Recent content by arshavin

Let V be a vector space and ℓ : V → R be a linear map. If z ∈ V is not in the nullspace of ℓ, show that every x ∈ V can be decomposed uniquely as x = v + cz , where v is in the nullspace of ℓ and c is a scalar.

Homework Statement Let G be a finite abelian group of odd order. Prove that the product of all the elements of G is the identity. The Attempt at a Solution easy to see the case when each element has inverse which is not itself.

If G is a group of order n, and n is divisible by k. Then must G have a subgroup of order k? proof or counterexamples?

"If you don't have anything useful to contribute, stay out." This is pretty offensive. When someone posts something, its because they think its useful. And this is without mentioning the fact that Mathwonk is a great sage.

Were you applying for math grad school, or something else?thanks

sorry for starting yet another one of these threads :p As far as I know, cantor's diagonal argument merely says- if you have a list of n real numbers, then you can always find a real number not belonging to the list. But this just means that you can't set up a 1-1 between the reals, and...

What is the typical session length(in terms of weeks) at a standard university in the US or UK? In Australia we have 2 semesters (12 weeks each) and we have a summer break of almost 4 months (during which no maths courses are offered). This just seems completely ridiculous to me...

hi mathwonk or anyone, Are gauss's books, in particular "General Investigations of Curved Surfaces" accessible to someone with only calculus and linear algebra knowledge?

Just out of curiosity, was your undergraduate program at UC Berkeley 3 or 4 yrs? cheers

Amongst people around me, there is no culture of intellectual inquiry. Of course this is true for society, in general. I guess if you had a group of friends with deep passion for math, then good things happen. This is probably the downside of being educated in a place like Australia, where...

Quick Question- Is it essential to have a network of math friends/teachers as a student? I just finished 2nd year of undergraduate math and I've pretty much been on my own so far.

You could have just applied to a better uni- USYD, Melbourne, ANU are all fine(I go to UNSW and find the courses quite decent). University admission requirements in Australia are almost nonexistent(high school curriculum is a joke) and you could go anywhere you like.

The courses at my uni treat the students as if they were little kids and absorb information at a vegetative rate. PhysicalAnomaly which uni to you go to?

I am curious if other people have same issues, on desire to do maths. In my case, motivation to study fluctuates alot, on some days I have intense interest and can work for hours. Then there are times where i can't be bothered to do anything, even when i know the stuff is supposed to be...

Homework Statement Suppose the matrix A , B are diagonalizable and have the same eigenvectors. Show AB=BA Homework Equations The Attempt at a Solution There exists a matrix P s.t. (P^-1)AP=(P^-1)BP I played around with this, and could not get anywhere..