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

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

#1

Post by 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.

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

#3

Post by susam »

tithe wrote: post #2

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!

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

#5

Post by throwaway81523 »

susam wrote: post #3
tithe wrote: post #2

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 b…

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

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

#6

Post by moomin »

tithe wrote: post #2

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

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”

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

#7

Post by e1gen-v »

throwaway81523 wrote: post #5
susam wrote: post #3

Earlier quoted context omitted.

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 b…

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.

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

#8

Post by 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!

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

#9

Post by impendia »

tithe wrote: post #2

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

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.

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

#10

Post by gsinclair »

impendia wrote: post #9
tithe wrote: post #2

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

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!
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