I know a lot of people who've been like "pursue a phd in stem, that way you delay joining the work force as much as possible" rather than for the academic career route
Wait do you mean like, they start by saying they want to be actuaries and then decide that math is the way to go to do it? Or do they start majoring in math and then go the actuary route?
yeah but most people don't use that much of the course material @Daniel, it's not a bad suggestion because math degrees teach you problem solving skills that are useful if you decide to be an actuary
@MikeMiller oh, a blast from the past: lately I've been getting interested in what I think you'd call instanton homology, albeit only the most simple version there of
Most of what I know about the stuff is Lawler just sorta being like "Yeah so about that academia stuff... Don't get too excited about it... Make sure you have some compsci/stats, or science if you can do that"
Demonark: Eric's suggestion about the Goursat proof of Cauchy's theorem is on the money. There one proves that holomorphic implies $\int_{\partial\Delta} f(z)\,dz = 0$ for any triangle $\Delta$.
But, Eric, look at it this way. It's your protection from my asking about geometry questions you don't have time to think about. ... But yeah, super technical. I totally warned you.
So let $A$ be a downwards-closed family of subsets of $\{1,2,\dots,n\}$. Is there always an involution $f:A\to A$ such that $f(V)\cap V=\emptyset$ for all $V$?
Note that if $A$ has an odd number of elements, we can map the empty set to itself (as the empty set is disjoint from itself).
If $A=\mathcal P(\{1,2,\dots,n\})$, then taking the complement works.
How does one draw the "snake" arrow for the connecting homomorphism when using the snake lemma?
I'd also be interested in drawing similar arrows act as "carriage returns" when considering a long exact sequence of cohomology.
I'm sorry if this is a little vague. I'm hoping that someone who's alr...
Can one of you please have a look at my solution and tell me if I am correct or completely wrong? https://math.stackexchange.com/questions/2361526/unknown-3x3-matrix
So wait you've executed those row operations on $A$ to get the identity, so now you want to find what the associated elementary matrices are, as well as what $A$ was, right?
No I mean like, the way to verify it would be to perform those row operations and see if it gets you the identity, that's how you would know that this is what you started with
I'm looking to find an expression for the highest power of 2 in $3^a\cdot(2b-1)-1$ but the only thing I can find that's close is mathoverflow.net/questions/29828/… which doesn't really help me, any ideas?
Also, is it worth posting the same question in mathoverflow as math.SE?
