Tropers that do NOT hate math

Yeah, Baez's blogs are impressive. I really need to go through his category theory one a bit more in-depth sooner or later — I know the fundamentals of category theory, but I never used it much and it's cool to see the crazy stuff that they can make out of it.

On a different topic, I have just finished Iamblichus' Theological principles of arithmetic. Pretty cool — it's basically a little bit of ancient basic arithmetic combined with a massive amount of late Pythagorean/Platonist philosophy, and it's really interesting.

But they seem to know where they are going, the ones who walk away from Omelas.

I've followed Baez's category theory blog for a while; it's quite advanced, much of it to the point where I can't make sense of it at all. (I also know the fundamentals of category theory, though I still have almost no intuition for some important stuff like adjoints and limits.) Higher category theory, which is what he talks about probably the most, operates at even higher levels of abstraction than ordinary category theory.

Speaking of category theory, Lang explains universal constructions in his Algebra much more clearly and intuitively than MacLane does in Categories for the Working Mathematician, or at least it seemed that way to me. I don't think I had any real intuition for comma categories, coproducts, or fibered products until I finished reading the first chapter of Algebra a few days ago. (Or maybe it just took that long to sink in — but Lang's explanations really helped.)

edited 30th Dec '11 1:44:41 AM by Enthryn

There's been talk about organizing a reading group about Categorical Logic later in the spring. Should be interesting.

But they seem to know where they are going, the ones who walk away from Omelas.

Sounds fun. Is the plan for it to be on categorical logic in general, or on a specific book on the topic?

It's uncertain for now, we are still trying to come up with a plan. It will be probably be very introductory, I think — no one of the possible participants so far has any previous experience in categorical logic, although many of them know category theory better than I do...

The main idea seems to be to use Awodey's lecture notes on the topic, for the most part, and perhaps Lambek and Scott's Introduction to Higher-Order Categorical Logic too.

edited 3rd Jan '12 9:56:26 AM by Carciofus

But they seem to know where they are going, the ones who walk away from Omelas.

Thanks for the link; those notes look interesting. Might be a while before I have time to look at them in much detail, though, since — as much fun as it would be to study categorical logic — I should probably spend most of my time on the three math classes I'm actually in.

I'm about to start being a Teaching Assistant for a course on Kolmogorov Complexity. It's really interesting stuff, I hope only I do not screw up — I took that course myself a few years ago, and I really enjoyed it, but apart from that I have basically no experience on the subject.

Well, should be an amusing refresher.

edited 30th Jan '12 11:26:12 AM by Carciofus

But they seem to know where they are going, the ones who walk away from Omelas.

-raises hand-

I guess it helps that I am a son to a mathematician. I'm more of a geographer though, and social sciences interest me more than any other science, although I normally do pretty well in sciences as well...

I now go by Graf von Tirol.

Aw, that reading group on categorical logic that I was looking forward to apparently fell through — everybody has other things to do*

and the project was aborted.

Gah. Perhaps I should explore a bit the possibility of online math reading groups? I'm pretty sure that they already exist somewhere, and they should not be difficult to set up in any case — fix a topic and a rough schedule, then discuss with the other group members about difficulties and the like...

Just as a random idea, would anybody here be interested in something like that?

edited 6th Feb '12 3:25:37 AM by Carciofus

But they seem to know where they are going, the ones who walk away from Omelas.

You know I would be, but I'm not sure how much time I'll have for it. Still, it can't hurt to at least plan on some reading and see how it works out.

Great!

Yeah, it's probably a good idea to have a slow schedule, or Real Life will mess up the plans.

About the topic, what would you prefer? Categorical logic intrigues me, mostly because I hope that it would give me some clearer intuitions about category theory, but it is not the only possible topic of interest.

For example, a while ago I was reading a little bit about matroid theory, and that's also something I would not mind learning properly. Or rough set theory, or so on.

Which topics would interest you?

But they seem to know where they are going, the ones who walk away from Omelas.

I would, although I know very very little about math.

Well, in the case, would you have any suggestions about topics and the like?

For the moment, I'm just throwing ideas around to see if something sticks.

For example, your page says that you are studying philosophy. If so, would something like mereology — the logical theory of part-whole relations — interest you?

It's a branch of mathematical logic which is relatively little studied, but which I always thought sounded fairly cool — plus, it is closely related to pointless topology, the mathematical specialty with the greatest name ever

But they seem to know where they are going, the ones who walk away from Omelas.

Categorical logic looks the most interesting to me, but I'd certainly consider studying the others if we'd get more people that way.

Set theory fascinates me, as does game theory.

The Revolution Will Not Be Tropeable

Puzzle time, because I'm bored and came up with one based on yet another fascinating side note in class:

What are two functions, besides the trivial case f(t) = e^t, such that f(t) = f'''(t)?

The Revolution Will Not Be Tropeable

I know one of them has to be f(t)=0, off the top of my head.

This "faculty lot" you speak of sounds like a place of great power...

...Okay, that's a case that I didn't think of. :P

The Revolution Will Not Be Tropeable

Now try to find two that aren't even more trivial than e^t.

I'm bad, and that's good. I will never be good, and that's not bad. There's no one I'd rather be than me.

If t is a complex variable, there are two more fairly trivial examples: f(t) = e^at, where a is any of the complex cube roots of unity.

Does that help you find non-trivial real examples? Yes, it gives you both of them.

I'm bad, and that's good. I will never be good, and that's not bad. There's no one I'd rather be than me.

I used to hate Math, until I relised I was good at it.

The smartest idiot you will ever meet.

Yay Math! :D

Where can I learn more about stuff like set theory? :o

ᐅᖃᐅᓯᖅ ᐊᑕᐅᓯᖅ ᓈᒻᒪᔪᐃᑦᑐᖅ

For set theory, I suggest "The joy of sets", by Devlin. The title is punny, and the book is very good. The level is about the one of an introductory college course on the topic — it has no prerequisites, although some familiarity with basic formal logic would come handy.

As is often the case for math textbooks, it is very dense: the book is slim, but you cannot really expect to read it very quickly — it'll take one at least a few months to go through it, I think, especially if you are going to solve the exercises and fill out the proofs left for the reader — that you should do, if you want to understand the topic.

But they seem to know where they are going, the ones who walk away from Omelas.

Ooh, okay. :o Any internet resources? :3

ᐅᖃᐅᓯᖅ ᐊᑕᐅᓯᖅ ᓈᒻᒪᔪᐃᑦᑐᖅ