Classical Analysis

<p>A conceptually clear induction to fundamental analysis theorems a tutorial for creative approaches for solving problems a collection of modern challenging problems a pathway to undergraduate research—all these desires gave life to the pages here.</p><p>This book exposes students to stimulating and enlightening proofs and hard problems of classical analysis mainly published in <em>The American Mathematical Monthly</em>. </p><p>The author presents proofs as a form of exploration rather than just a manipulation of symbols. Drawing on the papers from the Mathematical Association of America's journals numerous conceptually clear proofs are offered. Each proof provides either a novel presentation of a familiar theorem or a lively discussion of a single issue sometimes with multiple derivations.</p><p>The book collects and presents problems to promote creative techniques for problem-solving and undergraduate research and offers instructors an opportunity to assign these problems as projects. This book provides a wealth of opportunities for these projects.</p><p>Each problem is selected for its natural charm—the connection with an authentic mathematical experience its origination from the ingenious work of professionals develops well-shaped results of broader interest.</p>