# Week Five Meeting: §4.2

First apologies that technical difficulties prevented us from recording this week’s session — which incidentally may have been the best yet. Special thanks to those who joined us and helped to make it an interesting conversation.

Based on a few incoming emails as well as the feedback from the group in our conversation last Monday, it’s been suggested that we deviate a bit from our syllabus to slow things down a tad. Hopefully this will help everyone catch up and absorb the material we’re working on.

This week’s Google Hangout (RSVP here) will cover problems/questions from week five of the syllabus:

• 4.2 Groups

If you’re joining us in progress, please feel free to add in any questions you might have about previous material as well – it’s never too late to join us all.

If you’re stuck and can’t make it, it will be archived (barring any further technical difficulties) on our YouTube Channel for later consumption.

## Reminders

Many are keeping regular office hours, or are even generally available to help others out. Please be sure to use them if you need a bit of extra help.

You can also login and make a post here if you’d like. [Example]

In last week’s session, Mark Gomer has also specifically and graciously offered to help anyone who might need it.

I’ll also note that many of us keep the old window from past hangouts open throughout the week, so you can always hop in and see if anyone is available there as well.

# Exercise 4.1.1.7

Could someone explain Exercise 4.1.1.7?

Find an operation on the set $M = \{1, 2, 3, 4\}$, i.e., a legitimate function $f : M \times M \rightarrow M$, such that $f$ cannot be the multiplication formula for a monoid on $M$. That is, either it is not associative or no element of $M$ can serve as a unit.

Sincerely,
Max

# Week Four Meeting: §4.1 – §4.2

This week’s Google Hangout (RSVP here) will cover problems/questions from week four of the syllabus:

• 4.1 Monoids
• 4.2 Groups

If you’re joining us in progress, please feel free to add in any questions you might have about previous material as well – it’s never too late to join us all.

Those who aren’t able to jump into the hangout (due to hardware issues or the 10 person limit) are encouraged to chat within the hangout IM and follow along with the live stream. If you’re stuck and can’t make it, it will be archived on our YouTube Channel for later consumption.

## Participant count

As of this week there are now 32 participants in the group! Thanks to everyone who is participating, as I expected we’d have only about 4 when we started this whole thing.

# Dr. Martin Codrington’s “Category Theory: The Beginner’s Introduction”

Dr. Martin Codrington just uploaded an excellent-looking set of videos to YouTube:

# Week Three Meeting: §3.3 – §3.4

This week’s Google Hangout (RSVP here) will cover problems/questions from week three of the syllabus:

• 3.3 Finite colimits in Set
• 3.4 Other notions in Set

If you’re joining us in progress, please feel free to add in any questions you might have about previous material as well – it’s never too late to join us all.

Those who aren’t able to jump into the hangout (due to hardware issues or the 10 person limit) are encouraged to chat within the hangout IM and follow along with the live stream. If you’re stuck and can’t make it, it will be archived on our YouTube Channel for later consumption.

## Gitter Instant Messaging Client

Group participant Steven Shaw has kindly set up an open chat/IM space for us using Gitter through GitHub (apparently one of the benefits of having some hard-core coders in the group).  Gitter is one of the few IM clients out there that allows the use of LaTeX.  You can log in with your GitHub account and feel free to post questions/thoughts there as well. Since it’s always up, feel free to use it during our online meetings or throughout the week.

Thanks Steven!

## Coming Up: Week Four §4.1-§4.2

We’ll have finished some of the introductory material and be getting into some new material, so those who were waiting for the serious material to start, get ready. We’ll be covering:

• 4.1 Monoids
• 4.2 Groups

## Online video

For those who aren’t aware, or haven’t checked recently, we’ve been adding a lot of material in the resources section of the site here.  In particular, I’ll draw your attention to the video section which includes The Catsters’ Category Theory Videos.

# Week One Meeting: §1.1 – §2.2

## Week One’s Archived Video

For those who may have missed it, the video recording of our first meeting follows below.

I would usually intimate that some may also use it for review, but it primarily contains a brief overview of some of the resources available along with some administrative material overview. It’s much more scant on actual mathematics than I hope/expect they will generally be in the future.

