Recent content by MushroomPirat

Thanks for your help micromass. I thought about your advice and came up with a different proof: Suppose T is injective and let (v_1,...,v_n) be a basis of V. Because this basis is linearly independent and T is injective, then (Tv_1,...,Tv_n) is also linearly independent (this was a result...

Homework Statement Suppose that W is finite dimensional and T:V\rightarrow W. Prove that T is injective if and only if there exists S:W\rightarrow V such that ST is the identity map on V. Homework Equations The Attempt at a Solution First, suppose that T is injective and let...

That's good to hear I'm on the right track. Thanks for taking a look at it :)

Homework Statement I was trying to prove a theorem from Axler's Linear Algebra text and my proof is different from the one in the book, and I'm wondering if someone can check whether or not my proof works, since I'm just starting to write proofs. Theorem 2.6 (pg. 25): In a finite-dimensional...

Homework Statement I'm self-studying Daniel Velleman's How to Prove It, and I'm wondering if there is some way to write that "Sets A and B are disjoint" using symbols, other than the A \cap B = \emptyset given in the book.Homework Equations The Attempt at a Solution I'm thinking that if A...

Thanks for your input! I basically have the same mindset as you - aim for the top US schools, but don't get too sad if I don't get in. Hmm... Could I get a few more opinions on this? I know that most people are going to say that the US schools are superior, but is the difference between...

I know that I'm comparing Ivy's with Canada's best, but I was wondering HOW MUCH better the ivys are in the long run. I understand there is going to be a better program overall, with better professors, and a more competitive environment, but how does it compare with Canada's top universities...

Hello everyone, I'm currently a Grade 11 IB student living in BC Canada. For the last few years, it has been my goal to get into a good American university. I'm thinking of going into some sort of engineering in university (electrical or mechanical, or both!) However, for the past month, I've...

Hey Reedeegi, Thanks for your reply! I looked at the books you mentioned quickly on google books and I actually find them quite interesting. It really is a different approach than what I'm used to. I'm not trying to learn calculus from scratch; I've done calculus up to about the AP Calculus AB...

I'm looking to buy an undergraduate Calculus textbook, mostly for self-studying, since I'm currently in high school. I've been looking on here and on amazon for some texts, and the books by Larson seem to be pretty good. However, there's two books which seem to cover almost the exact same thing...