Math Is Fun Forum

I find that the most sadistic teachers give the most benefits -- at least in my case. I had an American history "professor" who was incredibly rigorous, and made your grade something you have to earn. "Professor" is in quotes because he is a high school teacher, but he was a college preparatory crazy kind of guy. Every time someone would complain about the volume of work, he'd bring out a chart comparing high school and college, and often some statistics and the horrible lives of slackers(he had statistics on EVERYTHING, and he'd bring them out at any random situation that could use them). Every class was 90 minutes of lecture. All reading was done at home, no study guides were offered. Tests were usually over 200 pages of material from the book, and the format was primarily essay, with many topics directly from inclass lecture. Papers and additional readings were frequent and tedious. I lost many nights of sleep to this course. This man knew if you wrote a paper just to get it done, and it was likely that he would make a fool out of you in front of the class if you were particularly lazy. Despite how horrible this all sounds, I am very happy to have had him as a teacher. It was the first time I had to actually work for an A, and it felt good to get it. I feel that my writing and note-taking skills benefited substantially due to the class. Someday when I'm in college I'm going to email this man and thank him for what he has done.

Yeah, the only downside is that a lot of the stuff is college level. I'd define everything here but that would probably make it fail (like if someone doesn't get a joke and you have to explain it to them, it just isn't funny anymore). They must have done this around some math majors or something though, judging by the amount of laughs at just the right times.

Haha, I just noticed that at the end the lead guy makes a square with his hands, like he has ended a proof.

I foresee this being the greatest thread ever to exist.

I have to run, but I think I see the problem with your proof and it is a short issue, so I'll type it up:

Just a small note, there is an integer n > 1 that divides p, and that is p itself. This lends to my disproof: The number 2 is a prime number, because it is only divisible by one and itself, but the number itself is 2, which is a contradiction to the original claim that no prime number p may be divisible by 2. 2 is obviously an even number. Therefore not all prime numbers are odd.

(If the problem says prove we can possibly disprove it, right? Perhaps we should just make conjectures in some cases so people don't feel like the proposal is necessarily true?)

Edit: As I said, I have to leave for a while, and therefore I don't have time to think up a proof until later tonight. So if someone else would like to continue the game as soon as possible (assuming I was correct), feel free to go ahead.

Edit 2: Also, how advanced should the material being proved be? Should we keep the level somewhere from artihmetic to precalculus? Would it be alright to post a normal proof and a challenge proof, and participants may do either or both, but the challenge proof is more difficult and/or possibly contains calculus and beyond?

Edit by Ricky - Pass

The Laplace Transform

The Laplace transform is a useful tool for solving differential equations. The Laplace transform F(s) of f(x) is defined by

The Laplace transform is a linear operator, and thus

The inverse Laplace transform

is also a linear operator:

Solution of a Linear Differential Equation of Constant Coefficients using a Laplace Transform

Consider the linear differential equation

Taking the Laplace transform of both sides, and noting that

we may write the differential equation as

or, collecting coefficients,

Now, given that we have the initial conditions at x = 0, we can proceed to solve for L[y], and once we have an equation for L[y], we may simplify it (often by means of partial fractions) and then find the inverse Laplace transform, and thus find y. If initial conditions are given at some x[sub]0[/sub] ≠ 0, let  u = x - x[sub]0[/sub] and solve the differential equation in terms of u, then substitute the value of x back in when the solution is finished.

List of Selected Laplace Transforms

Note: Taking the inverse Laplace transform of these equations will give an expression for the inverse Laplace transform of a function F(s).

Feel free to request any other Laplace transforms/inverse Laplace transforms. I have about 150 other transforms for a wide variety of cases, but they seem too obscure for posting.

Example problems may be posted on request to aid in clarity.

It's a special case of the polylogarithm known as the dilogarithm, this specific case is -Li[sub]2[/sub](1). Note that Li[sub]s[/sub](1) = ζ(s).

That's good so far.

But QED makes me think of Feynman, such a nice guy.

I feel like such an act may ruin some of my mysterious qualities. Oh well, it's always nice to have another math guy on Facebook. Look for a flying head.

Ah, do you mean quantum theory of histories? As in the Feynman path integral?

Are you German? (Geschichte = story or history)

All this hate for MythBusters Ricky, what did they do to you!?

But you're right, maybe they should take a statistics course and reform their testing style afterwards.

Is the competition today? Good luck, and be sure to tell us all about it when it's over.