Recent content by eastside00_99

exposure if you learned something, you won

I don't see anything wrong with starting with commutative algebra from the get go. I think it could make sense to talk about fields first. I mean geez these are the things that say an a lot of undergraduates work with if they study engineering and physics. I could see a course where you start...

well, the best source, I would say, is Hatcher's Algebraic Topology: http://www.math.cornell.edu/~hatcher/AT/ATpage.html But, be warned, in some ways chapter 0 is the hardest in the book. I would definitely start with chapter 1. I was looking at my copy yesterday to refresh on algebraic...

exactly, the circle is the boundary of an open disk in R^2.

i don't know if you can learn how to read research papers in a field by just learning all the definitions. For instance, for cocycles to have very much meaning for you, you will want to learn at least a little algebraic topology. I don't know what a knot really is, but i know that at least...

All I am saying is the obvious fact that there exists distinct diffeomorphic smooth structures. the statement you wrote is just plain false. another way of saying what you said is that you can conclude that the smooth structures are not distinct when your manifolds are diffeomorphic and give...

If it were true that two diffeomorphic smooth structures admit the same smooth maps, then there would not exist distinct diffeomorphic smooth structures, which is absurd (see 2nd paragraph). there most certainly does exist two distinct diffeomorphic smooth structures. (R,{identity}) and (R...

I think the first thing you want do is the third problem in Lee's introduction to smooth manifolds. it says that given any topological manifold of dim > 0 with a smooth atlas, one can construct uncountably many distinct smooth structures. with this in mind, it seems that the equivalence relation...

well, math research, at least today, seems to be increasingly collaborative. i feel like whenever i look a people's past papers, unless they are the top guy in the their field, half of them have two or three coauthors. it seems having some smart people around to talk to really does help.

arshavin, when i was an undergrad, I had few friends who studied mathematics. most of my friends were intellectually curious in other was. for instance, they cared about the enviroment, or learning a foreign language, or reading literature. its good to know people like this...one learns a lot...

Well, its only the first semester so we started out with Complex Analysis Lars V. Ahlfors, secondary sources are Theory of Functions by Knopp and Hyperbolic Geometry from a Local Viewpoint by my teacher Linda Keen.

Hey mathwonk. I am taking a year of complex analysis now. Its good stuff!

Oh, I don't know if that is really necessary. I assume you already have your language requirement to graduate since you took three years of spanish in high school. Passing the language exam doesn't require taking formal classes because you do not have to be able to speak or even use the language...

I would say avoid doing things like complex variables, topics in analysis, and topology or say combinatorics, number theory, topics in algebraic structures. If you are preparing for graduate school, I would recommend topics in algebraic structures and topics in analysis. Then I would say you...

in my language, permutation group = finite symmetric groups. Whether or not I call his work concrete or not would mean me reading his work. I'm not doing that.