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Introduction to Real Analysis

Introduction to Real Analysis Book
Author : Robert G. Bartle,Donald R. Sherbert
Publisher : John Wiley & Sons Incorporated
Release : 2000
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

In recent years, mathematics has become valuable in many areas, including economics and management science as well as the physical sciences, engineering and computer science. Therefore, this book provides the fundamental concepts and techniques of real analysis for readers in all of these areas. It helps one develop the ability to think deductively, analyze mathematical situations and extend ideas to a new context. Like the first two editions, this edition maintains the same spirit and user-friendly approach with some streamlined arguments, a few new examples, rearranged topics, and a new chapter on the Generalized Riemann Integral.

The Real Analysis Lifesaver

The Real Analysis Lifesaver Book
Author : Raffi Grinberg
Publisher : Princeton University Press
Release : 2017-01-10
ISBN : 0691172935
Language : En, Es, Fr & De

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Book Description :

Real analysis is difficult. For most students, in addition to learning new material about real numbers, topology, and sequences, they are also learning to read and write rigorous proofs for the first time. The Real Analysis Lifesaver is an innovative guide that helps students through their first real analysis course while giving them the solid foundation they need for further study in proof-based math. Rather than presenting polished proofs with no explanation of how they were devised, The Real Analysis Lifesaver takes a two-step approach, first showing students how to work backwards to solve the crux of the problem, then showing them how to write it up formally. It takes the time to provide plenty of examples as well as guided "fill in the blanks" exercises to solidify understanding. Newcomers to real analysis can feel like they are drowning in new symbols, concepts, and an entirely new way of thinking about math. Inspired by the popular Calculus Lifesaver, this book is refreshingly straightforward and full of clear explanations, pictures, and humor. It is the lifesaver that every drowning student needs. The essential “lifesaver” companion for any course in real analysis Clear, humorous, and easy-to-read style Teaches students not just what the proofs are, but how to do them—in more than 40 worked-out examples Every new definition is accompanied by examples and important clarifications Features more than 20 “fill in the blanks” exercises to help internalize proof techniques Tried and tested in the classroom

Fundamentals of Real Analysis

Fundamentals of Real Analysis Book
Author : Sterling K. Berberian
Publisher : Springer Science & Business Media
Release : 2013-03-15
ISBN : 9780387984803
Language : En, Es, Fr & De

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Book Description :

"This book is very well organized and clearly written and contains an adequate supply of exercises. If one is comfortable with the choice of topics in the book, it would be a good candidate for a text in a graduate real analysis course." -- MATHEMATICAL REVIEWS

Real Analysis

Real Analysis Book
Author : Jay Cummings
Publisher : Unknown
Release : 2019-07-15
ISBN : 9781077254541
Language : En, Es, Fr & De

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Book Description :

This textbook is designed for students. Rather than the typical definition-theorem-proof-repeat style, this text includes much more commentary, motivation and explanation. The proofs are not terse, and aim for understanding over economy. Furthermore, dozens of proofs are preceded by "scratch work" or a proof sketch to give students a big-picture view and an explanation of how they would come up with it on their own. Examples often drive the narrative and challenge the intuition of the reader. The text also aims to make the ideas visible, and contains over 200 illustrations. The writing is relaxed and includes interesting historical notes, periodic attempts at humor, and occasional diversions into other interesting areas of mathematics. The text covers the real numbers, cardinality, sequences, series, the topology of the reals, continuity, differentiation, integration, and sequences and series of functions. Each chapter ends with exercises, and nearly all include some open questions. The first appendix contains a construction the reals, and the second is a collection of additional peculiar and pathological examples from analysis. The author believes most textbooks are extremely overpriced and endeavors to help change this.Hints and solutions to select exercises can be found at LongFormMath.com.

