Real Analysis: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series) 2nd Edition (Spiral Bound)

Master Real Analysis with In-Depth Explanations – Long-Form Mathematics Textbook, 2nd Edition

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.

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.

For students and professionals diving deep into mathematical theory, Real Analysis: A Long-Form Mathematics Textbook (2nd Edition) is a comprehensive and detailed guide. This textbook covers fundamental concepts with thorough explanations and proofs, making it a go-to resource for serious learners. The spiral-bound edition is particularly practical, allowing it to lay flat for easier note-taking and study sessions. For a reliable and accessible study companion, the spiral-bound version is an excellent choice.

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