Recent content by abiyo

I am at a point where I have to decide what I want to do at this point in my life. I am currently finishing a Masters program and I am doing quite well with my research and school. I see myself going to Academia or industry here in US. As much as I like this country and however hard I...

I think ZombieFeynman gave a lot of useful comments above. In your second paragraph, " and I am certain I won't grow bored in your lab." I think this is unnecessary. In the second paragraph as a whole, it will be nice to be specific of a problem you like that the group does. Reading it as...

Long story short: I got into a lower ranked school for PhD in Mathematics and a top ranked school for Masters in computational mathematics. My interest is theory and my only reason for applying to computational program was as a backup. What I ultimately want to do is mathematics(analysis) and I...

I didn't get into any of the Maths Phd schools I applied for. I thought I was a decent applicant with some research experience(no publications), solid gre(above 90%) and good recc. letters. I did apply to top ranked, medium ranked and even some with lower ranks. Such is life. I want to...

When I took Analysis, I studied from Rudin and Apostol. I think for a starter Rudin on its own might be a tough so having a complementary book will help. As others noted above, it also depends how good the teacher is and whether you will have people to work with. ++ for spivak if you want...

I have to think more about this but it is necessary to specify i)the number of rectangles ii) is any cut allowed? Can I cut a triangle out of the square and fill it in the rectangle? Is there a restriction on the shape or size of the cut area? The more rectangles you need to fill, the more...

what you have as the conditions is right. When the determinant is zero, the test fails. This is to say that we might have a maximum, minimum or saddle but the test will not help us identify such a critical point. You might have to plot the function or see some values to be able to identify...

Here again no offense intended but you should show the implication of your number system to other areas of mathematics. In what does this idea help or connect to other ideas/concepts in mathematics? Also if you want people to read your idea, you should write it in a mathematical style...

You applied the divergence theorem correctly. The flux over the circle is also correct. The mistake you made is when you computed the flux over S1: the cone. To define the normal for z=f(x,y) first write it in a format as follows: \sqrt{x^{2}+y^{2}}-z=0 Then the normal N will be...

Working on campus, relaxing and studying. I don't study for the next semester but review some stuff I forgot, or learn a proof I put off during the semester, read some journals and on an area I am interested. Where ever I fill there was a hole in my foundation, I put all the effort during the...

If I get what you said above, the choice function exists since the set is non-empty and a non-empty set, by definition, contains an element. So in the finite case the condition the sets are non-empty is equivalent to the existence of a choice function. I think this is making sense slowly. Thanks...

To help you see how an equivalence relation is related to partition, let me give you a fictitious example. Consider a town. This town has rivers and mountains. So sometimes to be able to visit a friend means to be able to climb a mountain or swim a river. Let's define an equivalence relation in...

Thanks Jarle for the explanation and micromass I will take a look at your blog. Hurkyl, here is my understanding. From Jarle's explanation, I know that for the infinite case we won't be able to say at any point explicitly what the choice function is. What is bothering me this line of thought...

So if we have a finite collection of disjoint non-empty sets, one can show using ZF only(with no need of AC) there is a choice function. I understand the reason for this. My confusion is when one goes to non-finite collection of sets. For example if the index set is the Natural numbers, why do...

Landau; Thanks for the correction. Locally compactness is just weaker. I don't know what I was thinking.