How do you learn new math?

[MikeH]

Exactly. Those people. Gah. I hate those people.

[Kuciwalker]

@those who are bad at math: I'm sorry

math is like breathing

[MikeH]

It's like the process by which air moves in and out of the lungs?

[DriXnaK]

I look at the examples and then start working the problems. I don't bother reading the explanations and stuff. I find it more fun to try and figure out the problems on my own having only a few examples of how it's done and the answers to some of them in the back of the book. I feel like you'll have a better understanding of the problem and how it works if you go through the problem on your own with no explanations and are forced to try and essentially reverse engineer the problem and how it works. Granted, it takes much longer since you're forced to go through a large amount of possibilities and come up with a theory on each one on how and why it works. Still, the feeling of figuring it out and coming to the conclusions that others before you had come to is an amazing feeling.

[Bugs ****ing Bunny]

If it only includes numbers it's merely Arithmetic

Fortunately "=" is not a number.

[Bugs ****ing Bunny]

math is like breathing

Unworthy of study in higher education.

[Elok]

Unworthy of study in higher education.

And hard to do while a fat person is sitting on you. Of course, that's true of most things, so I don't think it's a useful parallel.

[Al B. Sure!]

@those who are bad at math: I'm sorry

math is like breathing

You are such a simplistic inhuman thing... when the AI's take over, they'll confuse you for one of their own.

[KrazyHorse]

Math is possibly the most human endeavor of all.

[Cort Haus]

Hmmm ... my stats lecture was ok, but the guy was very good and was actually a programmer, not a statistician. In fact I think he was good *because* he wasn't a mathematician, and so he was able to empathise with people who didn't like the greek stuff and explain things very clearly.

What does get me though, is why it's often necessary to accept and use the magic formulae without understanding them. Why do we square the thing when calculating the variance for example? Is it to force it positive? Apparently not, it's for some other mystic purpose which is revealed unto the acolyte at a later stage of their enlightenment. Fair enough, but with maths I just get troubled having to use a thing without understanding what I'm doing.

Obviously many will assume that this is because I am retarded, but I can look at, say, a piece of code that calculates the mean to = sum/count and it's obvious what's happening, whereas the mathematical language isn't obvious to me. Perhaps that this is because I just never managed to learn it properly. It doesn't explain the block at not being able to use the magic spells though.

[KrazyHorse]

I think the simplest reason to describe why the square is there is with the following example:

say you have a coin where one side is a 0 and one side is a 1

If you flip it once, then you end up with 0 0.5 of the time and 1 0.5 of the time

so,
result | prob
0 | 0.5
1 | 0.5

what is the variance (using the squares formula)?

First find the mean (0.5). Then apply the summation 0.5 * (-0.5)^2 + 0.5 * (0.5)^2 = 0.25

if, instead of flipping once you flipped twice and summed, the results would be

0 | 0.25
1 | 0.5
2 | 0.25

and the variance is 0.25 * (-1)^2 + 0.5 * (0)^2 + 0.25 * (1)^2 = 0.5

similarly for three flips

0 | 0.125
1 | 0.375
2 | 0.375
3 | 0.125

and the variance is 0.75

notice something? that's right, the variance grows linearly with the number of flips! magic!

in fact, it doesn't even need to be identical flips. for example, I could sum the result of flipping this coin and rolling a regular six-sided die and the result would be that the variance of the sum is the sum of the variances!

the only condition for this to be true is that the covariance of the two flips be zero. covariance is a complicated word, but in some sense it's a measure of the statistical independence of two flips. In fact, statistical independence is a stronger statement than covariance being 0 (it is a sufficient but not necessary condition).

To summarize, if A and B are independent random variables (like the result of flipping our coin or rolling a die or looking at the last digit in the FTSE) then var(A + B) = var(A) + var(B), which is why we define variance the way we do

[Bugs ****ing Bunny]

A real man would just punch you and steal the coin.

[Kuciwalker]

To summarize, if A and B are independent random variables (like the result of flipping our coin or rolling a die or looking at the last digit in the FTSE)

Friends don't let friends use public data to seed their prngs.

[Lul Thyme]

What does get me though, is why it's often necessary to accept and use the magic formulae without understanding them.

Of all things that humans study, mathematics is probably the one about which this statement is the LEAST true.

[KrazyHorse]

To summarize, if A and B are independent random variables (like the result of flipping our coin or rolling a die or looking at the last digit in the FTSE)

Friends don't let friends use public data to seed their prngs.

a) There's nothing "pseudo" about any of those things
b) I wasn't planning to seed a rng with them
c) The requirements for rngs are different than the requirements for crypto (generally less stringent)