Recent content by lawsofform

Or, you can add those two equations, then use the fact that 1 + (-x)^5 = 1 - x^5 to make the integral over (-inf,inf).

This is sort of what I meant by distinguishing logic from philosophy, though. Obviously there's not a strict divide--for example, Godel's ideas were influenced by Betrand Russel, who was a philosopher. But since Russel's time, philosophy of mathematics and mathematical logic have mostly diverged...

Fair enough :) It would indeed be very hippocritical for someone interested in pure math to dismiss philosophy as pointless! I only meant that philosophy of mathematics have very little to do with actually doing mathematics, so it can be safely disregarded by a mathematician. I do find...

Also, I completely neglected to mention probability, which is a more applied but extremely applicable branch of math, and logic, which is sort of the interface where math meet philosophy (not to be confused with philosophy of mathematics, which doesn't actually have much to do with math, though...

I mainly lurk around here, but I've noticed that you like to say a lot (often dismissively) about things you don't seem to have much experience with, and also that you like to throw in your (often dismissive) opinion when it hasn't been asked for. Calc III, Linear algebra and differential...

It is very easy. There is a theorem that says there is a mobius transformation to take any three points on the plane to any three other points. Typically, we take (a,b,c) to (0,1,\infty), because this transformation has the simple form: f(z) = \frac{(z-a)(b-c)}{(z-c)(b-a)} If you want to...

If you want to do well in any subject you need to spend several hours a day doing it. That's why you go to school, right?

The reason a lot of people are (unjustly, imo) putting you down is that you're putting the horse before the carriage. It's good to be ambitious, but a lot of people have dreams of discovering a grand unifying theory only to find calculus too hard and end up graduating as C students in...

Having a non-genius IQ will not keep you from becoming a mathematician, but confusing correlation with causation might!

Firstly, I'd like to point out that university tuition is very much shaped by market forces already. If you want a PhD in any subject (where the emphasis is on doing academic work rather than gaining marketable skills), chances are good that you won't have to pay for it. If you want something...

Do more homework. Do all of the problems in the book. Make up your own problems--not just arbitrary problems, but try showing other results of problems you've already done. Ask your professor for suggestions on how to practice using different concepts. If you're not a person who does well on...

Where did you go to grad school, ancient Greece?

It seems as if you are taking offense at the suggestion that you ought to study philosophy. It isn't that people are dismissing you as stupid or frivolous, but in fact what you want to know is outside the realm of any science. The fact is, only atoms and their ilk experience reality directly...

Remember that the integrals you are probably used to seeing are of one-dimensional functions, so thinking of it as an area is somewhat misleading. Instead, think of it as "adding up" the values at every point of a function. Now for a line integral, instead of adding up the value of a...

Look up the trig identitites again. arccosh identifies with a rather complicated log function. The log comes from the y^2 in the demoninator of the path length. If you take the derivative of that log function you should be able to work backwards and see how it works out, but it looks like it...