Then i think my conception of adding vectors is incorrect. If i think of vectors as directed line segments, i cant think of a way to add vectors on the x-axis to other vectors to get something parallel.
But if you add a vector to the x-axis, how can that be a line parallel to the x-axis. More importantly, what is an element of the x-axis? Is it just a point?
I'm having a bit of trouble seeing Vector Quotient Spaces.
Lets say I have a vector space $V$ and I want to quotient out by a linear subspace $N$. Then $V/N$ is the set of all equivalence classes $[N + v]$ where $v \in V$.
For example, let me try to take $\mathbb{R}^{2} /$ x-axis. This...
Hello,
I am currently a high school student and I have been accepted into both UC Berkeley and the University of Chicago. I plan to major in math or physics, but I have no idea which college I want to go to. From what you know of their undergraduate mathematics or physics programs, which...
This site was linked at the top of the physics forums website. www.relativitychallenge.com I guess everybody has freedom of speech. Do people just get a kick out of proving Einstein wrong?
This problem comes from Halmos's Finite Dimensional Vector Spaces. Given that we can re-define addition or multiplication or both, is the set of all nonnegative integers a field? What about the integers? My thinking is that since the Rational numbers form a field, and they are countable, we...
Has anyone read Cours d'analyse mathématique (Course in Mathematical Analysis)? If you have, do you find some the the problems just a might challenging? I've found that this is pretty characteristic of books of that time period. Why have problems in textbooks today gotten so much easier?
What is the Latest age at which one can acquire this ability? Are there people who can learn languages easily at older ages given that they had not been exposed at a younger age?
Wow, so many responses. I was just wondering and all. I have another question now. This is not homework, I was just thinking. Lets say we take a definite integral from 0 to 1 of an arbitrary real valued function, and answer is x. Clearly if we take away any random point from the interval 0...
Why do you need to graduate from high school? Is it because it is required to graduate from college? - Because it would be pretty cool to say, in the future when you become succesful, that you were a high school dropout.
Where is mathematics learning going today? There are many books nowadays, that emphasis conciseness and rigour over all else. The Rudin "series" is a perfect example. There is hardly any motivation, and emphasis is put on rigour, rather than intuition. I am sure that this could be argued...
I think the school of engineering and the school of arts and sciences are two different schools. I think that if you want to major in physics you have to apply to the other college.
point to a road and ask if the other person would say if it was the road to gondor. This way if you are pointing to the correct road, and the person you are speaking to is the truth person, he would say no. Similiarily, if it was the lying person, then he would also say no. Thus you know to...
"I'm not looking to discover the Theory of Everything, but I'd like to be able to understand it when someone else finally does." Well if this is the case, then I am afraid most community college classes will not come close to the level of mathematics that is involved with the various theories...
First of all, it would be helpful to know what you have learned so far. There are quite a few prerequisites before surgery. You should have had a good graduate level classes in Algebra, Algebraic Topology, and some Differential Topology at very least. If you have enough Alg. Top. under your...
Surgery on Compact Manifolds: "Part 1 consists of the statement and proof onf our main result, namely that the possibility of successfully doing surgery depends on an obstruction in a certain abelian group, and that these 'surgery obstruction groups' depend only on the fundamental groups...