(Ebook) A Problem Book in Real Analysis by Asuman G. Aksoy, Mohamed A. Khamsi ISBN 9781441912954, 9781441912961, 9781493951093, 1441912959, 1441912967, 1493951092, B0074F457I

(Ebook) A Problem Book in Real Analysis by Asuman G. Aksoy, Mohamed A. Khamsi ISBN 9781441912954, 9781441912961, 9781493951093, 1441912959, 1441912967, 1493951092, B0074F457I

Education is an admirable thing, but it is well to remember from time to time that nothing worth knowing can be taught. Oscar Wilde, “The Critic as Artist”, 1890. Analysis is a profound subject; it is neither easy to understand nor summarize. However, Real Analysis can be discovered by solving problems. This book aims to give independent students the opportunity to discover Real Analysis by themselves through problem solving.

The depth and complexity of the theory of Analysis can be appreciated by taking a glimpse at its developmental history. Although Analysis was conceived in the 17th century during the Scientific Revolution, it has taken nearly two hundred years to establish its theoretical basis. Kepler, Galileo, Descartes, Fermat, Newton and Leibniz were among those who contributed to its genesis. Deep conceptual changes in Analysis were brought about in the 19th century by Cauchy and Weierstrass. Furthermore, modern concepts such as open and closed sets were introduced in the 1900s.

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 this book is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, we hope that learning analysis becomes less taxing and thereby more satisfying.

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