Recent content by fk378

Hi all, Saw this problem and was wondering if there was a simpler way to do this besides listing out the possible combinations. In a game, each token has one possible value: 1, 5, or 10. How many different combinations of these tokens will give us a total sum of 17?

Is the only way to do this just to get a3b2=432, then find the factors of 432? I tried this and then got 16*27=432, so then a=3, b=2. But I feel like there must be a different way to do this problem...

Yes, I did that. Don't know where to go from here. Seems like I just go in circles when I try to make two equations to solve for the two unknowns.

If a,b are positive integers and (a1/2b1/3)6 = 432, then what is the value of ab?

Don't really know how to think about these... (1) Give an example of a 1-dimensional ODE of form x' = f(x), x(0)=x* where f: R->R is continuous but there exists more than one differentiable solution. Prove your assertion. (2) Is it true that a 1-dimensional ODE of the same form as (1)...

When you say this, do you mean the epsilon delta definition of continuous?

Can you explain how the determinant function is continuous? And also, my professor mentions how *because* the determinant is continuous, we can change the entries in small amounts and still have the matrix be invertible. Huh?

The only places that my professors know about are top tier schools, which I doubt I can get into. I need a school that has a good math department, but not THAT good. Any other suggestions?

Yes, I understand the smooth and bijective part, but what about the non-diffeo part?

Suppose F: M-->N is a diffeomorphism. For every Y in TM (tangent bundle to M), there is a unique smooth vector field on N that is F-related to Y.

In the definition of F-related vector fields, F must be a diffeomorphism. Why must it be a diffeomorphism? What if F is smooth and bijective, but not a diffeo?

So any real number is the limit of a sequence of rationals. Is any real number also a limit of a sequence of irrationals? I found this proof of the latter statement... http://answers.yahoo.com/question/index?qid=20080921221913AAsHFAp it seems contradictory to have that every real number...

I'm trying to find PhD programs in math that offer number theory as a focus. Where do I find this sort of information besides looking at each individual school? Is there some sort of catalogue or list that readily offers this information?

Homework Statement I want to find the limit as n approaches infinity of (n^n)*(x^(n^2)), and Homework Equations My teacher told us to look at the log. 0<x<1. Also, since the log of this goes to -infinity, then the original limit in question goes to 0. (1) why is looking at log valid...

So if you write it out as (x,y,z) is it still considered to be a 2-dimensional surface? The point is that you *can* write it out in terms of 2 parameters, is this correct?