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

Cummings, Jay

ISBN 13: 9798595265973

Published by Unknown, 2021

About this Item

Item may have minor cosmetic defects (such as marks, wears, cuts, bends, or crushes) on the cover, spine, pages, or dust cover. Dust cover is intact and pages are clean and not marred by notes. Item may contain remainder marks on outside edges. Item may be missing bundled media. Satisfaction guaranteed. Thank you!

Seller Inventory # 08-13-2026-Bulk-Case 15/ Shelf F0218

Bibliographic Details

• Title: Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)
• Publisher: Unknown
• Publication Date: 2021
• Language: English
• ISBN 13: 9798595265973
• Binding: paperback
• Condition: As New

About this title

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.