Recent content by Hurin

I found this theorem on Prasolov's Problems and Theorems in Linear Algebra: Let V be a \mathbb{C}-vector space and A,B \in \mathcal{L}(V) such that rank([A,B])\leq 1. Then A and B has a common eigenvector. He gives this proof: The proof will be carried out by induction on n=dim(V). He...

Hi everyone, I've had some troubles to solve some exercices of real analysis.1. Prove that card( \mathbb{R}^{\mathbb{N}}) = card(\mathbb{R}). In this one I have considered that card(0,1)= card(\mathbb{R}) and tried to construct a bijection f: (0,1)\rightarrow \mathbb{R}^{\mathbb{N}}.2...

I'm in my first year. But, could you post your list please.

Hi, this is my first year in college, and I want to participate of the IMC (International Mathematics Competition for University Students). Can someone indicate good textbooks, problem books and other related tips to win a gold medal? -Thanks.

Thank you everyone. I can take classes in diurnal and nocturne periods.

Probability and statistics 1 is an introductory course and has no prerequisites. Real analysis has, indeed, calculus II as prerequisite. But, the professor told me that I can do both (calculus and analysis) if I require. Algebra I has no prerequisites. I don't know yet, if it's a hard class...

Yeah, it is allowed. i think that is a kind of trap, but it's allowed. If I keep only Algebra and analysis (and, of course, the mandatory ones) will it be difficult yet?

Hi, this is my first post here. I'm now in my first semester of my freshmen year. This semester is about to over, and I'm planning my classes for the next one. I have a huge interests in pure mathematics and theoretical physics. But my doubts are regarding time; 9 classes in one semester (42...