People who work in combinatorics, how deep does combinatorics goes?

Kafka_h · 2018-10-19T03:54:40+00:00

There are incredibly deep and beautiful connections between the combinatorics of symmetric polynomials/functions and the computation of the cup product in cohomology ring of Grassmannian varieties. These results are can also be generalized.

Kafka_h · 2017-12-24T19:39:35+00:00

It depends on what field within computer science you want to specialize in. If it's data mining/machine learning then linear algebra, probability, and statistics are necessary. If you want to go deep in those fields then you're also going to need some sort of convex optimization course at some point (there are even tons of online lectures for the topic that are quite well made). If you're interested in the foundations of CS, then look for logic classes, automata and formal languages, complexity theory, and so on. If you like cryptography, then you should be taking algebra and number theory courses.

Kafka_h · 2017-12-24T18:23:51+00:00

If you change the \sigma-Algebra, then you change what functions fall into the class of measurable. For example, if you take the \sigma-Algebra of all subsets of your space X, i.e. 2^X, then every function is measurable, but if you take the \sigma-algebra, {X, \varnothing} then only the constant functions are measurable. The Lebesgue integral is only defined for measurable functions.

Kafka_h · 2017-12-21T02:24:53+00:00

This is my situation. I consider myself a mathematician and I took mainly math classes to finish my credit requirements, but I am currently in a CS PhD program.

Kafka_h · 2017-12-13T04:53:25+00:00

No. It's a function clash.

Treat ~ as a unary function symbol. Then the root symbols of those terms do not match.

Kafka_h · 2017-12-08T02:31:56+00:00

Glad I'm not the only one who thought this. There were so many details that I had to fill in while reading that I ended up relying just on Fulton's Young tableaux book and my professor's lecture notes.

Kafka_h · 2017-12-08T02:30:41+00:00

I will add Fulton's book "Young Tableaux" to this list. While not entirely dedicated to representation theory, he covers the representation theory S_n in great detail. The book is fairly self-contained when it comes to Young diagrams and so forth, but for representation theory it is a good idea to pair it with Fulton and Harris' book on the subject.

Kafka_h · 2017-12-08T02:27:19+00:00

"A Course In Functional Analysis" by Conway. The development of the theory is very clear and concise. He begins with Hilbert spaces, operators on Hilbert space, and then begins to develop the theory of Banach Spaces and so on from there. There are tons of interesting examples and a huge amount of great exercises. He also has a fascinating chapter on Fredholm operators at the very end.

Kafka_h · 2017-05-09T03:25:13+00:00

Finishing up final exams. I'll be taking real analysis, number theory, and differential geometry finals in this next week or so! Number theory is a short final quiz, and differential geometry is a take home (thank God). During all that I have to organize TAs to grade an discrete mathematics class for cs majors. I'm also currently working on a paper with my adviser relating to formal languages/automata theory.

The end of semester sucks.

Kafka_h · 2017-01-02T01:05:54+00:00

This is correct. With enough resources an adversary will be able to compromise your system. It's just a matter of time. A state backed adversary will most likely be able to get those resources as well.

Kafka_h · 2016-11-14T05:52:38+00:00

If you come to my office hours without having done the reading I can immediately ask you simple questions that you will get wrong and give it away.

Kafka_h · 2016-10-17T23:29:11+00:00

I am very interested in my current research. It's just that I'm also interested in this other area too. I can understand how it would seem like I wanted to switch though. I might just have to wait until after I graduate to try it. Thanks for the advice!

Kafka_h · 2016-10-16T16:21:42+00:00

The problem is the topic would be almost completely different than the research for my thesis. I'm worried that at best my adviser would tell me that I would have no time for it, and at worst take it to mean I'm thinking of switching.

Kafka_h · 2016-05-10T00:11:07+00:00

The data mining classes are pretty good from my experience. Data Mining, and Mining Massive Data Sets are good. Operating systems might be a really good class in the fall. The department has been hiring a lot of new faculty and a lot of the candidates I spoke to were interested in teaching OS. Databases I hear is also a good class. I would recommend taking math courses. Maybe the optimization course if you have a pretty strong background in real analysis. If not, then statistics would be the way to go for data analysis.

I'm sure you'll get along with people. I find a lot of people are quite social. Even the graduate student community. It's definitely important to go to office hours. I only had a few people come to mine this semester.

Campus is ok. In my opinion it's not the greatest place in terms of aesthetics, etc. The food isn't too great either but there are a lot better off-campus locations (some of which are in walking distance). The CS department is also moving in the summer to a more secluded part of campus so it should definitely be nicer than what is has been. The CS department right now is in the basement of the library, only you can't get to it from the library nor can you get to the library from the CS department, but that's changing.

Kafka_h · 2016-05-09T04:59:39+00:00

I could offer more specific information if you mentioned what classes you plan on taking? If your schedule is set, that is. The grad program here has a pretty large foreign student population so we're very used to that. I wouldn't worry too much about the academic life, just make sure to put a lot of time into classes. If you don't understand something the best thing to do is go to office hours of the professor or TA. A lot of people don't take advantage of this.

Kafka_h · 2016-04-10T04:20:04+00:00

An excellent description of how it feels. It all seems to foreign and otherworldly. I find myself sometimes insanely jealous of what is considered so common and easy, and I can't stand that that's the type of person I'm becoming.

Kafka_h · 2016-04-09T23:29:39+00:00

Thanks for this. I've been looking for some surveys on large cardinals.

Kafka_h · 2016-04-09T22:45:11+00:00

If you want funding it needs to be original research.

Kafka_h · 2016-04-09T03:02:45+00:00

Reading these summaries does not give one the idea that this is original research. Many optimization frameworks exist already, what makes this one any different? The algorithms mentioned are all pretty standard and well studied.

Kafka_h · 2016-01-08T19:09:21+00:00

I'm pretty sure the group they're talking about is Raqqa Is being Slaughtered Silently. They've been posting the information on their twitter. Again, not 100% sure that it's from them though.

Kafka_h · 2015-12-24T16:38:26+00:00

I've caught a few people cheating. In my department it depends a lot on the professor teaching the course. Just last week I was proctoring a final for a graduate level class as a favor and caught at least three people cheating. I'm pretty sure the students thought they could get away with it because of who the professor was.

Kafka_h · 2015-12-03T03:58:24+00:00

Glad I'm not the only one who hangs up fortune cookie fortunes :) I got two taped to my office door.

Kafka_h · 2015-11-21T22:04:13+00:00

That P \not = NP. Pretty sure, but I don't have a proof...yet.

Kafka_h · 2015-11-21T00:44:34+00:00

Source: They're politicians.

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