All posts by Chris Aldrich

Category Theory Lecture series from Steven Roman

Steven Roman has a series of six lectures on category theory from 2015:

Week Ten Meeting: §5.1 and §5.2 of David Spivak’s Category Theory for the Sciences

Week Ten

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

  • 5.1 Categories and functors
  • 5.2 Common categories and functors from pure math

Last week we made it through most of section 5.1, so we’ll finish it up and hopefully make it through 5.2, and pending time and people’s motivation this past week, possibly break into the beginning of 5.3.

Pace

We’re behind our original schedule, but still making some relatively good progress with a core peleton of people.  Given the participation, we’ve slowed down a tad in an effort to not lose anyone, particularly with a variety of schedules and time zones.

More Resources

Now that we’re into chapter 5 where the real fun has begun, people might also consider branching out to some of the alternative and more advanced texts. Some of the video resources are probably more germane to everyone now as well. In particular, I spent some time last week with Dr. Codrington’s youtube videos (1-6 of his “Lesson One”) which are generally excellent and which follow reasonably enough the presentation of Spivak that one won’t become lost.

Technical Update

Again, as a reminder for those who have had difficulties joining in the weekly live conversation, be sure to log into Google+ a few minutes before the start of the meeting.  Once it starts the moderators send out additional invitation reminders to join the conversation which should result in a pop up on your Google+ page inviting you into the live video/audio feed.

Alternately you can go to the Category Theory Study Group’s Google+ posts page where you should see a button with a camera icon on the particular week’s post that says “Join Hangout”. Clicking it should put you into the live conversation.

Another option should be to join from your events page. If you don’t see the hangout event there, make sure we have your G+ account so we can ensure you’re included in the invitation.

Week Seven Meeting: §4.4 and §4.5

Week Seven

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

  • 4.4 Orders
  • 4.5 Databases: schemas and instances

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.

Week Six Meeting: §4.3

Week Six

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

  • 4.3 Graphs

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.

 

Technical Update

For those who have had difficulties joining in the weekly live conversation, be sure to log into Google+ a few minutes before the start of the meeting.  Once it starts the moderators send out additional invitation reminders to join the conversation which should result in a pop up on your Google+ page inviting you into the live video/audio feed.

Alternately you can go to the Category Theory Study Group’s Google+ posts page where you should see a button with a camera icon on the particular week’s post that says “Join Hangout”. Clicking it should put you into the live conversation.

Another option should be to join from your events page.

Pace of Material & Syllabus

Some will notice that we’ve slowed down a tad to accommodate the peleton who have been doing the diligence to keep up. Hopefully the last week “off” for the July 4th holiday in the states will have let everyone catch up a bit.  The syllabus will be changing to meet our needs as we proceed.

For those with some general background in Category Theory, we’ll be getting into the serious material shortly.

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.

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.

Administrative Note

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:

Remarks to Students Learning Mathematics in Small Groups
Remarks to Students Learning Mathematics in Small Groups

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.

Julian Weissglass Small Groups: An Alternative to the Lecture Method. The College Mathematics Journal, Vol. 7 (1976), pp. 15-20