Yes, this is the first half of the book, and these are the subjects I'd like to see some examples of.
I may try this, the applications to graph theory look promising. To be honest though, this seems more like an equivalently abstract formulation of the subject in terms of matrices. I'm more...
I've been studying graduate level Linear Algebra from Steven Roman's Advanced Linear Algebra (Springer, GTM). It is a terrific book, but many of the concepts are extremely abstract so that I find it difficult to retain what I've learned. Can anyone point me to some books/reading on the...
Okay I think I understand now. However, I am noticing that the first definition invokes right multiplication whereas the second definition invokes left multiplication. In a module over a commutative ring this obviously won't make a difference, but is there some sort of subtle significance in the...
So I've been studying advanced linear algebra and have started learning about modules. However, I am having a hard time understanding the difference between a zero divisor and a torsion elements. The definitions seem extremely similar. Can someone offer a good definition of each and an...
Why not? Sorry if this seems like a stupid question, but I'm only just now learning (and trying to understand) the definitions of these things. Open means that it belongs the standard topology on R2, right? Why doesn't it?
Well why don't we form a chart (U, x) where U is an element of the subset topology of the standard topology on R2. Then U can be a subset of of the branch containing the point of branching with open endpoints on each of the three branches. x can then map each of these points to a point in R2...
Is there a topologist out there that wants to explain why exactly a branched line in R2 is not not a topological manifold? I know it's because there doesn't exist a chart at the point of branching, but I don't understand why not. I'm just starting to self study this, so go easy on me :).
1. Whoops, it's attached now.
3. He kept on stressing that streams had to be passed by reference, so I thought he was implying it was necessary to pass streams in this assignment, and I didn't really think about it.
4. I'll play with that, thanks.
5. I had it as an integer initially...
See this link for the given assignment.
note: on the last page the output aa4bcdd0cc1 is actually supposed to be aa3bcdd1cc1c.
I have no idea why my encoder function doesn't work. No...
Most definitions of a matrix that I have seen involve entries that are elements of a field. What if I have a unorderd set with no operations defined on it, say a set of different colored marbles or a set of historical events. Can I have a matrix whose entries are elements of such a set?
Ah, thanks. I guess I'm going to have to get off my ass and finish that MIT OCW Multivariable Calculus course I've been studying. I'm about halfway through, so I've seen double integrals and differentials, but not stoke's theorem.
So for a function of a single variable
How can this be extended to the integration of the total differential of a multivariable function over a region (specifically one of two variables)?
That is, how do you integrate
Say over the circular region
Thanks for taking the time to read and reply!
hmm, you're right. I should have done the derivation purely in terms of momentum.
Well, I was assuming a constant R.
There is no delta m in the integral.
Huh. I guess I just assumed that air resistance was always anti-parallel to direction of...
can anyone convert the relation tan y=(Vsin(y)-gx)/Vcos(y) to an explicit function y=f(x) in terms of V, x and g?
g is a constant
V is the function V(x)= -aln(b/b-cx)-dx
a,b,c,and d are also constants.
While fiddling around with some very simple linear ODEs, I "discovered" a formula that gives a solution to ODEs of the form: ##y'+y=ax^n ##.
here it is:
i'm sure that this was discovered before, but i was just wondering if it had any official name or something.
Thanks, guys! To be clear, I knew that that was my teacher's point, and that the solution of the ODE doesn't even actually apply to the electron, I was just interested in the theoretical process of solving such an ODE. I was assuming it was a relatively simple ODE that could be solved using...