A Radical Approach to Real Analysis

A Radical Approach to Real Analysis Book
Author : David M. Bressoud
Publisher : MAA
Release : 2007-04-12
ISBN : 9780883857472
Language : En, Es, Fr & De

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Book Description :

Second edition of this introduction to real analysis, rooted in the historical issues that shaped its development.

Problems in Real Analysis

Problems in Real Analysis Book
Author : Charalambos D. Aliprantis,Owen Burkinshaw
Publisher : Unknown
Release : 1999
ISBN : 9780120502530
Language : En, Es, Fr & De

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Book Description :

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.

Basic Real Analysis

Basic Real Analysis Book
Author : James Howland
Publisher : Jones & Bartlett Learning
Release : 2010
ISBN : 9780763773182
Language : En, Es, Fr & De

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Book Description :

Ideal for the one-semester undergraduate course, Basic Real Analysis is intended for students who have recently completed a traditional calculus course and proves the basic theorems of Single Variable Calculus in a simple and accessible manner. It gradually builds upon key material as to not overwhelm students beginning the course and becomes more rigorous as they progresses. Optional appendices on sets and functions, countable and uncountable sets, and point set topology are included for those instructors who wish include these topics in their course. The author includes hints throughout the text to help students solve challenging problems. An online instructor's solutions manual is also available.

Real Analysis

Real Analysis Book
Author : S. Nanda,V.P. Saxena
Publisher : Allied Publishers
Release : 2000-09-07
ISBN : 8177640623
Language : En, Es, Fr & De

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Book Description :

This book would be useful as text for undergraduate students of all Indian universities and engineering institutes, including the Indian Institutes of Technology. Real Analysis is a CORE subject in mathematics at the college level. The prerequisite for this course is Higher Secondary level mathematics including calculus. The authors have, however, included a preliminary chapter on Set Theory to make the book as self contained as possible. In addition to discussing the “basics” of a first course, the book also contains a large number of examples to aid better student understanding of the subject.

Problems and Solutions in Real Analysis

Problems and Solutions in Real Analysis Book
Author : Masayoshi Hata
Publisher : World Scientific Publishing Company
Release : 2016-12-12
ISBN : 9813142847
Language : En, Es, Fr & De

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Book Description :

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.

Basic Real Analysis

Basic Real Analysis Book
Author : Houshang H. Sohrab
Publisher : Springer Science & Business Media
Release : 2003-06-03
ISBN : 9780817642112
Language : En, Es, Fr & De

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Book Description :

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.

A Guide to Advanced Real Analysis

A Guide to Advanced Real Analysis Book
Author : G. B. Folland
Publisher : MAA
Release : 2009-11-30
ISBN : 9780883853436
Language : En, Es, Fr & De

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Book Description :

A concise guide to the core material in a graduate level real analysis course.

Resources for the Study of Real Analysis

Resources for the Study of Real Analysis Book
Author : Robert L. Brabenec
Publisher : Cambridge University Press
Release : 2004
ISBN : 9780883857373
Language : En, Es, Fr & De

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Book Description :

A collection of materials gathered by the author while teaching real analysis over a period of years.

Exploratory Examples for Real Analysis

Exploratory Examples for Real Analysis Book
Author : Joanne E. Snow,Kirk E. Weller
Publisher : Cambridge University Press
Release : 2003
ISBN : 9780883857342
Language : En, Es, Fr & De

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Book Description :

Every mathematician must make the transition from the calculations of high school to the structural and theoretical approaches of graduate school. Essentials of Mathematics provides the knowledge needed to move onto advanced mathematical work, and a glimpse of what being a mathematician might be like. No other book takes this particular holistic approach to the task. The content is of two types. There is material for a ""transitions"" course at the sophomore level; introductions to logic and set theory, discussions of proof writing and proof discovery, and introductions to the number systems (natural, rational, real, and complex). The material is presented in a fashion suitable for a Moore Method course, although such an approach is not necessary. An accompanying Instructor's Manual provides support for all flavors of teaching styles. In addition to presenting the important results for student proof, each area provides warm-up and follow-up exercises to help students internalize the material. The second type of content is an introduction to the professional culture of mathematics. There are many things that mathematicians know but weren't exactly taught. To give college students a sense of the mathematical universe, the book includes narratives on this kind of information. There are sections on pure and applied mathematics, the philosophy of mathematics, ethics in mathematical work, professional (including student) organizations, famous theorems, famous unsolved problems, famous mathematicians, discussions of the nature of mathematics research, and more. The prerequisites for a course based on this book include the content of high school mathematics and a certain level of mathematical maturity. The student must be willing to think on an abstract level. Two semesters of calculus indicates a readiness for this material.

