Articles liés à Proofs: A Long-Form Mathematics Textbook

Proofs: A Long-Form Mathematics Textbook - Couverture souple

Livre 1 sur 3: The Long-Form Math Textbook Series

Cummings, Jay

 
9798595265973: Proofs: A Long-Form Mathematics Textbook
Couverture souple
ISBN 13 : 9798595265973
Editeur : Independently published, 2021

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Éditeur
Independently published
Date d'édition
2021
Langue
anglais
ISBN 13 
9798595265973
Reliure
Broché
Nombre de pages
511
Coordonnées du fabricant
Manufactured by Amazon on behalf of the author
https://www.amazon.fr/hz/contact-us

c/o Amazon Media EU S.à.r.l., 38 Avenue John F. Kennedy
Luxembourg
L-1855
Luxembourg