I have exams in June so I could have to be in Trento depending on the days. But there are also direct Trains from Trento to Munich and I've been told it's a beautiful city and I should visit it sometime so I might be able to arrange something
@Ted Do the Soug approach and assign an ungodly number of linear algebra problems as homework each week so you don't have to worry about covering it in class.
Hi, I have a tiny question: why do we have 0 < |x-b| < delta in the epsilon delta definition of limit, but we dont need the 0 < |x-b| part in the definition of continuity?
@Ted how does one become a math teacher at undergraduate/graduate level in the US? In France there's a very competitive written exam followed by thorough oral tests (l'agrégation)
@Alessandro Ah, those are the beautiful pictures. I'll tell you more about it after you figure it out (it might take some time; I didn't come up with this proof myself and I don't think I could have but let's see if you can)
There are zillions more math teachers/professors in the US than in France, Dodo. At least until our current administration dismantles all of education. Here anyone with a Masters degree is "allowed" to teach at lower level schools and anyone with a Ph.D. is "allowed" to teach at research universities and colleges.
@Ted damn... by the way, is there a significant difference in the quality of courses and teachers at community colleges and private universities ? Is there a difference in how the teachers get paid as well ?
@TedShifrin I wasn't supposed to be working on forms and differential geometry? Although I do want to learn differential geometry again after this month - both the surface theory and Riemannian.
Dodo: Some graduate schools try to actually train grad students to be competent teachers, but most do not. I'm proud to say that at U Georgia we worked hard at that (and I spent countless hours watching grad students teach, planning lectures, and helping write exams ... and giving not infinitesimal amounts of feedback).
when we have 1 zero, we either have no solutions ( both coefficients < 0 ), a hyperbola that goes infinitely up and down in one direction ( one coefficient < 0), or an ellipse (both coefficients > 0 )
Dodo, for the most part, people with just a masters make less money than people with a Ph.D. But some people with a Ph.D. end up doing adjunct work and it pays horridly.
@Zach: You're still messing up. It's always a surface.
Dodo: I think it is not unfair to say that I devoted more energy to students and teaching than the average professor at a research university. But I would never survive in today's world.
@Ted the Master of Financial Engineering at Berkeley is 70k$ for one year, while the top notch master in financial math here costs 400$ a year. I've looked around and there's no grant available. Are they expecting people to take a loan or what ? The only reason I'd go for a masters in the US is the huge rep bonus on the CV. In my opinion, it's like buying the diploma
How do you prove the spectral theorem by Lagrange multipliers? For 2x2 matrices I can do this, by seeing the corresponding quad. form has a maximum and a minimum on the sphere.
@Alessandro: It's more interesting to understand (nonsingular) conics (curves) projectively and quadratic surfaces. In one case they're all projectively the same; in the other, that's false.
Dodo: In math programs, most students get supported in the US. Financial engineering they're expecting people to get loans, I guess, and make a ton of money. Have you switched from math to finance?
@Balarka: As Daminark just pointed out, the key thing is that symmetric linear maps that have an invariant subspace must also have the orthogonal complement as an invariant subspace :)
@TedShifrin I got into an engineering Grande Ecole, not an Ecole Normale Supérieure, so most of what we do is applied math. My Ecole focuses on statistics, data science, finance and economics. Sometimes I miss pure math though :P
Oh, Dodo, I didn't know that. I have nothing against applied math, nothing whatsoever. It was just not what I had seen you talking about a few years ago.
Ah yeah you can use weak compactness to construct a subsequence that maximizes your quadratic form in the limit and some algebra shows this is an eigenvector, then you mess around on the orthogonal complement and do some analysis to show the eigenvalues go to 0 using compactness or something @Daminark
