Recent content by faradayslaw

Thanks very much for your replies, I was thinking just what you were saying--that essentially, its as if I just did a 4 year degree, whether it's called an "MS" and two BS or not

sorry- I forgot to add that most of my advisors said that it won't hurt, but when looking at e.g. Princeton's admissions page, it says that "undergraduate work" will be reveiwed, so I don't know if that means that if I do research as part of a master's, that won't be counted for some reason? I...

I am currently a us student in undergraduate math and physics, doing well in courses, having taken graduate courses in both areas, and have finished degree requirements for both math and physics during my second year in undergrad, but I stayed for one more year anyway. So, now, its my third...

This clarifies it! Thank You !

It's obvious to me that n(s) is perpendicular to z-axis, but I guess I don't really understand the following: The line L(t) must be in the direction of the vector n(s), but when we take the dot of L(t) with e_3 (the third basis vector in the canonical basis for R^3), we don't get 0 since the...

Homework Statement DoCarmo Section 1.5 problem 1 part d. Show that the lines containing n(s) and passing through a(s) [a is the curve, and n(s) is the unit normal vector] meet the z axis under a constant angle of pi/2. Helix: a(s) = (a cos(s/c_, a sin(s/c), b*s/c), so I computed n(s) =...

Thanks, there is a series of questions which leads to the result. Also, for those wondering, I was referring to Theorem 2.41 (ch. 2) in which it states if E subset of R^k has one of the following three properties, then it has the other two: E is closed and bounded E is compact Every infinite...

In studying Rudin's Mathematical Analysis, it seems that he uses the following statement: If every infinite subset of a set C, has a limit point in C, then C is compact. I can prove the converse of this statement, and its converse is also proven in the text, but I am unsure on how to prove...

Thanks for the reply: The constant term in h(y+1) is 29, a prime, and 29|\ all other coefficients. That of h(y-1) is 11, another prime which does not divide any other coefficeints. Thus, I don't think we can use Eisenstein Criterion. However, if we consider b(x) = x^4*g(1/x) we obtain: b(x) =...

Homework Statement Determine if 1+8x-12x^3+2x^4 irreducible over Q[x] Homework Equations Gauss's Lemma, Eisenstein Criterion The Attempt at a Solution If we multiply g(x)=1+8x-12x^3+2x^4 by 2^3, and then make the substitution y=(2*x), we recover a monic polynomial: h(y) =...

Worked well, I showed the following: I is maximal in R, since if we have N an ideal with N=/= I then, there is a/b in N with p|\a -> a=/= 0, for if a=0, p|a. Then, there exists a^-1 in Q s.t. a*a^-1 = a^-1 * a = 1. b=/= 0 -> there exists b^-1 with the same property. Since N is an ideal...

Homework Statement Show that the ring of rational numbers whose reduced form denominator is not divisble by a prime, p, mod an ideal the set of elements of the above set whose numerators are divisible by p is isomorphic to Z_pHomework Equations The Attempt at a Solution It seems very trivial...

worked well, thanks

Hi, I wish to listplot a list object against a scale that is NOT the component number of the vector, but is actually a well defined function of the component number, and I am lost how to do this? changing "Ticks" didn't help, or I did it wrong, so I am wondering if anyone knows how to do this...

Suppose a^m =e -> a=e, then suppose d>1 is s.t. d=(m,n). d>1 -> d is a prime or a product of primes. If d is a prime, since d|n, by Cauchy's Thm, there exists an element, x in G s.t. o(x) =d. But then since d|m, x=/e, but x^m =e, a contradiction. So, then d is a product of primes. But d|n ->...