Real Analysis
by Jay Cummings · first published 2018
100% recommend
Why HN recommends it
Accessible, fast-paced introduction to elementary real analysis for readers who already know proofs. Its conversational tone suits self-study and works well as a companion to a more advanced text.
Summarised by Claude from recommending comments
Affiliate links. As an Amazon Associate I earn from qualifying purchases.
Mentions per year
What Hacker News says
Related books
Proofs
Jay Cummings
Recommended by 8 · mentioned by 98 recommend · 9 mention8 recommend · 98 recommend
2017–2023What doesn't kill us
Scott Carney
Recommended by 3 · mentioned by 33 recommend · 3 mention3 recommend · 33 recommend
Linear Algebra
Kuldeep Singh
Recommended by 9 · mentioned by 119 recommend · 11 mention9 recommend · 119 recommend
2008–2024A first course in abstract algebra
John B. Fraleigh
Recommended by 10 · mentioned by 1510 recommend · 15 mention10 recommend · 1510 recommend
Book of Proof
Richard Hammack
Recommended by 54 · mentioned by 6654 recommend · 66 mention54 recommend · 6654 recommend
2009–2026Finite-dimensional vector spaces
Paul R. Halmos
Recommended by 24 · mentioned by 3824 recommend · 38 mention24 recommend · 3824 recommend
2016–2025Shoe Dog
Phil Knight
Recommended by 77 · mentioned by 10377 recommend · 103 mention77 recommend · 10377 recommend
2008–2026Calculus
Michael Spivak
Recommended by 88 · mentioned by 13088 recommend · 130 mention88 recommend · 13088 recommend
If you have taken some "intro to proofs" or "intro to abstract algebra" or "intro linear algebra" or any other such course where you've seen rigorous proofs, then Jay Cummings' "Real Analysis: A Long-Form Mathematics Textbook" [0] is simply a phenomenal introduction to real analysis. It's a fast paced tour de force through rigorous analysis. I actually wrote a longer comment, but I had to…
on “Best book/paper you read in 2018?” ↗…Hammack (tools of the trade) Linear Algebra by Kuldeep Singh (rigorous tutorial: combines the rigor of a textbook and the ease of use of tutorial) Abstract Algebra by the Dos Reis (rigorous tutorial) Real Analysis by Lara Alcock (this books makes the rigorous definition of sequences trivial) Real Analysis by Jay Cummings (contains much more info than the one above and is very similar in spirit) Real Analysis…
on “Robert Langlands: The Greatest Mathematician You’ve Never Heard Of?” ↗Real Analysis: A Long-Form Mathematics Textbook by Jay Cummings [0] finally helped me conquer elementary real analysis. It was fast, smooth and streamlined experience. Your millage may vary, though, as this one wasn't…
on “Ask HN: Favorite nonfiction books of 2018?” ↗Real Analysis: A Long-Form Mathematics Textbook by Jay Cummings. It's a very brisk read and lacks that heavy-handed feel you get from even looking at math books. That said, it's been edited by bajillion people (mostly…
on “Ask HN: What are the best books you've read in 2018?” ↗there is a book by jay cummings called real analysis: a long-form mathematics textbook that i highly recommend checking out. used with a more "advanced" book, it could be a nice complement. Real Analysis: A Long-Form Mathematics Textbook https://www.amazon.com/dp/1724510126/
on “Elementary Applied Topology (2014)” ↗…intro books are so easy anyone and they momma can read these with utmost ease: Discrete Math by Susanna Epp How to Think about Analysis by Lara Alcock Linear Algebra: Step by Step by Kuldeep Singh Real Analysis: A Long-Form Mathematics Textbook by Jay Cummings A Tour Through Graph Theory by Karin Saoub The above mentioned books are a few examples of elementary books that you can get started with right this…
on “New math book rescues landmark topology proof” ↗Something more talky is Real Analysis by Jay Cummings. Great book!
on “Tell HN: I am going to host "Real Analysis" book club meetings” ↗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” ↗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” ↗One of my favourite dedications is in the preface to “Real Analysis: A long-form mathematics textbook” by Jay Cummings (which is as it sounds a maths textbook). The dedication reads “To my loving wife, who read this entire book, apart from the maths parts.”
on “Book Dedications” ↗