Recent content by Justabeginner

I apologize - I meant post-baccalaureate when I said post-doc. I am hoping to graduate early because of loans/lack of FA. I have already studied the major requirements for these colleges, and with placement exams, it already significantly reduces the time I need to graduate. I'm trying to...

Don't feel discouraged by this one grade. Use it as a motivator to improve in the courses you're taking now and those you will take in the future. I know of people who have gotten B's in Calc I, and even slightly lower grades in undergrad math, but they went on to obtain PhDs in MIT, Harvard...

Thanks for the replies all! I've decided to do a Neuroscience major, but I intend to use my knowledge in upper-level math to find research opportunities in computational neuro.

Hi all! I'm trying to decide between Smith, Wellesley, and Wesleyan. I'm interested in their neuroscience programs, and have heard great things about all of them. However, quite a few factors are at play here: FA, Post-doc optionality if I want to do med school (not sure about career path yet)...

A = G * G, as in G cross G. I do not understand how T is directly isomorphic to G.

Homework Statement If p(x) ∈F[x] is of degree 3, and p(x)=a0+a1∗x+a2∗x2+a3∗x3, show that p(x) is irreducible over F if there is no element r∈F such that a0+a1∗r+a2∗r2+a3∗r3 =0. Homework Equations The Attempt at a Solution Is this approach correct? If p(x) is reducible, then there...

Homework Statement Let G be a group, A = G * G. In A, Let T = {(g, g)|g ε G}. Prove that T is isomorphic to G. Homework Equations The Attempt at a Solution A is abelian. Therefore, G * G is abelian. T is a subgroup of G. I am not sure if my above inferences are even correct...

I'm interested in studying mathematics at the undergraduate level, and have been studying some upper-level courses on my own (technically, for the college I hope to go to, I would only have six courses left to complete a math major). I also am interested in connecting my knowledge of upper level...

Is G, technically the non-abelian group GL(2, R)? I approached this problem in that manner.

For A, B in Zp, where p is prime, Det(A)Det(B) = Det(AB).

If Det(A) ≠0 and Det(B)≠0, then Det(AB)≠0 too.

M has an inverse because M= (a b c d) has another matrix such that M * (other matrix) = Identity Matrix. We know that the det(M-1) ≠ 0 because det(M) ≠0, and 1/det(M)≠0, ever. This ring is specifically an integral domain, I believe. The property of a ring is closure under multiplication and...

M * M-1 = I. The original matrix times its inverse is equal to the Identity Matrix. If an element exists, then its inverse must exist because the identity element is always in a group (definition of group). Groups are always closed under products, as well.

It means 1*n = n. The identity should be (1 0 0 1). Sorry, I completely forgot to insert them. I failed to mention that the elements are from Zp, p being a prime. Zp is a field if and only if p is prime, and the properties hold true because of this. Since the determinant is nonzero, and...

1. Multiplicative identity in a ring is 1, right? But 1 is not in G, because G consists of the set of matrices for which ad - bc ≠ 0, but (1) is not a 2*2 matrix. 2. Yes; [(ab)c]ij = (ab)ik ckj = (ailblk)ckj = ail(blkckj) = ail(bc)lj = [a(bc)]ij 3. Yes, for A= (a b c d), and B= (e f g h), it was...