A Problem Book in Real Analysis

  • Filename: a-problem-book-in-real-analysis.
  • ISBN: 1441912959
  • Release Date: 2009-12-17
  • Number of pages: 254
  • Author: Asuman G. Aksoy
  • Publisher: Springer



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.

Problems in Real Analysis

  • Filename: problems-in-real-analysis.
  • ISBN: 9780387773780
  • Release Date: 2009-05-29
  • Number of pages: 452
  • Author: Teodora-Liliana Radulescu
  • Publisher: Springer Science & Business Media



This comprehensive collection of problems in mathematical analysis promotes creative, non-standard techniques to solve problems. It offers new tools and strategies to develop a connection between analysis and other disciplines such as physics and engineering.

Problems and Solutions in Real Analysis

  • Filename: problems-and-solutions-in-real-analysis.
  • ISBN: 9789812776013
  • Release Date: 2007
  • Number of pages: 292
  • Author: Masayoshi Hata
  • Publisher: World Scientific



This unique book provides a collection of more than 200 mathematical problems and their detailed solutions, which contain very useful tips and skills in real analysis. Each chapter has an introduction, in which some fundamental definitions and propositions are prepared. This also contains many brief historical comments on some significant mathematical results in real analysis together with useful references.Problems and Solutions in Real Analysis may be used as advanced exercises by undergraduate students during or after courses in calculus and linear algebra. It is also useful 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. The book is also suitable for non-experts who wish to understand mathematical analysis.

Selected Problems in Real Analysis

  • Filename: selected-problems-in-real-analysis.
  • ISBN: 0821897381
  • Release Date:
  • Number of pages: 370
  • Author: M. G. Goluzina
  • Publisher: American Mathematical Soc.



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.

Problems in Real Analysis

  • Filename: problems-in-real-analysis.
  • ISBN: 0120502534
  • Release Date: 1999
  • Number of pages: 403
  • Author: Charalambos D. Aliprantis
  • Publisher:



This volume aims to teach the basic methods of proof and problem-solving by presenting the complete solutions to over 600 problems that appear in the companion "Principles of Real Analysis", 3rd edition.

Problems in Real and Complex Analysis

  • Filename: problems-in-real-and-complex-analysis.
  • ISBN: 038797766X
  • Release Date: 1992-06-18
  • Number of pages: 488
  • Author: Bernard R. Gelbaum
  • Publisher: Springer Science & Business Media



In the pages that follow there are: A. A revised and enlarged version of Problems in analysis (PIA) . (All typographical, stylistic, and mathematical errors in PIA and known to the writer have been corrected.) B. A new section COMPLEX ANALYSIS containing problems distributed among many of the principal topics in the theory of functions of a complex variable. C. A total of 878 problems and their solutions. D. An enlarged Index/Glossary and an enlarged Symbol List. Notational and terminological conventions are to be found for the most part under Conventions at the beginnings of the chapters. Spe cial items not included in Conventions are completely explained in the Index/Glossary. The audience to which the current book is addressed differs little from the audience for PIA. The background of the reader is assumed to include a knowledge of the basic principles and theorems in real and complex analysis as those subjects are currently viewed. The aim of the problems is to sharpen and deepen the understanding of the mechanisms that underlie modern analysis. I thank Springer-Verlag for its interest in and support of this project. State University of New York at Buffalo B. R. G. v Contents The symbol alb under Pages below indicates that the Problems for the section begin on page a and the corresponding Solutions begin on page b. Thus 3/139 on the line for Set Algebra indicates that the Problems in Set Algebra begin on page 3 and the corresponding Solutions begin on page 139.

Berkeley Problems in Mathematics

  • Filename: berkeley-problems-in-mathematics.
  • ISBN: 0387204296
  • Release Date: 2004-01-08
  • Number of pages: 593
  • Author: Paulo Ney de Souza
  • Publisher: Springer Science & Business Media



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.

Principles of Real Analysis

  • Filename: principles-of-real-analysis.
  • ISBN: 0120502577
  • Release Date: 1998
  • Number of pages: 415
  • Author: Charalambos D. Aliprantis
  • Publisher: Gulf Professional Publishing



With the success of its previous editions, Principles of Real Analysis, Third Edition, continues to introduce students to the fundamentals of the theory of measure and functional analysis. In this thorough update, the authors have included a new chapter on Hilbert spaces as well as integrating over 150 new exercises throughout. The new edition covers the basic theory of integration in a clear, well-organized manner, using an imaginative and highly practical synthesis of the "Daniell Method" and the measure theoretic approach. Students will be challenged by the more than 600 exercises contained in the book. Topics are illustrated by many varied examples, and they provide clear connections between real analysis and functional analysis. * Gives a unique presentation of integration theory * Over 150 new exercises integrated throughout the text * Presents a new chapter on Hilbert Spaces * Provides a rigorous introduction to measure theory * Illustrated with new and varied examples in each chapter * Introduces topological ideas in a friendly manner * Offers a clear connection between real analysis and functional analysis * Includes brief biographies of mathematicians

Advanced Real Analysis

  • Filename: advanced-real-analysis.
  • ISBN: 0817644423
  • Release Date: 2008-07-11
  • Number of pages: 466
  • Author: Anthony W. Knapp
  • Publisher: Springer Science & Business Media



* Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician

Real Analysis

  • Filename: real-analysis.
  • ISBN: 0521497566
  • Release Date: 2000-08-15
  • Number of pages: 401
  • Author: N. L. Carothers
  • Publisher: Cambridge University Press



This is a course in real analysis directed at advanced undergraduates and beginning graduate students in mathematics and related fields. Presupposing only a modest background in real analysis or advanced calculus, the book offers something to specialists and non-specialists alike, including historical commentary, carefully chosen references, and plenty of exercises.

Basic Real Analysis

  • Filename: basic-real-analysis.
  • ISBN: 0817642110
  • Release Date: 2003-06-03
  • Number of pages: 559
  • Author: Houshang H. Sohrab
  • Publisher: Springer Science & Business Media



Basic Real Analysis demonstrates the richness of real analysis, giving students an introduction both to mathematical rigor and to the deep theorems and counter examples that arise from such rigor. In this modern and systematic text, all the touchstone results and fundamentals are carefully presented in a style that requires little prior familiarity with proofs or mathematical language. With its many examples, exercises and broad view of analysis, this work is ideal for senior undergraduates and beginning graduate students, either in the classroom or for self-study.

Real Analysis

  • Filename: real-analysis.
  • ISBN: 9780486445243
  • Release Date: 2005-11-03
  • Number of pages: 448
  • Author: Gabriel Klambauer
  • Publisher: Courier Corporation



This text for graduate students introduces contemporary real analysis with a particular emphasis on integration theory. Explores the Lebesgue theory of measure and integration of real functions; abstract measure and integration theory as well as topological and metric spaces. Additional topics include Stone's formulation of Daniell integration and normed linear spaces. Includes exercises. 1973 edition. Index.

Problems and Theorems in Analysis I

  • Filename: problems-and-theorems-in-analysis-i.
  • ISBN: 3540636404
  • Release Date: 1997-12-11
  • Number of pages: 393
  • Author: George Polya
  • Publisher: Springer Science & Business Media



From the reviews: "The work is one of the real classics of this century; it has had much influence on teaching, on research in several branches of hard analysis, particularly complex function theory, and it has been an essential indispensable source book for those seriously interested in mathematical problems." Bulletin of the American Mathematical Society

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