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Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series) - Softcover
Book 1 of 3: The Long-Form Math Textbook Series
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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Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)
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Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)
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Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)
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The Long-Form Math Textbook Series: Proofs: A Long-Form Mathematics Textbook
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Softcover. Condition: Fine. Vergilbt / ausgeblichen. This textbook is tailored for students, moving beyond the typical definition-theorem-proof format to include extensive commentary, motivation, and explanations. The proofs prioritize understanding over brevity, with many preceded by "scratch work" or sketches to provide a broader perspective and guide students in developing their own proofs. Key topics include intuitive proofs, direct proofs, sets, induction, logic, the contrapositive, contradiction, functions, and relations, all supported by over 200 illustrations. The writing style is relaxed and conversational, featuring moments of humor. Additionally, the text serves as an introduction to higher mathematics, with selected examples and theorems that lead into various mathematical areas, such as Ramsey theory, number theory, topology, sequences, real analysis, big data, game theory, cardinality, and group theory. Each chapter concludes with "pro-tips" that offer insights on the material, study strategies, historical context, and aspects of mathematical culture. Following the exercises, readers will find introductions to unsolved problems in mathematics. The appendices cover further proof methods, showcase particularly beautiful proofs, and provide writing advice. Seller Inventory # e0439468-93f4-4855-ac04-ef10ed780d9d
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paperback. Condition: Gut. 511 Seiten; 9798595265973.3 Gewicht in Gramm: 500. Seller Inventory # 1002840
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