Recent content by chhan92

Hello! Stanford math PhD application deadline is coming up, and I have my SOP ready, but I am not sure whether it is mediocre or good. Can you guys read over my statement of purpose? I will not post it as public, but I can send it to you via email. Thank you.

Also, have you taken topology class? That is very important. Also, having a course about smooth manifolds is a plus, but not a must-have. Make sure to take topology class of any sort, whether it is general, algebraic, or a course on manifolds.

For linear algebra, upper division as it means mainly module theory? Or is it going to be about inner product space, spectral formula, bilinear & quadratic forms, symplectic forms, tensor products? This needs to be clarified, because what you call it upper division might be freshmen course in...

I am currently taking graduate algebra as an undergraduate (junior) in University of Toronto, and I just took a midterm today. Since I am an undergraduate, the grade matters. In order to get a good chance to go into graduate schools for Mathematics in Canada and USA, is it must have to get a A...

Hi! I usually choose my courses in advance then prepare for those courses before term starts. Background: I have taken: Multivariable Calculus (little spivak), Real Analysis (Pugh), Abstract Algebra (Dummit and Foote chapters 1-5,7-9,13,part of 14(including FTGT)), Ordinary Differential...

Thank you for your kind response.

Hello! I am a student in University of Toronto, and I am currently in Math Specialist (basically Math Major with more required courses and forced to take honors class) and Computer Major, but my Computer Major forces me to pay twice of the regular tuition. Also, I have to take a Computer...

Oh I completely forgot about it. It is rival of John Lee, but has distinctive pros & cons relatively (meaning that both books are somewhat masterpiece) John Lee: -pros: Relatively easy to learn despite being in GTM (reads like UTM), nice set of examples to work through, topological...

Spivak is the way to go (maybe not for first learning), but you won't regret that you bought it. One thing to mention is that Gullemin/Pollack is more concerned with topological aspects of smooth manifolds rather analytical aspects. After Spivak (for smooth manifolds books focusing on...

How about Cartan's differential forms? Other than calling manifold "variety", I heard this is good book. Actually, it depends on how much you want to learn differential forms. If you just want to learn differential forms living in R^n, spivak is perfect. If you want to learn differential...

But is Arnold self-contained in terms of physical intuition? Do you think Arnold is readable without freshman-level physical knowledge?

Hi! I am looking for suitable ways to learn mechanics in mathematician's perspective. I went through: - multivariable calculus from Spivak, - real analysis from Pugh, - differential equations from Hirsh/Smale/Devaney (mostly focusing on linear system, existence & uniqueness, nonlinear...

Hi! I am currently planning to get a book on Real Analysis for self studying before diving into my 4th year real analysis course. The standard textbook for my 4th year course is Stein's Measure, but I do not like much about abstract measure introduced near the end. Perhaps because I am...

z-filter is the collection F of nonempty zero sets (f^{-1}(0) of continuous f:X -> I) such that a) P_1, P_2 in F implies P_1 intersection P_2 in F b) P_1 in F and a zero set P_2 containing P_1 implies P_2 in F. A z-filter is prime if P_1 and P_2 belong to set of zero sets and P_1 union P_2...

Can you help me on this problem please? I tried searching online, but I cannot find the proof: In T_3 space (or regular and T_1 (any one-point set is closed)), show that every prime z-filter is contained in a unique z-ultrafilter. I feel so stupid because I spent lots of time and I cannot...