A Course in Real Analysis

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9780123877741: A Course in Real Analysis
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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.

  • New chapter on Hausdorff Measure and Fractals
  • Key concepts and learning objectives give students a deeper understanding of the material to enhance learning
  • More than 200 examples (not including parts) are used to illustrate definitions and results
  • Over 1300 exercises (not including parts) are provided to promote understanding
  • Each chapter begins with a brief biography of a famous mathematician

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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.
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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.

"About this title" may belong to another edition of this title.

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