Another math problem! (Not HW)

[Trajan]

So yea I know what you meant in your last post, Woozie. As far as I know, as long as the determinant is nonzero it really doesn't matter what the value is. The only exception being that two nxn matrices with different determinants have different volumes formed by the n vectors, as we said before. Kind of hard to picture volumes and shapes in more than 3-d though so..

[Kaylia]

So, what programming languages do I need to become familiar with as a scientist and mathematician? I know for sure Java isn't one of them. I don't know why that's even required for math majors.

I'm okay at matlab, and I really suck at everything else. Which languages should I be trying to learn? I'm guessing Fortran and/or C++? Or will matlab alone be enough?

Assembler > fortran > C++ > C# > java in term of speed for the most efficient code
C#/java > c++ > fortran > assembler in term of difficulty to learn/use.



I never used fortran, but since computing problem are generally small, fortran is probably not too bad in the context. However, you should still start with c#/java.


For object programing, I personally prefer C# with visual studio, it's probably the easiest environment.

if L is an invertible linear transformation, X is a Lebesgue measurable subset of R^n, and m denotes lebesgue measure, then

m(L(X)) = |det L|m(x)

if F is a C^1 diffeomorphism (so it's Jacobian JF has nonzero det) then for any
integrable function g

integral g dm = integral g of F |det JF| dm

I'm probably retarded, but I don't understand. oh well, maybe next year.

[Max™]

Jacobian matrix and determinant - Wikipedia, the free encyclopedia

Jacobians.

If diffeomorphism loses you, check out: Bijection - Wikipedia, the free encyclopedia, after that makes sense, and someone saying "one to one, and onto" makes you think "bijective!", then remember that a differentiable function is simply one which you can show a derivative for, or simply put, they are smooth, continuous.

So a Diffeomorphism - Wikipedia, the free encyclopedia means there is a smooth bijective map between manifolds, or at least subsets of those manifolds.

Differentiable manifold - Wikipedia, the free encyclopedia

I am most accustomed to these: Riemannian manifold - Wikipedia, the free encyclopedia, for obvious reasons (General Relativity).

[Woozie]

Assembler > fortran > C++ > C# > java in term of speed for the most efficient code
C#/java > c++ > fortran > assembler in term of difficulty to learn/use.



I never used fortran, but since computing problem are generally small, fortran is probably not too bad in the context. However, you should still start with c#/java.


For object programing, I personally prefer C# with visual studio, it's probably the easiest environment.




I'm probably retarded, but I don't understand. oh well, maybe next year.

Okay, that makes sense. So the reason they start us off with Java even though we wont use it as scientist is because it's one of the easiest to learn. If I failed Java twice, and the stuff I need is way harder, then I imagine I would have failed those other classes too lol

I downloaded some books on C++ and fortran. I'm going to start learning these as soon as I have free time (so I guess never).

[Kaylia]

Okay, that makes sense. So the reason they start us off with Java even though we wont use it as scientist is because it's one of the easiest to learn. If I failed Java twice, and the stuff I need is way harder, then I imagine I would have failed those other classes too lol

I downloaded some books on C++ and fortran. I'm going to start learning these as soon as I have free time (so I guess never).

Well, "much harder" is an overstatement, because you probably won't have to use any of the less obvious functions (networks programming, dealing with input from material, hooking another program). As far as I know (I haven't done much scientific programming yet), most of the works is done on paper, trying to reduce the amount of operations of a given algorithm. The rest is just basic function call and assigning variable, which isn't very different than something you would do in mathematica.


Like I said earlier, I'm certain you won't have any trouble programming once you start. You just need to give yourself a little push, and thing will eventually work out (I can understand why you wouldnt want to in the middle of a semester though). I still recommend starting with java or c# before moving to C or fortran, they are much more forgiving. If you understand a language well enough to program, it's just a matter of hours before you can use other language...it's almost always the same thing.

And use internet example or ask people around here for help if you struggle on something. It's almost always little details you forgot, and not a real understanding problem.