Real Analysis: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)

Name: Real Analysis: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)
Price: 22.5 USD
Availability: InStock
Rating: 4.7 (614 reviews)

4.7 of 5 Stars: Mathematics - Real Analysis: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)

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$22.50

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Description

Book Synopsis: 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 of 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.

Details

Looking for a mathematics textbook that breaks the mold? Look no further than Real Analysis: A Long-Form Mathematics Textbook. This innovative textbook goes beyond the traditional style of definition-theorem-proof-repeat to deliver a truly engaging learning experience for students. With extensive commentary, motivation, and explanation, this book ensures understanding is prioritized over economy.

What sets Real Analysis apart is its focus on providing students with a big-picture view of proofs. Before delving into the formal proof, "scratch work" or a proof sketch is presented, giving students insight into how they would approach the problem on their own. This approach fosters critical thinking and challenges readers' intuition, making the learning journey truly transformative.

Visual learners will rejoice with Real Analysis as it boasts over 200 illustrations that bring mathematical concepts to life. The text aims to make ideas tangible and accessible, ensuring students can grasp even the most abstract concepts with ease.

But it doesn't stop there. Real Analysis is not just a dry textbook; it is a captivating read filled with interesting historical notes, periodic attempts at humor, and delightful diversions into fascinating areas of mathematics. This engaging writing style keeps students hooked from cover to cover, making learning an enjoyable adventure.

Covering a wide range of topics including real numbers, cardinality, sequences, series, topology, continuity, differentiation, integration, and sequences and series of functions, Real Analysis has something for every math enthusiast. To reinforce learning, each chapter concludes with exercises that challenge and expand students' understanding. What's more, the book includes open questions that encourage critical thinking and exploration.

Real Analysis is not just another overpriced textbook. The author believes in making quality education accessible and aims to break the norm of exorbitant prices. For hints and solutions to select exercises, visit LongFormMath.com and embark on a math journey like never before.

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