Proofs
by Jay Cummings · first published 2021
89% recommend11% neutral
Why HN recommends it
Gentle, humorous introduction to writing mathematical proofs, with a long-form textbook style and plenty of exercises; suited to self-learners and adults starting proof-based math.
Summarised by Claude from recommending comments
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- Linear Algebra: Gilbert Strang videos + book - Calculus and basics of Analysis: Spivak - Group Theory: Visual Group Theory - Complex Analysis: Visual Complex Analysis - Writing proofs: Proofs: A Long Form Textbook by Jay Cummings - Abstract Algebra: Dummit-Foote book. First few chapters if you like. ___ Pop-Sci: 1. The Joy of X by Steven Strogatz 2. Fermat's Enigma by Simon Singh…
on “Ask HN: Serious mathematics books that can replace a good teacher?” ↗I have checked several books. The best one right now is Proofs: A Long Form Textbooks by Jay Cummings. I wholeheartedly recommend it. And this is exactly the one you are looking for. It is fully intended to teach learners how to write proofs, and not to impress…
on “Ask HN: How to learn mathematical proofs from scratch?” ↗I recommend Proofs by Jay Cummings as an exceedingly gentle introduction of proofs. It's not as serious as your typical math textbook; it has plenty of jokes to keep you entertained. https://www.amazon.com/dp/B08T8JCVF1…
on “Ask HN: How to learn mathematical proofs from scratch?” ↗I highly recommend Proofs: A Long-Form Mathematics Textbook by Jay Cummings. https://www.amazon.com/Proofs-Long-Form-Mathematics-Textbook... I have not read this particularly entry from him, but I have his analysis book. He…
on “Ask HN: How to learn mathematical proofs from scratch?” ↗I highly recommend the one that I am currently reading: Proofs: A Long Form Math Textbook by Jay Cummings [0]. There are two lists [1][2], one by Mark Saroufim, another one by Susan Rigetti that I have been following for quite some time now and intend to follow…
on “Ask HN: Math books you recommend just for the way they are written?” ↗…mathematician, currently working as a private tutor for adults who want to learn proof-based math. I had a quick glance through this book and it seems to me like a pretty nice version of this "intro to proofs" sort of book. This is a topic that's done well in a lot of different books, though, so if you really want to dig into this topic I'd maybe recommend looking at a couple different ones and finding the…
on “A Gentle Introduction to the Art of Mathematics” ↗…Bertsekas and John Tsitsiklis. - Graphs: Plenty nice books. Can also choose GT specific chapters from Discrete Math books. Edit: If you haven't have formal Math training, you need to learn how to write proofs. For Proofs, I wholeheartedly recommend Jay Cummings's book "Proof: A Long Form Text Book".
on “Ask HN: Anyone Considering Getting a Math/Phys Msc/PhD” ↗Real Analysis. I know Baby Rudin is probably the gold standard, but Jay Cummings' Proofs and Real Analysis have been great for people like me delving deeper into mathematics.
on “Ask HN: What Are You Learning?” ↗One the same subject and as accessible, I love the two books from Jay Cummings: Proofs and Real Analysis. Each just $16 on Amazon. It is a joy to read these books and try some of the exercises. I wish PDF versions were also available... For those interested: https://webpages.csus.edu/jay.cummings/Books.html
on “A Gentle Introduction to the Art of Mathematics” ↗One of my favourite acknowledgements in a book is from "Proofs: A long-form mathematics textbook" by Jay Cummings[1]. Which as it sounds like is a maths textbook. Anyhow the acknowledgement reads: "To my loving wife, who read this entire book, apart from…
on “The unexpected poetry of PhD acknowledgements” ↗As a PSA for anybody who wants a very readable introduction to "real" math, check out Jay Cummings' two books: Proofs and Real Analysis at https://longformmath.com/ Each paperback book costs less than $20 on Amazon.
on “The Greatest Educational Life Hack: Learning Math Ahead of Time” ↗…Structured Approach" but I only got so far, mostly because I decided to prioritize upskilling and getting a new job first. There's also a relevant hackernews post[0], and one of the suggestions there was "Proofs: A Long Form Textbooks by Jay Cummings". [0] https://news.ycombinator.com/item?id=31800081
on “Ask HN: Which books are the best to self study proof based math?” ↗