calculus. ... The authors see their book primarily as an aid to undergraduates ... but I view it as being helpful to teachers in supplementing their courses or in preparing exams. ... However, kept on a course reserve shelf of an academic library, the book under review might entice and benefit the more dedicated student. It certainly merits the attention of instructors of elementary analysis." (Henry Ricardo, The Mathematical Association of America, June, 2010)

"A very readable collection of interesting problems of varying levels of difficulty. It is intended to build a bridge between ordinary high school or undergraduate exercises and more difficult and abstract concepts or problems. The book is so delightfully written that anyone who simply likes working on challenging problems could read it independently. ... recommends this book to all students curious about elementary real analysis and how to learn it through solving problems. ... a welcome resource for organizing their activities at a good level." (Vicentiu D. Radulescu, Zentralblatt MATH, Vol. 1186, 2010)

Spis treści

Elementary Logic and Set Theory.- Real Numbers.- Sequences.- Limits of Functions.- Continuity.- Differentiability.- Integration.- Series.- Metric Spaces.- Fundamentals of Topology.- Sequences and Series of Functions.

Blurb

Today, nearly every undergraduate mathematics program requires at least one semester of real analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of A Problem Book in Real Analysis is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, the authors hope that learning analysis becomes less taxing and more satisfying.

The wide variety of exercises presented in this book range from the computational to the more conceptual and varies in difficulty. They cover the following subjects: set theory; real numbers; sequences; limits of the functions; continuity; differentiability; integration; series; metric spaces; sequences; and series of functions and fundamentals of topology. Furthermore, the authors define the concepts and cite the theorems used at the beginning of each chapter. A Problem Book in Real Analysis is not simply a collection of problems; it will stimulate its readers to independent thinking in discovering analysis.

Prerequisites for the reader are a robust understanding of calculus and linear algebra.