It appears that we had over 20 people for the first session, though we’re limited to 10 active participants who have access to streaming their audio/video into the session. Apologies to others who weren’t able to more actively participate.

Keep in mind that one should hopefully still be able to add additional material via the hangouts IM functionality or by the Q&A functionality (see notes below). For those who are in the audio/video portion of the hangout, you’ll be expected to participate and contribute to the discussion.s (Perhaps you might present a problem/solution to the group?)

If you don’t have much to say (or don’t have the proper equipment (webcam or microphone)), kindly “step” out of the broadcast and watch the live stream for a while and allow others to have a shot as well. Perhaps we might arrange some method for people to rotate in/out on a regular basis? Suggestions for this are welcome.

Those not actively participating in the session can always watch the live stream through the group’s YouTube channel.

I did notice one or two interesting side-conversations taking place within the hangout’s chat (though I’m at a loss to know if/where it was archived). At present, we’ve got more than enough time in these sessions that instead of typing respondents are more than welcome to bring up their commentary to supply everyone with a more fleshed out conversation. (There does seem to be a difference between the IM/chat within the main window of the stream and that from the separate hangouts window, which is archived and accessible after the fact, so perhaps using the latter is preferable for archive purposes, as well as being more accessible to the balance of the group.

## Questions

Google Hangouts has a functionality known as Q&A to which one can write in questions that the group can work on answering during the session.  To access it at any time, go to the page for the hangout, click on the “play button” in the video portion of the screen, then in the top right hand corner of the “video” (which obviously won’t be playing until the set meeting time) click on the 3×3 square grid (just to the right of the question mark icon), and choose the Q&A pop up option. This will open up a bar on the right hand side of the screen where one can click on ask a new question at the bottom to post their question.

You can also always register at the group’s main site and post your questions there for everyone to work on/answer via the comments section during the week

## Coming Up: Week Two §2.3-§3.2

This week’s Google Hangout (RSVP here) will cover problems/questions from week two of the syllabus:

•  2.3 Ologs
• 3 Fundamental Considerations in Set
• 3.1 Products and coproducts
• 3.2 Finite limits in Set

Everyone will generally be expected to have read the appropriate sections and bring their questions/issues so the group can attempt to cover and clarify any issues anyone may be having.

If it helps one or more people to ensure that they’ve got the material down well, I’m sure the group would welcome anyone who might like to present/walk their way through one or more of the problems in the relevant sections – particularly problems whose answers left out some reasonable level of detail. If you’d like to offer to do this, please put a comment in below, so we can schedule some time during the session to accommodate this.

Though we’re off to a “slow” start, things will pick up rapidly as we progress, so please don’t hesitate to ask questions here on the blog, through hangouts, or via anyone’s office hours.

# Small Groups: An Alternative to the Lecture Method

I ran across an old paper today written by Julian Weissglass in 1976 and it seemed somewhat relevant to our group. It included the following list:

Most of the suggestions are fairly straightforward and entail general courtesy. I’m sure most are already aware of and use these suggestions regularly,  but as many in the group are teachers/professors who may be experimenting with flipped classrooms, you may find some of the commentary in this MAA paper from the 1970’s fairly useful, and may want to “borrow” portions for your own classes.

# Online Video Conference Meetings

Now that we’re a few days into the group and most everyone seems to be registered and has had some time to respond to the initial questionnaire, I thought I’d set a time for our online meeting(s)/sessions.

Most people have indicated to me that they’ve either already bought/received the text and have started reading, or are about to begin. I have a feeling  that most will find the first several chapters very basic, (but we’re all here to help those that don’t).

There are currently 25 people registered!

As a reminder, as mathematically “sophisticated” readers, we’ll be using a “flipped” format for our meetings, so everyone will generally be expected to have read the appropriate sections and worked on some problems/examples ahead of the meetings so that they can bring any problems/issues they may have to get some help from the rest of the group.

