Recent content by Szichedelic

Homework Statement I'm trying to prove the statement "Show that a subgroup of a quotient of G is also a quotient of a subgroup of G." Homework Equations See below. The Attempt at a Solution Let G be a group and N be a normal subgroup of G. Let H be a subgroup of the quotient...

Oh duh.. That makes things a lot easier.

Homework Statement A group G of order 12 contains a conjugacy class C(x) of order 4. Prove that the center of G is trivial.Homework Equations |G| = |Z(x)| * |C(x)| (Z(x) is the centralizer of an element x\inG, the center of a group will be denoted as Z(G)) The Attempt at a Solution Let G...

If anyone can help me find examples to work on, that would be great as well.

Sorry about the long title. I recently had a few homework problems which were similar to the title of the post. I struggled a bit with them so I'm trying to find additional problems to work on until I can master these ideas... Basically, if we have a group G s.t. |G|=n, and we know G has a...

I had a moment of insight last night around 1am. I understand now how ideals and affine varieties are linked. The vanishing ideal is the ideal of a variety. Ideals also give us a way to compute with affine varieties, correct?

Can someone please explain to me these two concepts and how they differ from each other? I'm taking a class entitled Math & Computers which emphasizes algebraic geometry in a symbolic-computational setting. That being said, the class is not very oriented towards explaining and understanding...

Grothendieck is one of my inspirations. I've been reading a lot about him lately. The hair comment was a joke.

I will use myself as an example. In high school, I flunked out of trigonometry. I liked the subject but it would take me a week to finish a single-day homework assignment. However, in CC, I put in a lot more work and I managed to ace the calculus sequence, differential equations, and linear...

I'll try to type this out as clearly as possible. I believe the reason why there are so many threads like this is due to the culture of mathematics. In two of my upper division classes, I have had an eight year sitting in the front row, yelling out answers before anyone even had a chance to...

I guess that's an insecurity issue. Hardy wrote in A Mathematician's Apology that math was a young man's game. I am surrounded by people who are a good 4 years younger than I am.

What are your plans for after the PHD? I'm just trying to get a sense of where I should go from here. Originally, I wanted to go for the postdoc after the Phd. My goal is to do research. I'm thinking a year off might kill my momentum.

Robert, out of curiosity, what schools did you apply to? I was thinking of doing the same thing. Also, did you get funding?

Hi all. Well, I was all prepared to apply to graduate school this year until I missed my subject test date due to unforeseen circumstances. Let me just say that my memory is not too great and this is definitely entirely my fault. A bit of background, I'm 25 now and it looks like by the time...

Any insight?