Real Analysis

Real Analysis Book
Author : Satoru Igari
Publisher : American Mathematical Soc.
Release : 2000
ISBN : 9780821821046
Language : En, Es, Fr & De

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Book Description :

This introduction to real analysis is based on a series of lectures by the author at Tohoku University. The text covers real numbers, the notion of general topology, and a brief treatment of the Riemann integral, followed by chapters on the classical theory of the Lebesgue integral on Euclidean spaces; the differentiation theorem and functions of bounded variation; Lebesgue spaces; distribution theory; the classical theory of the Fourier transform and Fourier series; and, wavelet theory. Features of this title include the core subjects of real analysis and the fundamentals for students who are interested in harmonic analysis, probability or partial differential equations. This volume would be a suitable textbook for an advanced undergraduate or first year graduate course in analysis.

Introduction to Real Analysis

Introduction to Real Analysis Book
Author : William C. Bauldry
Publisher : John Wiley & Sons
Release : 2009-07-14
ISBN : 0470371366
Language : En, Es, Fr & De

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Book Description :

An accessible introduction to real analysis and its connection to elementary calculus Bridging the gap between the development and history of real analysis, Introduction to Real Analysis: An Educational Approach presents a comprehensive introduction to real analysis while also offering a survey of the field. With its balance of historical background, key calculus methods, and hands-on applications, this book provides readers with a solid foundation and fundamental understanding of real analysis. The book begins with an outline of basic calculus, including a close examination of problems illustrating links and potential difficulties. Next, a fluid introduction to real analysis is presented, guiding readers through the basic topology of real numbers, limits, integration, and a series of functions in natural progression. The book moves on to analysis with more rigorous investigations, and the topology of the line is presented along with a discussion of limits and continuity that includes unusual examples in order to direct readers' thinking beyond intuitive reasoning and on to more complex understanding. The dichotomy of pointwise and uniform convergence is then addressed and is followed by differentiation and integration. Riemann-Stieltjes integrals and the Lebesgue measure are also introduced to broaden the presented perspective. The book concludes with a collection of advanced topics that are connected to elementary calculus, such as modeling with logistic functions, numerical quadrature, Fourier series, and special functions. Detailed appendices outline key definitions and theorems in elementary calculus and also present additional proofs, projects, and sets in real analysis. Each chapter references historical sources on real analysis while also providing proof-oriented exercises and examples that facilitate the development of computational skills. In addition, an extensive bibliography provides additional resources on the topic. Introduction to Real Analysis: An Educational Approach is an ideal book for upper- undergraduate and graduate-level real analysis courses in the areas of mathematics and education. It is also a valuable reference for educators in the field of applied mathematics.

Elementary Real Analysis

Elementary Real Analysis Book
Author : Brian S. Thomson,Judith B. Bruckner,Andrew M. Bruckner
Publisher : ClassicalRealAnalysis.com
Release : 2008-04-14
ISBN : 1434841618
Language : En, Es, Fr & De

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Book Description :

