Recent content by uman

Hi guys, This semester I was a total failure for a lot of reasons. To make a long story short I'm getting: an F in a computer science class, a C in Chinese, and a D and C in my math classes (2nd semester Abstract Algebra and 2nd semester Real Analysis, respectively.) Luckily I'm getting one...

The GPS thing should only use basic geometry and trigonometry; the other is based on complex analysis. The former should be much easier. The only issue is that I'm not sure if you could stretch it to anywhere near 4000 words. I did my extended essay on history, which you may want to consider...

Homework Statement Let f:\mathbb{R}^2\to\mathbb{R} be continuous everywhere except, possibly, at the origin. Furthermore, for any point p\in\mathbb{R}^2, let s_p:\mathbb{R}\to\mathbb{R}^2 be defined by s_p(t) = tp. Now assume that f\circ s_p is continuous, as a function...

This is math, not physics... but professors I've talked to said they hate hearing about things not related to math in personal statements.

Yes; for example, real analysis is of paramount importance in differential geometry, ODEs, PDEs, probability, statistics, and other subfields...

It depends on what you mean by "important". If you mean "useful in other branches of mathematics", then absolutely. If you mean "worth learning because math is an interesting subject for its own sake", then it depends on whether you appreciate mathematics as an art. If you mean "useful in one's...

One annoying example is that in France, open intervals are written with square brackets going the other direction, as opposed to parentheses. For example, what Americans write (0, 4] would be written ]0,4] in France.

What does everyone think about this? http://www.fordham.edu/academics/programs_at_fordham_/mathematics_departme/what_math/index.asp

If your school has an "applied math" track, study that. Otherwise stay far away from math if you don't like formal proofs!

Absolutely. Please remember NOT to get complacent and stop going to class or studying regularly if the material is easy at first... This is how I got lots of Bs and one C this semester.

Not necessarily. Taking analysis first has a lot of advantages. I'm just pointing out that taking topology first has advantages too. However, if you've never had any proof-based class, you'll probably flounder in topology more so than you would in analysis.

I took topology before analysis. In my experience the students who had already taken analysis (about 75% of the class) tended to be at a disadvantage because they found it difficult to avoid using theorems or facts that are true in R^n but not true in general topological spaces.

I'm not sure what you mean.

Not at all. If it humbles you so much that you think "I will never be at this level... I should quit math", then harm was done. On the other hand, if you think you're immune to that, go for it.

It might hurt your self-esteem...