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Real Analysis: A LongForm Mathematics Textbook (The LongForm Math Textbook Series),New
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This textbook is designed for students. Rather than the typical definitiontheoremproofrepeat 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 bigpicture 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.This is the 2 + epsilon edition of this book. The second edition was published in July 2019. In January 2024, an epsilon of changes were made and the manuscript was updated, without officially creating a new edition.
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This product may contain chemicals known to the State of California to cause cancer, birth defects, or other reproductive harm.
For more information, please visit www.P65Warnings.ca.gov.
- Q: What is the primary focus of 'Real Analysis: A Long-Form Mathematics Textbook'? A: The textbook is designed to help students understand real analysis through comprehensive commentary, motivation, and explanations, rather than a strict definition-theorem-proof format.
- Q: How does this textbook approach proofs in real analysis? A: The book provides detailed proofs aimed at understanding, often preceded by 'scratch work' or sketches to help students grasp the concepts before delving into formal proofs.
- Q: What topics are covered in this book? A: It covers essential topics such as the real numbers, cardinality, sequences, series, topology of the reals, continuity, differentiation, integration, and sequences and series of functions.
- Q: Are there exercises included in the textbook? A: Yes, each chapter ends with exercises, and many include open questions to encourage critical thinking and exploration of the material.
- Q: What is the significance of the '2 + epsilon edition' of this book? A: The '2 + epsilon edition' indicates that while it is the second edition, it has undergone updates and changes as of January 2024, enhancing the manuscript without creating an entirely new edition.
- Q: Who is the author of this textbook? A: The textbook is authored by Jay Cummings.
- Q: When was the second edition of this textbook published? A: The second edition was published on July 15, 2019.
- Q: What is the binding type of this textbook? A: The textbook is available in paperback binding.
- Q: How many pages does the textbook contain? A: The textbook has a total of 449 pages.
- Q: Where can I find hints and solutions for exercises in the textbook? A: Hints and solutions for select exercises can be found at LongFormMath.com.