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
✔ 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
Evie Ferguson
Discover the magic of first love and self-discovery in this enchanting coming-of-age story. The author's lyrical prose and relatable characters create a heartwarming narrative. Each chapter explores the joys and challenges of growing up with sensitivity and insight. The emotional journey is both poignant and uplifting. It's a story that resonates with readers of all ages. Ideal for fans of young adult fiction.
Elvenia Connolly
Experience the profound impact of art and creativity in this beautifully written novel. The author's evocative writing and compelling characters bring the story to life. Each chapter explores the transformative power of art with sensitivity and depth. The plot is both thought-provoking and emotionally resonant. It's a narrative that celebrates the beauty of human expression. Ideal for readers who appreciate stories about art and inspiration.
Louise Russell
Delve into a richly detailed fantasy world where magic and mystery abound. The author's imaginative world-building and captivating plot draw you in from the start. Each character's journey is thrilling and their development is relatable. The narrative is filled with enchanting elements that keep you hooked. It's a story that sparks the imagination and transports you to another realm. Perfect for fans of epic fantasy.
