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

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

1. Josh Park

   Rated 5 out of 5

   October 26, 2023

   5.0 out of 5 stars Better explanation than $100 books

   Great textbook, very clearly walks through each step and overall a good introduction to formal mathematical proofs

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   Edgar Merkle

   Rated 5 out of 5

   September 27, 2023

   5.0 out of 5 stars More valuable than the expensive books

   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 approac...More

   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.

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   Bernardo Rivas

   Rated 5 out of 5

   July 20, 2023

   5.0 out of 5 stars Fun and engaging

   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...More

   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.

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   Abraham

   Rated 5 out of 5

   July 15, 2023

   5.0 out of 5 stars Best intro book to formal proofs for a non-math major student like me.

   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 recommende...More

   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!

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   Mistique Issi

   Rated 5 out of 5

   July 9, 2023

   5.0 out of 5 stars Information overload!!

   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 ...More

   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.

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   Bob

   Rated 5 out of 5

   May 26, 2023

   5.0 out of 5 stars A Idiot Can Understand

   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 ...More

   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.

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   BrooklynDad

   Rated 5 out of 5

   May 17, 2023

   5.0 out of 5 stars An Extremely Helpful Book

   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...More

   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.

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   C. Coxwell

   Rated 5 out of 5

   May 13, 2023

   5.0 out of 5 stars Great For Self-Paced Learners

   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...More

   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.

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   Max. R

   Rated 5 out of 5

   April 26, 2023

   5.0 out of 5 stars Amazing book that keeps you interested!

   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...More

   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!

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   Geophysics student

   Rated 5 out of 5

   April 26, 2023

   5.0 out of 5 stars Excited after reading the first 20 pages so far!

   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. ...More

   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.

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   Saba K.

   Rated 5 out of 5

   April 21, 2023

   5.0 out of 5 stars Great book!

   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 i...More

   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.

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   City Smart Systems INC

   Rated 4 out of 5

   March 25, 2023

   4.0 out of 5 stars kindle verison

   Its great and all but i need a kindle verison

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   AJD

   Rated 5 out of 5

   February 7, 2023

   5.0 out of 5 stars Great intro to proofs and areas of math

   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 ...More

   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!

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   Wills

   Rated 5 out of 5

   December 16, 2022

   5.0 out of 5 stars Phenomenal

   High quality work that helps bridge the gap between upper division and lower division math. Well priced because the author believes math textbooks are...More

   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

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   Henrik

   Rated 4 out of 5

   October 10, 2022

   book

   goofy footnotes ngl, although its thorough and well worth the pricetag. bravo!

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   Daniel

   Rated 4 out of 5

   April 6, 2022

   4.0 out of 5 stars Great book, missing solutions

   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-learner...More

   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.

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   Napilopez

   Rated 5 out of 5

   February 6, 2021

   5.0 out of 5 stars If a math textbook could be a 'page turner,' this is it

   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 t...More

   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.

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