A Course in Real Analysis 2nd Edition by John N. McDonald (PDF)

Description

The second edition of A Course in Real Analysis provides a solid foundation of real analysis concepts and principles, presenting a broad range of topics in a clear and concise manner. The book is excellent at balancing theory and applications with a wealth of examples and exercises. The authors take a progressive approach of skill building to help students learn to absorb the abstract. Real world applications, probability theory, harmonic analysis, and dynamical systems theory are included, offering considerable flexibility in the choice of material to cover in the classroom. The accessible exposition not only helps students master real analysis, but also makes the book useful as a reference.

User’s Reviews

Editorial Reviews: Review “…truly marvelous…weaves an interesting, lively, and crystal clear sequence of ideas comprising the heart of modern analysis. The order of presentation is so carefully chosen and the exposition is so masterful as to possess the traits of a literary art form.” –MAA Reviews, January 2015″The exposition is very clear and unhurried and the book would be useful both as a text and a book for self-study. The last chapters go beyond what is usually covered in analysis courses and this is all to the good.” –Sigurdur Helgason, MIT”There is a literary quality in the writing that is rare in mathematics texts. It is a pleasure to read this book. The exercises are a strong feature of the book and the examples are well chosen and plentiful.” –Peter Duren, University of Michigan”The outstanding features of the book are the wealth of examples and exercises, the interesting biographical data, and the introduction to wavelets and dynamical systems.” –Duong H. Phong, Columbia University”McDonald and Weiss have crafted a treasure chest of exercises in real analysis. Just an amazing and broad collection. Students and researchers will surely benefit from the enormous amount of superb exercises.” –Enno Lenzmann, University of Copenhagen”I was very impressed by the motivating discussions of a number of difficult concepts, along with their fresh approach to the details following. Their general philosophy of starting with concrete ideas, and slowly abstracting, worked well in communicating even the most difficult concepts in the course.” –Todd Kemp, University of California, San Diego Review This is a core textbook for a course in real analysis appropriate for students at the upper undergraduate and graduate levels. Sample content available on a companion site, copy and paste this URL into your browser: http://www.elsevierdirect.com/v2/companion.jsp?ISBN=9780123877741 Scroll down for more information! From the Back Cover Now in its second edition, A Course in Real Analysis provides students with a modern, engaging, and thorough treatment of real analysis. Graduate and advanced undergraduate students, instructors, and researchers will appreciate the motivation of key concepts and wealth of examples, exercises, and applications offered in this book.Professors McDonald and Weiss present the elements of measure and integration by first discussing the Lebesgue theory on the line and then the abstract theory. They go on to discuss elements of probability theory, differentiation and absolute continuity, signed and complex measures, and topological, metric, and normed spaces. The book concludes with valuable application chapters on harmonic analysis and measurable dynamical systems—as well as a brand new chapter on Hausdorff measure and fractals.Key features:Motivation of key concepts—the significance and rationale of main ideas are underscored throughout the text. Detailed theoretical discussion—proofs of most results are provided, while some are assigned as exercises to fully engage the reader. Illustrative examples and abundant exercises—roughly 200 examples and over 1300 widely varied exercises solidify understanding. Diverse applications—these appear throughout as examples and as entire sections or chapters, such as the applications to probability theory that pervade the text. Biographies—each chapter begins with a brief biography of a famous mathematician.|Now in its second edition, A Course in Real Analysis provides students with a modern, engaging, and thorough treatment of real analysis. Graduate and advanced undergraduate students, instructors, and researchers will appreciate the motivation of key concepts and wealth of examples, exercises, and applications offered in this book.Professors McDonald and Weiss present the elements of measure and integration by first discussing the Lebesgue theory on the line and then the abstract theory. They go on to discuss elements of probability theory, differentiation and absolute continuity, signed and complex measures, and topological, metric, and normed spaces. The book concludes with valuable application chapters on harmonic analysis and measurable dynamical systems—as well as a brand new chapter on Hausdorff measure and fractals.Key features:Motivation of key concepts—the significance and rationale of main ideas are underscored throughout the text. Detailed theoretical discussion—proofs of most results are provided, while some are assigned as exercises to fully engage the reader. Illustrative examples and abundant exercises—roughly 200 examples and over 1300 widely varied exercises solidify understanding. Diverse applications—these appear throughout as examples and as entire sections or chapters, such as the applications to probability theory that pervade the text. Biographies—each chapter begins with a brief biography of a famous mathematician. About the Author Neil A. Weiss (deceased) received his Ph.D. from UCLA and subsequently accepted an assistant-professor position at Arizona State University (ASU), where he was ultimately promoted to the rank of full professor. Weiss has taught mathematics, probability, statistics, and operations research from the freshman level to the advanced graduate level.In recognition of his excellence in teaching, he received the Dean’s Quality Teaching Award from the ASU College of Liberal Arts and Sciences. He has also been runner-up twice for the Charles Wexler Teaching Award in the ASU School of Mathematical and Statistical Sciences. Weiss’s comprehensive knowledge and experience ensures that his texts are mathematically accurate, as well as pedagogically sound.Weiss has published research papers in both theoretical and applied mathematics, including probability, engineering, operations research, numerical analysis, and psychology. He has also published several teaching-related papers.In addition to his numerous research publications, Weiss has authored or coauthored books in real analysis, probability, statistics, and finite mathematics. His texts-well known for their precision, readability, and pedagogical excellence-are used worldwide. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I have used this book mainly for self-study, in particular, the measure theory and I admit that it did wonderful job. The thing that I like most about this book is that it provides a lot of examples along with definitions, theorems, proofs etc. Furthermore, it covers wide varieties of topics and those topics are mostly self-contained. Coming from Economics back ground, this book helps me a lot to understand those abstract mathematical models applied in recent Economic theories.

⭐The book is well written and clear with an abundance of exercises (with no solutions).There are two things that keeps me from giving it five stars.Firstly, it is a little too bloated for my taste. Chapter four (the lebesgue integral on R) could very well have been a subsection of chapter five (the “abstract” lebesgue integral). The result of spitting the two chapters is a lack of easy reference and overview of the general theory. But I’m sure many would disagree on this.Secondly, too many proofs are left as exercises for the reader, which is irritating when using it as a reference book.

⭐This book was used in my graduate course on measure theory and it is very good. I have a few other books I am going through in specialized areas of analysis and find myself referencing this book for definitions because they are stated much more clearly. Another thing that is nice about it is that it tells you what chapters are needed to be covered if you want to study one particular chapter. For example. if I wanted to study chapter 16, I would have to study chapters 1-5,7 and 12 (or something like that I cannot remember them exactly).Highly recommended

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