>tfw you finally learn the difference between dx and delta x from a geometric perspective and you understand that the use of the tangent plane in R3 to approximate is analogous to use of the tangent line in R2.
Post your recent breakthroughs in understanding math.
>>7924480
>the difference between dx and delta x from a geometric perspective
which is ?
I understood not to use toilet paper instead of my hand. I'd say the mental capacity it required to realize this was compatible to yours.
>>7924504
Oh, I misspoke. I meant the difference between dz and delta z (z being the dependent variable).
The difference is that dz is the change in z using the linearization and delta z is the change in z using the actual function.
For instance, in R2 with y = f(x). You find the derivative at x = a, which can be used to create a tangent line.
Moving from a to b, the dy added to f(a) will always land on the tangent line.
Moving from a to b, the delta y added to f(a) will always land on the original function.
>Tfw undergraduate probability theory is secretly just the theory of sigma algebras
>>7924529
>secretly
Did your probability course not start with the formal definition of a probability space?
>>7924568
Nope. As far as the professor is concerned, we're working with "likelihoods that experiments will have certain outcomes" and not measure spaces.
I asked him a question about Lebesgue integration and he said Q has nonzero measure.
I'm highly disappointed.
>>7924480
>tfw you realise OP is a massive faggot
>>7924522
can you use the ''delta y'' in a formula, because I do not see what you mean for this notation.
>>7924522
I sense further confusion in your future.
>>7925192
I took a CS probability and statistics course with more self respect than this, you should be disappointed. The head of stat department teaches it and he consistently fails half the class, if more people pass than he expects in the first term he makes up for it in the second term.
>>7926107
That's exactly what I'd prefer. I'm in graduate level classes as an undergraduate freshman. The class is a fucking joke.
>>7925711
he means the partial derivative you fucknigger
>>7926502
take a course in calculus before speaking
>tfw Watson integrals finally make sense
>fundamental groups finally become intuitive
>you finally understand how it is a measure of how many holes a space has
>you work through the computation of higher homotopy groups
>you did it just like the book did without looking
>all of those terrible analogies finally begin to make sense
i know it's a relatively simple concept to understand as far as algebraic topology goes but i feel good
