Real Analysis

† There are some exceptions to this schedule occasionally. Join #susam:matrix.org or #susam:libera.chat or follow @susam@mastodon.social to receive schedule updates.

‡ You only need to join either the Matrix channel or the Libera channel, not both. Both channels are bridged together. If you are not an active IRC user, prefer joining the Matrix channel because it is more convenient for someone unfamiliar with IRC. For example, you can close your browser or client and your chat session will still stay alive on Matrix. You can connect back the next day and catch up with the messages. Doing that with IRC requires slightly more work such as setting up IRC bouncers etc.

The primary reference book for these meetings is Real Analysis written by the Scottish mathematician John Mackintosh Howie.

These meetings are hosted by Susam and attended by some members of ##math channel of Libera IRC network as well as by some members from Hacker News.

You are welcome to join these meetings anytime. If you are concerned that the meetings may not make sense if you join when we are in the middle of a chapter, please free to talk to us about it in the group channel. I can recommend the next best time to begin joining the meetings. Usually, it would be when we begin reading a new section or chapter that is fairly self-contained and does not depend a lot on material we have read previously.

FAQ

1. What is this club about?

   This is a hobby club with a focus on mathematics and computation. This club picks reading material about concepts and technologies that have been around for a long time and have an air of timelessness around them. See the blog post Reading Classic Computation Books for more details.

2. Who runs this club?

   My name is Susam. This is my website. I run this club. I host the book club meetings. The last two series of book club meetings I hosted were about analytic number theory and Emacs. Some members of Libera IRC network and Hacker News participated in those meetings. This new series is going to be about real analysis.

3. What topics are you going to discuss in the meetings?

   We will discuss the content of the reference book. This includes topics like sequences and series, functions and continuity, differentiation and integration, Taylor's theorem, the Riemann integral, etc.

4. Why did you not pick Rudin's text for the meetings?

   The first series of book club meeting I organised focussed on the book Introduction to Analytic Number Theory written by Tom M. Apostol. 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 Journey to Prime Number Theorem for a related post.

   For the current series of meetings, I have chosen a more lightweight book that is easy to read. Howie's relaxed writing style in this book seems enjoyable. I do not know yet if this ease of reading comes at the cost of rigour. I might be able to assess that better as we make more progress through this book.

5. Have you read the entire book?

   No, I have read the first few chapters of the book. This means that I am a few chapters ahead of someone who has just begun reading this book, so I can maintain a steady pace in the club discussions and also be able to tell if some topics or areas of confusion in an earlier chapter will be clarified in a later chapter.

6. What is planned for the next few meetings?

   See the meeting log which contains a rough plan for the next few meetings along with an archive of all previous meetings.

7. Do I need to read the planned chapters/pages in advance before coming to the meetings?

   Not at all. It is up to you, really. If you would like to read the chapters in advance and come, that's great. But it is not necessary. We are going to discuss every page of the book in detail anyway.

8. Can I just lurk in the meetings?

   Yes! Lurking is absolutely fine in our club meetings. In fact, most members of the club join in and stay silent throughout the meetings. Only a few members talk via audio/video or chat. This is considered absolutely normal in this club, so please do not hesitate to join our meetings!

9. I have more questions. Where can I ask?

   Join the club channel at #susam:matrix.org or #susam:libera.chat to ask more questions.