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

I just finished reading another wonderful book by Jay Cummings.The book is titled "Proofs" and is intended to help the readerlearn how to write diverse kinds of proofs from many differentareas of mathematics.I especially liked Chapter 4 on Induction because the writingis very clear and to the point. He discusses both weak andstrong induction and his examples are extremely well chosen.I especially like his writing style.He also writes about math proofs by induction that containmistakes that can mislead the reader. His example of how allpeople have the same name is the same as a similar examplenot in his book that all horses have the same color. Tryingto find the mistakes in these proofs can be a real challenge,but once you do it you will understand math induction evenbetter than you did before.This book has a rather ambitious aim, as proof writing is allanyone does in upper division math courses. Trying to learnhow to write proofs in such a wide open field is not easy.However, the author does not try to teach you any advancedmath and that is another reason I am so attracted to hiswriting style.Here is another small but important example. In discussingfunctions, Jay explains that writing f(x) is standard for a1-tuple, but writing f((x,y)) with an order pair is notnecessary. This a small notational convention that can tripup some students. Jay gives you permission to be confused attimes and is aware that even very small things can make yourlife complicated!Jay has written three books that are all very different. Irecently learned that I read his three books in the reversetime order in which he wrote them. Nonetheless, I think mostpeople will find his books very worth while. The "Proofs" book isas good as any and contains a lot of information.

Not only does this textbook introduce proof-writing in a wonderfully clear and organized way, the text is also full of wildly amusing footnotes. I've laughed out loud MULTIPLE times while reading this text as a supplement to the very staid text assigned for my Intro to Abstract Mathematics class.This proofs book feels like my friend. Seriously. It's weird. I love it so much. I truly, genuinely look forward to reading each section.If you are a math or CS major, buy this book. It will help mold your intuition. It will make math feel fuzzy and warm and exciting and delightful and fun. It will be a wonderful complement to the (probably) staid and formal textbook you have been assigned for your proofs book.THANK YOU, Professor Cummings!

Solid book for the price. Self-published that's why it's cheap, but content is really good and approachable. Has answers to the problems on their website.

This books it's exactly what I'm looking for: I want/need to do the jump from calculus, Lin-Algebra, PDEs to further topics like Integral Equations. Those are formulated on the more abstract grounds of Hilbert Spaces (i.e infinite dimensional vector spaces), to go there I must (willingly) detour to Real Analysis, which in turns requires mathematical proofs, and that's why I acquired this title, influenced mostly from the video about it, here in AmazonFor me the wining point is the style on which the book is written: introductory, intuitive, chatty: not too terse, not too wordy; telling you what is going on between lines, and where concepts come from and to where they are headingI'm writing this just after reading those first 20 pages, and I'm excited about for what is yet to come!I will be reporting more as I advance. I will definitely purchase the author's other book on Real AnalysisUpgrade after completing Chapter 4I'm working out in detail the text and the problem sets. My opinion of the book hasn't changed. It's a great book.

I am a mid-career engineer with a need to have a better understanding of mathematical proofs for projects in work. I’ve just finished chapter 1. Normally, I prefer my mathematical instruction to come through YouTube as I find most textbooks are good at giving information, but not teaching it. This text is entirely different. The author has kept it engaging and understandable. The information isn’t just presented, but taught and taught well.Hopefully I will update this as I go through the book.

I liked this book a lot as a 50 year old learning how to do math proofs. A little easy, but a good primer