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

Jay Cummings

/ ISBN 13: 9798595265973

Published by Independently published 19 J, 2021

Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series) This book is in very good condition and will be shipped within 24 hours of ordering. The cover may have some limited signs of wear but the pages are clean, intact and the spine remains undamaged. This book has clearly been well maintained and looked after thus far. Money back guarantee if you are not satisfied. See all our books here, order more than 1 book and get discounted shipping. . Seller Inventory # 7719-9798595265973

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.

Bibliographic Details

Title: Proofs: A Long-Form Mathematics Textbook (...
Publisher: Independently published 19 J
Publication Date: 2021
Binding: Paperback
Condition: Very Good