So, let's suppose for a moment that I was interested in giving an informative but not-too-technical expository talk to fellow first-year math graduate students on the Monster Group. What books would you recommend I get my hands on to help achieve such a goal? Thanks in advance.
Hey guys, so this may be a really silly question, but I'm trying to grasp a subtle point about higher-order derivatives of multivariable functions. In particular, suppose we have an infinitely differentiable function
f: \mathbb{R}^{n} \rightarrow \mathbb{R}
I know that the first...
How would you embed the symmetric group on n letters in the alternating group of (n+2) letters? I'm actually trying to write down an explicit map but can't seem to come up with one. I know An will be a subgroup of A(n+2) but I have a feeling that a map that is the identity on An and...
Wellll why don't you begin by assuming that there do *not* exist elements of order 7 and 11? In this case the group must be cyclic, generated by, say, a (by Lagrange). What is the order of a^11?
This argument will prove that there must exist at least one element of order 7 OR 11. A similar...
The map that matt shows it not a ring isomorphism, for the exact reason that lurflurf gave: f(2 + 2) = f(2*2) which will contradict any isomorphism between the two structures.
So I am going through Serge Lang's Algebra and he left a proof as an exercise, and I simply can't figure it out... I was wondering if someone could point me in the right direction:
If f is a polynomial in n-variables over a commutative ring A, then f is homogeneous of degree d if and only if...
I imagine you forgot to put the summation notation before your terms?? McLaurin series are infinite summations; anyways, 1/(n+1) converges to 0, but this is not sufficient to prove that it converges. Can you think of a fairly famous series that this reminds you of?? Similarly for the...
I think most people are introduced to proof-based mathematics via analysis and Calculus. Thus people learn to utilize their geometric and physical intuition, whereas algebra is highly formal and more difficult to grasp with this type of intuition. I love analysis, and I find algebra to be very...
Ah, but for your proof you have assumed something that we aren't given, namely that x is an element of A. If x is not an element of A, then a neighborhood of x is not a subset of A.
Also, consider this example: let (X, T) be the discrete topology. Consider any proper subset A of X. Then...
Well, first off, the proof "proves" a reversed inclusion from the one you have listed. Also, I'm not sure what this is looking for: "give an example where equality fails." as you don't have any equality in your problem.
A few things about the proof though:
1.) Just because x is in a...
Based on the FAQ pages I've read, I would say an e-mail like that should wait until mid-March. There are a ton of programs that haven't begun sending out responses yet (that I know of).
You are very close; however,
\det(\alpha A)=\alpha^{n} \det(A)
where n is the order of the matrix A, in this case 3. To understand why this happens, think of the determinant of the identity and multiply it by a scalar.
You obviously missed *my* point also :
Somewhere someone has an explanation of the line integral's geometric and physical meaning. Go over *that* until you can recite and explain each step.