Tell HN: I am going to host "Real Analysis" book club meetings

[susam]

Hello HN! After two successful book club meetings on analytic number theory and Emacs in 2021 and 2022-2023, respectively, I am going to a host a new series of book club meetings.

This new series of book club meetings is going to be on Real Analysis. This is going to be a multi-month journey where we are going to cover topics like sequences and series, functions and continuity, calculus, logarithmic functions, exponential functions, circular functions, etc.

The first meeting is scheduled at 19:00 UTC today, i.e., about 40 minutes from the time of sharing this post.

If you are interested in this type of thing, please see https://susam.net/cc/real-analysis/ for more details.

[susam]

Since the link in the "Tell HN" post is not clickable, here is a clickable link: https://susam.net/cc/real-analysis/

[threatofrain]

Anyone looking at Real Analysis might look at Terry Tao's book, which is both conversational and friendly but also rigorous, starting from set theory and building all the way up.

[maxk42 → threatofrain]

What is it called?

[threatofrain → maxk42]

Analysis 1/2.

[analog31 → threatofrain]

That seems like a rational title.

[Cyphase → analog31]

Get real.

[lambda → Cyphase]

You are approaching the limit of good taste

[mondobe → lambda]

These jokes are getting too complex...

[dexwiz → mondobe]

Are you kidding, it’s prime material.

[fragmede → dexwiz]

I'm getting irrationally angry about how HN is turning into Reddit

[Cyphase → fragmede]

Okay, now you're just tying yourselves in knots.

[Cyphase → Cyphase]

for anyone who missed it: https://en.wikipedia.org/wiki/Knot_(mathematics)

[fuzztester → fragmede]

transcend your anger by realizing that we are, all really one, and let's join our arms in unity.

[_zoltan_ → fragmede]

because Reddit is good, no matter how much you think you're elite just becasue you're on HN as well.

[fragmede → _zoltan_]

too subtle?

tbc, that complaint is old as the hills and technically against the guidelines, but I couldn't help myself. I have no pretentions about HN and will usually call out other commentors for it.

This kills the pun train, unfortunately.

[Cyphase → fragmede]

Not if we transcend our miscommunications.

[fuzztester → dexwiz]

this subthread feels so natural. is it something integral to the topic?

[fuzztester → dexwiz]

we should factor your comment into the decision, of course.

[fuzztester → mondobe]

i am fine with having an infinite series of them ...

[fuzztester → mondobe]

yes, there should be a limit to them.

[TZubiri]

Can we do Newton's philosophia naturalis?

[tithe]

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

[susam → tithe]

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!

[throwaway81523 → susam]

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

[e1gen-v → throwaway81523]

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

[impendia → tithe]

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.

[zeitgeistcowboy → impendia]

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.

[impendia → zeitgeistcowboy]

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

[Gabriel54 → impendia]

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.

[oglop → impendia]

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.

[gsinclair → impendia]

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

[jhanschoo → tithe]

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..

[moomin → tithe]

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”

[antman]

This series of courses from Francis Su. It is not mentioned a lot but I think it succeeded in creating an intuition on Real Analysis for me. I think it could help people joining this https://youtu.be/sqEyWLGvvdw?si=RmS-JeC5WHKDsZ5D

[jhanschoo]

I'm interested in joining, and I'll be looking at the link and matrix. I've worked through baby Rudin's exercises up to ch 7., so I think I can provide guidance where necessary.

[ned_at_codomain]

Cool idea!

Am personally too scarred from taking analysis back in college to participate :)

[kqr]

Thanks for sharing. I have been interested in repeating the basics of analysis so I will buy and read the Howie book. With some luck, I might even find time to join the meetings!

[ww520]

Excellent idea. Real Analysis was the hardest course I took back in college. Too bad I've lost the book over the years. It's an old edition.

[koskanaiken → ww520]

Just curious, did you take other higher level math classes (complex analysis, topology, etc)? If yes, do you think they are easier?

[crystal_revenge → koskanaiken]

I suspect, for a lot of math students, Real Analysis is the first introduction to "real math" and is frequently taught assuming such. I found, at least in undergrad, that a fair bit of students that think they are "good at math" are really "good at calculation" and Real Analysis is quite a shock for anyone coming from that perspective.

It's unfortunate that many students studying math more causally or as a prerequisite for other fields don't get a chance to study Real Analysis because, in addition to this difficulty (from lack of exposure), it's also a great introduction to the beauty of mathematics.

I'm about as far as one can get from a practicing mathematician, but I still find myself pulling out the baby Rudin from time to time just for the pure pleasure of wandering through it.

[dunham → crystal_revenge]

I had baby Rudin for my undergrad class (I don't remember which book I had in grad school), and I kept that one when I downsized my book collection in case I want to refresh my memory someday. At the time, I was more interested in algebra and combinatorics. I also kept my copy of Herstein.

25 years later I've forgotten most of it. But recently I've turned my attention to type theory, category theory, and related topics. I have little spare time and the amount of interesting topics to explore is daunting, but it's fascinating. (I've always been interested in mathematical foundations, too.)

[ww520 → koskanaiken]

It was mostly because I had a terrible lecturer.

[chazeon]

Is there a calendar link I can subscribe to?

[throwaway81523]

Is the book online? I'd expect there are some that are.

Will there be any Fourier analysis?

[ksd482 → throwaway81523]

Judging from the initial topics listed "sequences and series, functions and continuity", it seems like this will be a beginning real analysis course.

Fourier analysis usually comes after we have covered differentiation, integration, metric spaces, basic topology at the very least.

[fuzztester]

very cool idea.

i feel inspired by this to start a similar club on some other interesting topic. I will have to think what topic to select.

good luck!

[BobbyTables2]

Sounds like they’ll have a ”ball”.

[oiphl]

This is awesome! Real Analysis is such a fundamental subject in mathematics, yet it often feels inaccessible without a structured environment. Hosting book club meetings sounds like a fantastic way to tackle this challenge together. Are you planning to follow a specific textbook or will it be a mix of different resources? Also, how will you structure the meetings to ensure everyone stays on track? Looking forward to hearing more about this and possibly joining in!

[kdamica]

Once you go Lebesgue, you never go back

[xiaodai]

covered this in uni.