This is the second edition of the title originally published by Prentice Hall (Pearson) in 2001. Here is the reference information for the first edition:[TBB] Elementary Real Analysis, Brian S. Thomson, Judith B. Bruckner,Andrew M. Bruckner. Prentice-Hall, 2001, xv 735 pp. [ISBN 0-13-019075-61]The present title contains Chapters 1-8. The full version containing all of the chapters is also available as a trade paperback. A hypertexted PDF file of the entire text is available free for download on www.classicalrealanalysis.com.Chapter 1. Real NumbersChapter 2. SequencesChapter 3. Infinite sumsChapter 4. Sets of real numbersChapter 5. Continuous functionsChapter 6. More on continuous functions and setsChapter 7. DifferentiationChapter 8. The integral

Real Analysis Foundations

Real Analysis  Foundations Book
Author : Sergei Ovchinnikov
Publisher : Springer Nature
Release : 2021-03-20
ISBN : 3030647013
Language : En, Es, Fr & De

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Book Description :

This textbook explores the foundations of real analysis using the framework of general ordered fields, demonstrating the multifaceted nature of the area. Focusing on the logical structure of real analysis, the definitions and interrelations between core concepts are illustrated with the use of numerous examples and counterexamples. Readers will learn of the equivalence between various theorems and the completeness property of the underlying ordered field. These equivalences emphasize the fundamental role of real numbers in analysis. Comprising six chapters, the book opens with a rigorous presentation of the theories of rational and real numbers in the framework of ordered fields. This is followed by an accessible exploration of standard topics of elementary real analysis, including continuous functions, differentiation, integration, and infinite series. Readers will find this text conveniently self-contained, with three appendices included after the main text, covering an overview of natural numbers and integers, Dedekind's construction of real numbers, historical notes, and selected topics in algebra. Real Analysis: Foundations is ideal for students at the upper-undergraduate or beginning graduate level who are interested in the logical underpinnings of real analysis. With over 130 exercises, it is suitable for a one-semester course on elementary real analysis, as well as independent study.

Real Analysis

Real Analysis Book
Author : Saul Stahl
Publisher : John Wiley & Sons
Release : 2012-01-10
ISBN : 1118096851
Language : En, Es, Fr & De

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Book Description :

A provocative look at the tools and history of realanalysis This new edition of Real Analysis: A Historical Approachcontinues to serve as an interesting read for students of analysis.Combining historical coverage with a superb introductory treatment,this book helps readers easily make the transition from concrete toabstract ideas. The book begins with an exciting sampling of classic and famousproblems first posed by some of the greatest mathematicians of alltime. Archimedes, Fermat, Newton, and Euler are each summoned inturn, illuminating the utility of infinite, power, andtrigonometric series in both pure and applied mathematics. Next,Dr. Stahl develops the basic tools of advanced calculus, whichintroduce the various aspects of the completeness of the realnumber system as well as sequential continuity anddifferentiability and lead to the Intermediate and Mean ValueTheorems. The Second Edition features: A chapter on the Riemann integral, including the subject ofuniform continuity Explicit coverage of the epsilon-delta convergence A discussion of the modern preference for the viewpoint ofsequences over that of series Throughout the book, numerous applications and examplesreinforce concepts and demonstrate the validity of historicalmethods and results, while appended excerpts from originalhistorical works shed light on the concerns of influentialmathematicians in addition to the difficulties encountered in theirwork. Each chapter concludes with exercises ranging in level ofcomplexity, and partial solutions are provided at the end of thebook. Real Analysis: A Historical Approach, Second Edition isan ideal book for courses on real analysis and mathematicalanalysis at the undergraduate level. The book is also a valuableresource for secondary mathematics teachers and mathematicians.

Real Analysis

Real Analysis Book
Author : Carothers
Publisher : Unknown
Release : 2021-10-19
ISBN : 9780521696241
Language : En, Es, Fr & De

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Book Description :

Download Real Analysis book written by Carothers, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Golden Real Analysis

Golden Real Analysis Book
Author : N.P. Bali
Publisher : Firewall Media
Release : 2005-12
ISBN : 9788170080145
Language : En, Es, Fr & De

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Book Description :

Download Golden Real Analysis book written by N.P. Bali, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.