It is well known that \sin x / x is not Lebesgue integrable on [0, +\infty) though it is (improper) Riemann Integrable. It is also fairly easily shown (integrating by parts) that
\Bigg\lvert \int\limits_{a}^{b} \frac{\sin x}{x} dx\Bigg\rvert \leq 4
Since [a,b] is compact, the Riemann and...
OK, so this is kind of related to a thread I started in the Books section. I am currently (well, I will be in a few weeks) a math grad student. We have to take grad-level courses from a school outside of math. I want to do Physics because I remember thinking it was interesting when I took the...
I want a good book on classical mechanics - one that would be considered to be a graduate level text. The only Physics courses I have taken are the two standard intro physics courses taught at what seems to be every university, and a course in Computational Physics. My (relevant) math...
This is a question for anyone who thinks he has an answer:
I'm a first year math grad student (well, I will be in August.) I think for the first year I will take Algebra I&II Analysis I&II, Advanced Linear Algebra, and Complex Analysis (note, this is over two semesters so three classes per...
I'm going to be a first year grad student in the Fall. What is a typical course load in grad school? I will be leading recitation for 2 hours a week, plus 2-3 hours of "office" hours. I know most people take 12-15 or so hours during underdrad, but this seems like too many for grad school. I was...
Does anyone know of a good resource for getting scholarship (or any funding) for math grad students? I will begin a MS program in the fall, and I would like to get as much funding as possible (if I get any from the school, it won't be much.) If this makes a difference, I plan to pursue a Ph.D...
We just started back at school on Monday and I am taking a graduate algebra course. I have taken undergrad Algebra I and Algebra II. Of course I expected that the graduate Algebra I would be much more in depth than the undergrad course, given that it is meant to prepare a student for the comps...
Homework Statement
This isn't exactly a homework question, but I saw it in a book, and I think it is interesting:
Let S_1,\ldots,S_n be a collection of subsets of [tex]\{1,\ldots,n\}[/itex] such that |S_i \cap S_j| \leq 1 whenever i\neq j. Then the total number of elements in all of the lists...
Homework Statement
So, this isn't a Homework problem, but I think I am having a little trouble understanding little oh notation, so here is a problem:
Show that Sum(k^3) (k=1 to n) = (1+o(1))(n^4)/4
Homework Equations
No relevant equations.
The Attempt at a Solution
Let S =...
Homework Statement
Let V be a vector space over the field F. Let Hom(V,F) be the set of all homomorphisms of V into F (this is a pretty standard definition, noting new here.) Now, let f and g be functions in Hom(V,F). If f(v)=0 forces g(v)=0 then g = \lamda f for some \lamda in F...