A Problem Book in Real Analysis de Asuman G. Aksoy

A Problem Book in Real Analysis: Problem Books in Mathematics

Autor Asuman G. Aksoy, Mohamed A. Khamsi

en Limba Engleză Paperback – 23 aug 2016

Subliniem relevanța capitolului dedicat spațiilor metrice și fundamentelor topologiei, secțiuni care transformă A Problem Book in Real Analysis dintr-o simplă culegere într-un instrument pedagogic esențial pentru studenții de la facultățile de matematică. Considerăm că structura celor 11 capitole oglindește riguros evoluția istorică a disciplinei, de la rigoarea lui Cauchy și Weierstrass până la conceptele moderne de mulțimi deschise și închise introduse în secolul XX. Progresia este logică și graduală: se începe cu logica elementară, se trece prin studiul limitelor de funcții, continuitate și diferențiabilitate, culminând cu serii de funcții.

Această lucrare reprezintă o alternativă practică la Real Analysis de John M. Howie pentru cursurile de analiză matematică, având avantajul celor 319 probleme rezolvate care permit studentului să descopere singur profunzimea teoriei. Spre deosebire de manualele clasice care pun accent pe demonstrații teoretice lungi, Asuman G. Aksoy și Mohamed A. Khamsi mizează pe o învățare activă. Această metodă este complementară abordării din Nonstandard Methods in Fixed Point Theory, unde aceiași autori au demonstrat o capacitate deosebită de a sintetiza dezvoltări complexe în structuri clare.

În comparație cu How to Think About Analysis de Lara Alcock, care este mai degrabă un ghid de pregătire conceptuală, volumul de față servește drept partener de lucru pe parcursul întregului semestru, oferind soluțiile necesare pentru a demitiza un subiect adesea considerat intimidant. Ritmul este susținut, iar tonul autorilor este unul de ghidaj constant, transformând analiza reală dintr-un obstacol academic într-o experiență de învățare satisfăcătoare.

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Specificații

ISBN-13: 9781493951093
ISBN-10: 1493951092
Pagini: 264
Ilustrații: X, 254 p.
Dimensiuni: 178 x 254 x 14 mm
Greutate: 0.56 kg
Ediția:Softcover reprint of the original 1st edition 2010
Editura: Springer
Colecția Problem Books in Mathematics
Seria Problem Books in Mathematics

Locul publicării:New York, NY, United States

De ce să citești această carte

Recomandăm această carte studenților care doresc să stăpânească analiza reală prin practică directă. Este un instrument excelent pentru pregătirea examenelor, oferind 319 probleme rezolvate care acoperă întregul curriculum, de la numere reale la topologie. Cititorul câștigă încredere în manipularea conceptelor abstracte și o înțelegere profundă a rigorii matematice, esențială pentru orice viitor matematician sau cercetător.

Descriere scurtă

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.

Cuprins

Elementary Logic and Set Theory.- Real Numbers.- Sequences.- Limits of Functions.- Continuity.- Differentiability.- Integration.- Series.- Metric Spaces.- Fundamentals of Topology.- Sequences and Series of Functions.

Recenzii

From the reviews:
“Spread out over 11 chapters, this is a collection of 319 problems in what used to be called Advanced Calculus. … The authors see their book primarily as an aid to undergraduates … but I view it as being helpful to teachers in supplementing their courses or in preparing exams. … However, kept on a course reserve shelf of an academic library, the book under review might entice and benefit the more dedicated student. It certainly merits the attention of instructors of elementary analysis.” (Henry Ricardo, The Mathematical Association of America, June, 2010)
“A very readable collection of interesting problems of varying levels of difficulty. It is intended to build a bridge between ordinary high school or undergraduate exercises and more difficult and abstract concepts or problems. The book is so delightfully written that anyone who simply likes working on challenging problems could read it independently. … recommends this book to all students curious about elementary real analysis and how to learn it through solving problems. … a welcome resource for organizing their activities at a good level.” (Vicenţiu D. Rădulescu, Zentralblatt MATH, Vol. 1186, 2010)

Textul de pe ultima copertă

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 A Problem Book in Real Analysis is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, the authors hope that learning analysis becomes less taxing and more satisfying.
The wide variety of exercises presented in this book range from the computational to the more conceptual and varies in difficulty. They cover the following subjects: set theory; real numbers; sequences; limits of the functions; continuity; differentiability; integration; series; metric spaces; sequences; and series of functions and fundamentals of topology. Furthermore, the authors define the concepts and cite the theorems used at the beginning of each chapter. A Problem Book in Real Analysis is not simply a collection of problems; it will stimulate its readers to independent thinking in discovering analysis.
Prerequisites for the reader are a robust understanding of calculus and linear algebra.

Caracteristici

Helps instructors enhance lectures with problems beyond the classroom Helps prepare students for examinations Text encourages students to find different solutions to problems than those presented Includes supplementary material: sn.pub/extras