/sci/ - Science & Math

>>11617917
Fix a basis for U and extend it to V, the vectors not generating U generate W.

>>9628232
No u. Have you done any interesting stuff lately? I was thinking about finding some quick rundown on Hopf algebras, so I could understand how Steenrod's algebras work. Rudyak gave some references.

>>9604645
That's when I have to become an adult and get a job or be unemployed, and neither of those will have any interesting math stuff in them.

>>9432399
A proof method. Practice by proving the five lemma using diagram chasing.

>>9028906
Sorry for reminding of such things. I've been taught by strict men and harsh women. It has affected the way I correct mistakes, but I believe it is a good thing to get a few things wrong and fixed every now and then. Being too sure is not necessarily a good thing.

>>8760503
Try making some sort of flow chart how things lead to one another, one for each studied chapter. For example:

(Compactness if you are familiar with this ->) closed interval [math][a, b][/math] -> for every continuous function [math]f \colon [a, b] \to \mathbb{R}[/math], there are [math]c, d\in [a, b][/math] such [math]f(c), f(d)[/math] are the minimum and maximum of the image set.

If you could do this, you'd maybe see the connections better. Proving is, basically, just a chain of implications, and the chart would consist of precisely those.

>>8529596
Yeah, that's what I was pretty certain you meant.

About the rest of your post, I'm not quite sure what Tao writes in his blog, but I agree it is not a good thing to tell anyone they can solve some difficult things with only hard work. It just doesn't work like that for most people. I'd call it a waste of potential, too, as there are smaller things to look at, and these people wasting their years trying to prove the Riemann hypothesis or some similar statement could look at those instead.

>>8529619
So, you are saying STEM ambition is peer pressure of some kind? Or to make dad proud, that could be one reason, too. That's an interesting point of view.