[HN Gopher] Tell HN: I am going to host "Real Analysis" book clu...
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Tell HN: I am going to host "Real Analysis" book club meetings
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.
Author : susam
Score : 39 points
Date : 2024-07-27 18:19 UTC (4 days ago)
| tithe wrote:
| Just curious, any reason why Rudin's text wasn't selected?
| (Although I see Howie's text is for an undergraduate level.)
| susam wrote:
| 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 wrote:
| You might like Michael Spivak's "Calculus" as a rigorous
| approach to what might as well be called introductory real
| analysis.
| e1gen-v wrote:
| I remember being recommended that text in college. It's a
| very approachable book.
| moomin wrote:
| 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"
| impendia wrote:
| 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.
| gsinclair wrote:
| Something more talky is Real Analysis by Jay Cummings. Great
| book!
| oglop wrote:
| 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.
| throwaway81523 wrote:
| Is the book online? I'd expect there are some that are.
|
| Will there be any Fourier analysis?
| ksd482 wrote:
| 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.
| threatofrain wrote:
| 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 wrote:
| What is it called?
| threatofrain wrote:
| Analysis 1/2.
| ned_at_codomain wrote:
| Cool idea!
|
| Am personally too scarred from taking analysis back in college to
| participate :)
| ww520 wrote:
| 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.
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