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Comment by tithe | Hacker News Reader

Just curious, any reason why Rudin's text wasn't selected? (Although I see Howie's text is for an undergraduate level.)

The first book club I organised focussed on "Introduction to Analytic Number Theory" by Apostol (1976). While the book excelled in rigour, some members, especially those without a strong mathematics background, found the constant alternation between theorems and proofs a bit too dry. Personally, I thoroughly enjoyed it. See <https://susam.net/journey-to-prime-number-theorem.html> for a related post.

For the current book club, I've chosen something more lightweight with a more relaxed writing style. Although I'm slightly concerned about the level of rigour in this new book, I'll be able to assess it better as we make more progress through the book.

Rudin is also on my mind. But maybe that's for a future series of book club meetings!

You might like Michael Spivak's "Calculus" as a rigorous approach to what might as well be called introductory real analysis.

I remember being recommended that text in college. It’s a very approachable book.

I'm a math professor, who got through most of Rudin as an undergrad. Felt like a form of hazing at the time ;)

In my opinion, Rudin is a great book if you're reading it under the guidance of a good teacher. For self-study, I don't know of any particular alternative to recommend, but I would select something more "talky" -- i.e. which goes more into the background, motivation, and philosophy of the subject.

Something more talky is Real Analysis by Jay Cummings. Great book!

I love Bartle’s Real Analysis myself. Little history each chapter on a figure who impacted the specific topic and good explanations. Not sure how it compares to Rudin though.

I was a CS undergrad at MIT and took the fancy math people’s analysis class for a math requirement and they used Rudin and it killed me. We went through like 170 pages of it for one semester. The professor was Sigurdur Helgason. I went into office hours one day and ask him a question. He slowly walked to his window and replied “the ravines in Iceland are deep” and it was at that point that I realized I was an engineer and not a mathematician.

Lol. Did you figure out what that was supposed to mean?

Not the OP but as a mathematician I can say this, if you study analysis and start to ask questions about why or how certain things work, you will quickly fall deeper and deeper into a rabbit hole until you reach the basic axioms. In analysis the distance between these axioms and what people use analysis for on a daily basis can be quite large.

As someone who worked through Rudin in their free time as a working adult, I cannot recommend it to someone for self-study who doesn't already have a calibrated mathematical sense. By that I mean that they are good at figuring out how to adapt a proof sketch with many omissions (more typical at higher undergrad/grad/research) into one that is more conscientious about tying up all the "trivial" technical details.

In my case, I was a CS major, and I had experience with proof assistants, so it was doable with many excursions to Wikipedia, math overflow, ProofWiki, etc..

The thing I loved about Rudin’s book was that the start of it basically ignores the standard pedagogy and goes “Compact spaces go brrrr”

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