A Problem Book in Real Analysis

Author: Asuman G. Aksoy
Publisher: Springer Science & Business Media
ISBN: 1441912967
Format: PDF, ePub, Mobi
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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. ThedepthandcomplexityofthetheoryofAnalysiscanbeappreciatedbytakingaglimpseatits developmental history. Although Analysis was conceived in the 17th century during the Scienti?c 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.

Selected Problems in Real Analysis

Author: M. G. Goluzina
Publisher: American Mathematical Soc.
ISBN: 9780821897386
Format: PDF, Docs
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This book is intended for students wishing to deepen their knowledge of mathematical analysis and for those teaching courses in this area. It differs from other problem books in the greater difficulty of the problems, some of which are well-known theorems in analysis. Nonetheless, no special preparation is required to solve the majority of the problems. Brief but detailed solutions to most of the problems are given in the second part of the book. This book is unique in that the authors have aimed to systematize a range of problems that are found in sources that are almost inaccessible (especially to students) and in mathematical folklore.

Modern Real and Complex Analysis

Author: Bernard R. Gelbaum
Publisher: John Wiley & Sons
ISBN: 111803080X
Format: PDF, ePub, Mobi
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Modern Real and Complex Analysis Thorough, well-written, and encyclopedic in its coverage, this text offers a lucid presentation of all the topics essential to graduate study in analysis. While maintaining the strictest standards of rigor, Professor Gelbaum's approach is designed to appeal to intuition whenever possible. Modern Real and Complex Analysis provides up-to-date treatment of such subjects as the Daniell integration, differentiation, functional analysis and Banach algebras, conformal mapping and Bergman's kernels, defective functions, Riemann surfaces and uniformization, and the role of convexity in analysis. The text supplies an abundance of exercises and illustrative examples to reinforce learning, and extensive notes and remarks to help clarify important points.

Problems and Solutions in Real Analysis

Author: Masayoshi Hata
Publisher: World Scientific Publishing Company
ISBN: 9813142847
Format: PDF, Kindle
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This second edition introduces an additional set of new mathematical problems with their detailed solutions in real analysis. It also provides numerous improved solutions to the existing problems from the previous edition, and includes very useful tips and skills for the readers to master successfully. There are three more chapters that expand further on the topics of Bernoulli numbers, differential equations and metric spaces. Each chapter has a summary of basic points, in which some fundamental definitions and results are prepared. This also contains many brief historical comments for some significant mathematical results in real analysis together with many references. Problems and Solutions in Real Analysis can be treated as a collection of advanced exercises by undergraduate students during or after their courses of calculus and linear algebra. It is also instructive for graduate students who are interested in analytic number theory. Readers will also be able to completely grasp a simple and elementary proof of the Prime Number Theorem through several exercises. This volume is also suitable for non-experts who wish to understand mathematical analysis. Request Inspection Copy Contents:Sequences and LimitsInfinite SeriesContinuous FunctionsDifferentiationIntegrationImproper IntegralsSeries of FunctionsApproximation by PolynomialsConvex FunctionsVarious Proof ζ(2) = π2/6Functions of Several VariablesUniform DistributionRademacher FunctionsLegendre PolynomialsChebyshev PolynomialsGamma FunctionPrime Number TheoremBernoulli NumbersMetric SpacesDifferential Equations Readership: Undergraduates and graduate students in mathematical analysis.

Problems in Real Analysis

Author: Teodora-Liliana Radulescu
Publisher: Springer Science & Business Media
ISBN: 0387773797
Format: PDF, ePub, Docs
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Problems in Real Analysis: Advanced Calculus on the Real Axis features a comprehensive collection of challenging problems in mathematical analysis that aim to promote creative, non-standard techniques for solving problems. This self-contained text offers a host of new mathematical tools and strategies which develop a connection between analysis and other mathematical disciplines, such as physics and engineering. A broad view of mathematics is presented throughout; the text is excellent for the classroom or self-study. It is intended for undergraduate and graduate students in mathematics, as well as for researchers engaged in the interplay between applied analysis, mathematical physics, and numerical analysis.

Problems in Mathematical Analysis

Author: Biler
Publisher: Routledge
ISBN: 135142145X
Format: PDF
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Chapter 1 poses 134 problems concerning real and complex numbers, chapter 2 poses 123 problems concerning sequences, and so it goes, until in chapter 9 one encounters 201 problems concerning functional analysis. The remainder of the book is given over to the presentation of hints, answers or referen

Exercises in Analysis

Author: Leszek Gasiński
Publisher: Springer
ISBN: 3319278177
Format: PDF
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This second of two Exercises in Analysis volumes covers problems in five core topics of mathematical analysis: Function Spaces, Nonlinear and Multivalued Maps, Smooth and Nonsmooth Calculus, Degree Theory and Fixed Point Theory, and Variational and Topological Methods. Each of five topics corresponds to a different chapter with inclusion of the basic theory and accompanying main definitions and results,followed by suitable comments and remarks for better understanding of the material. Exercises/problems are presented for each topic, with solutions available at the end of each chapter. The entire collection of exercises offers a balanced and useful picture for the application surrounding each topic. This nearly encyclopedic coverage of exercises in mathematical analysis is the first of its kind and is accessible to a wide readership. Graduate students will find the collection of problems valuable in preparation for their preliminary or qualifying exams as well as for testing their deeper understanding of the material. Exercises are denoted by degree of difficulty. Instructors teaching courses that include one or all of the above-mentioned topics will find the exercises of great help in course preparation. Researchers in analysis may find this Work useful as a summary of analytic theories published in one accessible volume.

Berkeley Problems in Mathematics

Author: Paulo Ney de Souza
Publisher: Springer Science & Business Media
ISBN: 9780387204291
Format: PDF, Docs
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This book collects approximately nine hundred problems that have appeared on the preliminary exams in Berkeley over the last twenty years. It is an invaluable source of problems and solutions. Readers who work through this book will develop problem solving skills in such areas as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra.

Problems and Theorems in Classical Set Theory

Author: Peter Komjath
Publisher: Springer Science & Business Media
ISBN: 0387362193
Format: PDF, Kindle
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This volume contains a variety of problems from classical set theory and represents the first comprehensive collection of such problems. Many of these problems are also related to other fields of mathematics, including algebra, combinatorics, topology and real analysis. Rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. They vary in difficulty, and are organized in such a way that earlier problems help in the solution of later ones. For many of the problems, the authors also trace the history of the problems and then provide proper reference at the end of the solution.