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

Name: Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)
Price: 18.35 USD
Availability: InStock
Rating: 4.8 (654 reviews)

4.8 of 5 Stars: Mathematics - Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)

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$18.35

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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. This book covers intuitive proofs, direct proofs, sets, induction, logic, the contrapositive, contradiction, functions and relations. The text aims to make the ideas visible, and contains over 200 illustrations. The writing is relaxed and conversational, and includes periodic attempts at humor.

This text is also an introduction to higher mathematics. This is done in-part through the chosen examples and theorems. Furthermore, following every chapter is an introduction to an area of math. These include Ramsey theory, number theory, topology, sequences, real analysis, big data, game theory, cardinality and group theory. After every chapter are "pro-tips," which are short thoughts on things I wish I had known when I took my intro-to-proofs class. They include finer comments on the material, study tips, historical notes, comments on mathematical culture, and more. Also, after each chapter's exercises is an introduction to an unsolved problem in mathematics.

In the first appendix we discuss some further proof methods, the second appendix is a collection of particularly beautiful proofs, and the third is some writing advice.

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Looking for a refreshing take on traditional mathematics textbooks? Look no further than Proofs: A Long-Form Mathematics Textbook! This innovative book breaks away from the mundane definition-theorem-proof cycle and instead focuses on providing students with thorough commentary, motivation, and detailed explanations. With over 200 illustrations to make concepts visually accessible, this textbook is designed to enhance understanding and foster a deeper appreciation for mathematical proofs.

Step into the world of higher mathematics with Proofs: A Long-Form Mathematics Textbook! This comprehensive text not only covers fundamental topics like induction, logic, functions, and relations but also delves into advanced areas such as Ramsey theory, number theory, and real analysis. Each chapter is accompanied by insightful "pro-tips" to help students navigate through the material and gain valuable insights that go beyond the classroom.

Are you tired of dry, impersonal math textbooks? Embrace a more conversational and engaging approach with Proofs: A Long-Form Mathematics Textbook! Written in a relaxed and humorous style, this book not only equips students with essential proof techniques but also offers a glimpse into the fascinating world of unsolved mathematical problems. Plus, with bonus content on unique proof methods and beautiful mathematical gems, this textbook is a must-have for aspiring mathematicians.

Ready to elevate your understanding of mathematical proofs and embark on a captivating learning journey? Explore the unparalleled depth and clarity offered by Proofs: A Long-Form Mathematics Textbook today! Get your copy now!

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