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.
✔ Author(s): Jay Cummings
✔ Title: Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)
✔ Rating : 4.8 out of 5 base on (637 reviews)
✔ ISBN-10: B08T8JCVF1
✔ ISBN-13: 978B08T8JCVF4
✔ Language: English
✔ Format ebook: PDF, EPUB, Kindle, Audio, HTML and MOBI
✔ Device compatibles: Android, iOS, PC and Amazon Kindle
Readers' opinions about Proofs by Jay Cummings
Virginia Savage
What an intellectual journey! The themes explored in this book challenged my perceptions and sparked introspection. It's refreshing to read a book that provokes such thought.
Sarah Franklin
I loved the powerful messages hidden within the story. The book tackled important social issues and made me ponder the world we live in. It's a must-read for everyone.
Iris Watts
The themes of resilience and hope resonated deeply with me. This book taught me valuable life lessons that I'll carry with me for years to come.