## Upcoming meetings

As an initial meeting, let’s aim for:

Friday, June 5, 2015 at 6:45 pm Pacific / 9:45 pm Eastern on Google Hangouts.

In this session, we can get any  basic administrative things out of the way and discuss any problems/issues anyone may have with the first two chapters which primarily cover some initial basics including set theory and functions.

For our regular, weekly standing meetings, let’s shoot for

Monday evenings at 6:45pm Pacific / 9:45 pm Eastern.

Hopefully this weekly time will work for those on both coasts of the Americas without any undue burden.  We can attempt to record sessions for those who aren’t able to make it due to time zone or other conflicts, but no one seemed to have any issues with Mondays and we seem to be roughly split with participants on both coasts.

The second meeting will be on:

Monday, June 8, 2015 at 6:45 pm Pacific / 9:45 pm Eastern on Google Hangouts.

We’ll cover everyone’s questions from the following sections (which everyone will have been expected to have read beforehand):

2.3 Ologs; 3.1 Products and coproducts; and 3.2 Finite limits in Set

If necessary, outside of this, we can try to hold an alternate time on Saturday, which was the other day no one seemed to have issues with. An earlier time may help those who live outside the Americas as well. Anyone who’d like an alternate time is invited to mention it in the comments below.

Due to platform requirements and the diversity of the participants, Google Hangouts seems to work for everyone and allows video, audio, screensharing, and most of the other useful features we might want.  As I recall, one doesn’t necessarily need a Google+ account, but can login through their gmail interface (typically with a browser plugin), or via the hangout app on the bigger cell phone platforms.

You can click on the individual links for the appropriate date to find/join the particular hangout on this page (above), or on the individual links listed within the syllabus.

## Office Hours

As a reminder, most participants have indicated office hours during which they are available to chat with others to offer assistance or help. I’d hope that everyone would try to login to Google Hangouts and make themselves relatively available to others to offer assistance, if they’re able during their stated office hours. Remember that helping others can assist you in reviewing/clarifying the material for yourself as well.

As always, additional assistance can also be easily had by making a post here to the “blog” with a specific question or problem and everyone can take a stab at helping out through the comments on that particular post.

If you haven’t already done so, feel free to do the following:

We all look forward to seeing you soon!

# How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics

For those who are intimidated by the thought of higher mathematics, but are still considering joining our Category Theory Summer Study Group, I’ve just come across a lovely new book by Eugenia Cheng entitled How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics.

It just came out in the U.S. market on May 5, 2015, so it’s very new in the market. My guess is that even those who aren’t intimidated will get a lot out of it as well. A brief description of the book follows:

“What is math? How exactly does it work? And what do three siblings trying to share a cake have to do with it? In How to Bake Pi, math professor Eugenia Cheng provides an accessible introduction to the logic and beauty of mathematics, powered, unexpectedly, by insights from the kitchen: we learn, for example, how the béchamel in a lasagna can be a lot like the number 5, and why making a good custard proves that math is easy but life is hard. Of course, it’s not all cooking; we’ll also run the New York and Chicago marathons, pay visits to Cinderella and Lewis Carroll, and even get to the bottom of a tomato’s identity as a vegetable. This is not the math of our high school classes: mathematics, Cheng shows us, is less about numbers and formulas and more about how we know, believe, and understand anything, including whether our brother took too much cake.

At the heart of How to Bake Pi is Cheng’s work on category theory—a cutting-edge “mathematics of mathematics.” Cheng combines her theory work with her enthusiasm for cooking both to shed new light on the fundamentals of mathematics and to give readers a tour of a vast territory no popular book on math has explored before. Lively, funny, and clear, How to Bake Pi will dazzle the initiated while amusing and enlightening even the most hardened math-phobe.”

Dr. Cheng recently appeared on NPR’s Science Friday with Ira Flatow to discuss her book.  You can listen to the interview below. Most of the interview is about her new book. Specific discussion of category theory begins about 14 minutes into the conversation.

Dr. Eugenia Cheng can be followed on Twitter @DrEugeniaCheng. References to her new book as well as some of her syllabi and writings on category theory have been added to our resources pages for download/reading.