Surprised both that this thread got revived and that I stumbled into it after being away from the board for a year or so. Anyway, these sorts of feelings have passed for the most part, mostly due to necessity. I don't really even have any advice for getting over these sorts of problems, I just...
I would consider that, but I've already started the third year of my degree and it would be difficult to switch to engineering and still graduate in a timely manner (also, I'm funded by scholarships, and my family isn't in the best position to help pay for additional years once those run out.)
Thanks for the replies. Unfortunately for my pure mathematical career, I think I'm going to try to stop it here, before I go too far down the academic track. The primary reason is my continued anxiety over the dismal employment prospects for a Ph.D in academia, and the subpar salaries that those...
What makes you so sure at this point in your undergrad career? I'd recommend keeping your eyes open, as you may not like upper level math courses, or not do well in them, or any number of other things could go wrong...
Grad schools won't care too much about your grades in lower level...
This problem has gotten much less severe for me than it used to be. I've been through several episodes of clinical depression and this remains a trigger for me. I can say that I really do want to work in math doing research, but my difficulty handling failure makes it hard.
First a little background. I'm a 3rd year undergrad in mathematics. By most measures, I've been rather successful up to this point: I'm taking graduate courses, I've coauthored a paper with a professor (currently seeking publication) and am writing a second paper on my own, and I've started...
I am giving a short presentation on Fermat's polygonal number theorem (any number may be written as the sum of n n-gonal numbers). I need books that provide some exposition/history on the theorem as well as a proof. I acquired Nathanson's Additive Number Theory from my university's library, but...
First, that formula for evaluating geometric series is only valid for -1 < r < 1, so your application to a ratio of -1 is incorrect.
Second, your evaluation of the term itself for n=2 is incorrect. It should be 1/2, so the sum is 1 - 1/sqrt(2) + 1/2 thus far.
Determine the form of the...
If F'(z) has an antiderivative in the set described, then its integral around any closed curve in that set will be zero. Are you sure that happens? Consider what form an antiderivative of F'(z) would have, and what functions would be involved.
You want to prove that these two sets are equal, right? Two sets are equal if they are subsets of each other, so if you can show that every element in the left-hand set is in the right-hand set, and vice-versa, you will be done.
I have no idea what that string of abbreviations is, by the way.
Well, y = 8/x gives you a relation between the two variables that allows you to write the distance from (x,y) to (3,0) in terms of one variable, which can then be easily minimized.
I'll give you a hint for rotating around a point other than the origin: The origin is just that, a point. You can perform a coordinate transformation to reduce the case of a point not at the origin to the case at the origin. If you understand that methodology, you should also be able to reflect...
Remember that, if k is a scalar and A is an n x n matrix, then |kA|=k^n*|A|, not k*|A|. In this case, your proof is correct, but only because the matrix has an odd dimension, as that allows you to "pull out" the negative sign