Saturday, 28 July 2018

A PROBLEM BOOK IN REAL ANALYSIS BY ASUMAN G AKSOY AND MOHAMED A KHAMSI

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. 


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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 glimpseatits developmental history. Although Analysis was conceived in the 17th century during the Scientic 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. 

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