Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)
Original price was: $39.99.$18.99Current price is: $18.99.
Description
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.
17 reviews for Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)
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Napilopez (verified owner) –
I’m not done with the book yet, but I had to leave a review because this intro to proofs is fantastic. As a self learner I can’t say how it compares to other books in terms of thoroughness, but I can say I feel like I’m actually *learning.*
The author writes with a kind of clarity and humor that is far more engaging than almost any other serious math book I’ve read. If a math book could be a ‘page turner,’ this is it. It may be written in ‘long-form,’ style but the time you spend reading more words than typical for a math book, you more than save in understanding concepts on your first or second read through (rather as opposed to staring at a sentence or equation 10 times in a row and failing to understand what’s going).
Reading this book feels like you are genuinely being guided through topics, while still requiring you to struggle with the material. Other books just drop you in a sea of knowledge and hope you can fend for yourself.
I love this series and can’t wait to see what other books the author comes up with! I just wish there were digital versions so I can read on my phone, kindle, or laptop when I am not home.
Daniel (verified owner) –
The top reviews are spot-on. I really appreciate the approach the author took to this book. It is not the best stand-alone solution for self-learners (no solutions), but few things are. This book is great supplementary material for many undergraduate learners.
Henrik (verified owner) –
goofy footnotes ngl, although its thorough and well worth the pricetag. bravo!
Wills (verified owner) –
High quality work that helps bridge the gap between upper division and lower division math. Well priced because the author believes math textbooks are overpriced and tries to bring more equity into the math field. I highly recommend buying this book if you are new to proof writing and taking upper divisions soon. It expands on topics in discrete math and other subjects like pigeonhole principle etc. I bought this book out of curiousity and think it is a killer deal. I support this author’s genuine intentions and hope you enjoyed the book as much as I did
AJD (verified owner) –
My precocious 13-year old wasn’t challenged in his middle school math classes. He’s already completed multivariate calculus on Khan Academy and wants to be a mathematician. This book has been great for him because it is engaging and he’s enjoying learning about different areas of math. I highly recommend it!
City Smart Systems INC (verified owner) –
Its great and all but i need a kindle verison
Saba K. (verified owner) –
I’m not a big reader… but I really enjoy reading this. I’m a math undergrad student and this has really helped me understand concepts without making it boring. I definitely recommend it.
Geophysics student (verified owner) –
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 Amazon
For 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 heading
I’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 Analysis
Upgrade after completing Chapter 4
I’m working out in detail the text and the problem sets. My opinion of the book hasn’t changed. It’s a great book.
Max. R (verified owner) –
I bought this book to refresh my memory on mathematical proofs and relearn things I’ve forgotten from my undergrad studies. The book is an easier read to comprehend and learn from than others I’ve studied. Dr. Cummings has taken the time to truly keep the reader engaged and gives practical and theoretical cases to ponder. I have worked through examples in the first few chapters and they all have been challenging and thought provoking. He gives “pro-tips” at the end of each chapter to give a background on things to keep in mind as you progress through the book. Can’t recommend this book enough!
C. Coxwell (verified owner) –
If you’re learning math through self study and wondering, as I did, if this text is a good resource, wonder no more. It’s excellent. It’s rigorous and conversational, nothing like a typical text that might cost 10x what this one does.
BrooklynDad (verified owner) –
This book has come to my rescue many times already in the first week of owning it. I appreciate the clear explanations and genuinely funny math humor. I feel like this book was made for my style of learning and a key to unlock others I otherwise might not have enjoyed.
Bob (verified owner) –
I am a moron I don’t have a college degree I don’t have a high IQ and sometimes it takes me up to a hour just to read through and understand what the author is trying to explain in a certain proof. And yet this is one of the most enjoyable math books I have ever read. The author injects a lot of his own personality and it makes it a delight to read instead of it sounding like a professor is trying to explain hard concepts to you. It sounds like a friend is excitedly trying to tell you how he figured a puzzle out. I try to do every exercise it takes me days sometimes to think it out and even with hints. If an idiot like me can make his way through the books anyone can.
Mistique Issi (verified owner) –
I’m so grateful for this book series. I’ve been struggling to understand intro to analysis so when I found this book I ordered both in the series. My summer and fall project is devouring all of both of these books, because dang it….I will pass this class! Thank you to the author for bringing this class down to a conversation meant to be understood.
Abraham (verified owner) –
I purchased this book with the intention of preparing for a Real Analysis course I had planned to enroll in. While many of my acquaintances recommended “Book of Proof” by Richard Hammack, which is generously available for free, I found this particular book to be exceptional. It goes beyond merely presenting proofs; it teaches you how to approach the process of proving something. The author emphasizes the importance of “scratch work” in developing your proof-writing skills. Additionally, I appreciate the author’s inclusion of helpful tips and tricks at the end of each chapter, as well as thought-provoking open questions in the field. The book even provides a glimpse into more advanced topics related to each chapter. Moreover, the author’s use of witty and pun-filled footnotes-feetnote as the author would like to call it- adds an entertaining aspect to the reading experience. I absolutely love it!
Bernardo Rivas (verified owner) –
One of the best introductory books to writing mathematics that I’ve ever seen. It is fun, engaging and easy to read. It should be the perfect material for an active learning setup as students won’t struggle to read the mathematics written in there.
Edgar Merkle (verified owner) –
This book doesn’t assume you already know all the material, which is somewhat unusual for a college-level math book. More books should take an approach like this, at the price of this.
Josh Park (verified owner) –
Great textbook, very clearly walks through each step and overall a good introduction to formal mathematical proofs