I was always aware that AP classes were, in general, not equivalent to their respective college courses, but I'm beginning to wonder if the gap is much larger than what I previously thought.
Many of my suite mates are engineers/physicists, and so most of them are taking the same physics...
Home from college for labor day weekend, college wasn't as bad as I thought it would be ^^
I'm still sort of sticking with my group of close high school friends, but I'm beginning to become friendly with my suitemates as well. Playing Mortal Kombat and League together can do that I guess. I...
After you get a bit more comfortable with the program, one really valuable tool I used when learning LaTeX was http://detexify.kirelabs.org/classify.html
The website is basically a database of symbols that you can search through if you find yourself needing a specific symbol. Just draw what...
Yes, you probably should, as like Student100 said above, faulty foundations will ruin you in college.
From what my premed friends tell me, you will want to, at the very least, be able to master basic differential and integral calculus so you can get better scores in your physics classes and...
Wait, were you just asking for a way you could get a computer to numerically calculate ## \pi ##?
Well, that theorem technically only holds true because of the metric we have defined, and we could probably easily find a metric for which that isn't true.
Dividing the area by its diameter...
Thanks for the advice guys :)
Life is going to be a bit hectic as I first move into my dorms, but I'll see what I can do after I adjust in a few weeks.
How exactly should an undergraduate approach a professor to ask about research opportunities? Would it be preferable to send an email or go talk about it during their office hours? A call perhaps?
Also, out of curiosity, is it annoying when an undergraduate wants to do research in math? In...
The reason why ##\pi## is 3.14…… is simply because we have defined ##\pi## to be that constant. It is defined to be the ratio of the circumference of a circle to its diameter, and in our world it just happens to be 3.14….
This happens to be the case because of the way we have defined length in...
In addition to the clarifications above, Terrence Tao has a nice article that could help give one some intuition with the notion of compactness if you are interested: http://www.math.ucla.edu/~tao/preprints/compactness.pdf
We know that if a function ## g ## has a derivative ## h ##, then ##dom(h)\subseteq dom(g)##.
Let ## f ## be our function and ## F ## be any of its corresponding antiderivatives. Then since ## F ## has a derivative ## f ##, it follows that ##dom(f)\subseteq dom(F)##.
Are you asking for a proof there exists a bijection or for an explicit sequence?
If it is the first case, there is a simple bijection from f:\mathbb Q_+\rightarrow\mathbb N\times\mathbb N where ## f(\frac{p}{q})=(p,q) ##. Then you can find some bijection ## g: \mathbb N \times \mathbb N...
Ugh, I was afraid you guys were going to say that, especially since number theory is a big wall for me. :cry:
Although I guess we all encounter walls at some point, anyway, and from what you guys say I guess I should try to get by it. Thanks for the perspective guys!
It seems that no matter how unrelated two subjects of mathematics appear to be, there are always ways to use techniques from one area of math and use it to prove many useful results in the other, and vice versa.
However, from my (inexperienced) point of view, number theory seems to be the only...