Recent content by waddlingnarwhal

This post and your mathoverflow post were very inspiring. Thank you for sharing. I recently had an experience that illustrates why (for me) doing math provides a level of satisfaction that just reading about math does not. A few years ago my number theory class stated and proved Hensel's Lemma...

I've had success teaching myself things from books without solutions. The process of figuring out if my response is correct is very instructive at times. If you're just studying the book by yourself, then you can ask online for help if you get stuck on a problem. There are an extensive number of...

I have used a few of the Rudin books in classes, and I suggest that you read the exposition quickly the first time, marking but not dwelling on roadblocks like the one you mentioned above. Then as you do the exercises, go back to the exposition and study a proof further if you need some of the...

mrnike992 - Good luck with the application process! Have you considered applying to some private schools? Although the sticker prices are usually higher, the financial aid packages are usually better as well. Many of my friends found that is was cheaper to go to a private school than our...

I know that the University of Chicago, Duke University, and the University of Illinois at Urbana Champaign award merit-based scholarships. The latter two offer some full-tuition merit scholarships. All three schools have good physics programs. You could also try looking at the top ranked physics...

I believe that S8 has no element of order 21 because the order of a permutation is the least common multiple of the lengths of the disjoint cycles in the disjoint cycle decomposition. If anyone is interested, here is another interesting problem I did this term. It is a probability problem. You...

Hi mathwonk. I've read your solution, and I think everything you said is correct. I will look at it again tomorrow to see if anything sticks out. Thanks for the reply! For now, I would like to offer two short, alternative solutions. (1) This was how I eventually did it. The cyclic group of...

I was reading through the older posts in the thread and came across this question. I decided to take a stab at it since I just finished my group theory course. G acts on the cosets of H by left multiplication, and this gives a homomorphism of G into S_n. The image of this homomorphism is...

sunny79 - On page 2 of this thread, mathwonk gives some advice for undergraduate students. His suggestions and book recommendations seem spot-on to me. I also noticed that he linked this article in another thread -...

mathwonk - It's very interesting to read about your personal experiences in this thread. Anecdotes like the one you just shared are one reason I enjoy learning in school or from forums more than just working by myself. As I begin thinking about whether I want to continue my mathematical...

If you want something very down-to-earth, there's a "Schaum's Outline of Real Variables and Lebesgue Measure". It's out of print, but I've seen copies in my school's library, and there are used copies online. It seems like most of the Schaum's Outlines aimed at upper-division undergraduate...

Hi Mathmaybe. From the books you listed, it sounds like you are looking for a second course in analysis. I found the real analysis volume of the Stein and Shakarchi series to be good. It is clearly written and provides historical motivation. The pace of the exposition is fairly slow.

mathwonk - That makes a lot of sense. I guess I was only thinking of "very nice" essential singularities like e^(1/z). Complex analysis is such a great class. I feel that I've internalized the theorems and their proofs, at least those we covered in class, a lot better than those from real...

Thanks for the recommendation! I don't think I'll be able to finish that during winter break though...

Hi Y'All. I have two questions, one specific and one general. (1) Why is the Residue Theorem often stated specifically for meromorphic functions. In the statements I've read or Googled, it is specified that the singularities are isolated poles. Wikipedia mentions that the theorem also holds for...