James S. Cook

2,761 reputation

213

bio	website	supermath.info
	location	Virgina USA
	age	34
visits	member for	10 months
	seen	17 hours ago
stats	profile views	374

I'm interested in mathematics which is used to frame physical theory. I guess that means I'm at least a little interested in just about anything. Currently I'm trying to find a good open question to attack.

	2,761 reputation	bio	website	supermath.info	visits	member for	10 months
213 badges		location	Virgina USA		seen	17 hours ago

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1d	comment	For x < 5 what is the greatest value of x Who says $x$ is a real number. I say $x$ is a number which is less than or equal to $4$ hence the greatest such $x$ is 4. Problem solved ;)
1d	awarded	Constituent
May 14	answered	Does this ODE have an exact or well-established approximate analytical solution?
May 13	awarded	Caucus
May 12	comment	Stokes' theorem - circle cross section in a sphere @LaPrevoyance the intersection of the cylinder and the sphere is a curve. Why would you need $x$ and $y$ to parametrize it? My answer already explains that when you plug in CAF's equations they don't satisfy the Cartesian equation of a sphere, so, they don't parametrize the sphere. On the other hand, his equations do have $x^2+y^2=y$ hence his parametrization falls on a cylinder.The question you need to ask yourself is what is a parametrization? How do we check to see if a given parametrization is correct? Or, perhaps, what is a sphere, what is a cylinder in Cartesians?
May 8	comment	the role of logic in math and education In regular coursework, with few exceptions, you are not called upon to do creative mathematics. Rather, you are placed in a realm with well-defined rules and asked questions which have clear guides by set definitions. In this setting, it is mostly logic which matters. However, in the world beyond coursework, when we consider questions of motivation or innovation, there we find logic is a poor guide. Intuition is key. But, logic cannot be abandoned. So, no, I don't think your education is bad, your experience is just limited.
May 5	comment	Not getting $-\frac{\pi}{4}$ for my integral. Help with algebra @User69127 the expression $log(z)$ is multiply-valued (depending on what you read). Somewhere the angle has to jump. When the angle jumps the $log(z)$ is discontinuous hence non-analytic. Theorems you use often require analyticity in and on the contour, so this jump must be carefully considered. Generally, $log(z) = ln\|z\|+iarg(z)$ is undefined at $z=0$ this is a point shared by all branches. So, what to do? Depends on the example. But, you should think more on this issue, it is the issue which forces your path in these problems.
May 5	comment	Not getting $-\frac{\pi}{4}$ for my integral. Help with algebra But, your integral is not of the form $P(z)/Q(z)$. You need to think about the branch-cut of the log etc...
May 2	answered	Help with algebraic manipulation to prove that $\Omega (M)$ constructed from $\Omega^1 (M)$ forms an algebra over $C^\infty (M)$
Apr 25	comment	simple linear differential equation @Zack sorry I didn't get back to earlier. I guess you see what I meant now given the nice answer below :)
Apr 25	comment	simple linear differential equation use separation of variables.
Apr 13	comment	partial differentiation on differentials @MykeArya none taken.
Apr 12	comment	partial differentiation on differentials @MykeArya not really, I understood the method of differentials far before I understood the exterior calculus. Moreover, I also gave your answer in my original post, granted you have included a few details which are nice.
Apr 12	comment	partial differentiation on differentials @mary sorry for the delay, I forgot about this post for a bit... I just added the bit on differentials.
Apr 12	revised	partial differentiation on differentials added details to part requested my mary.
Apr 12	comment	non-vanishing k-form on a k-manifold in $\mathbb{R}^n$ implies orientability was my answer helpful?
Apr 9	answered	Gradient of scalar potential
Apr 9	comment	Gradient of scalar potential what exactly is the natural log of a cross product? This is a typo?
Apr 8	comment	Units of polynomial rings over a field Sounds like a good start. Now equate coefficients.
Apr 8	comment	How can I find explicit solutions of this ODE $\dot x=e^x\sin x$? separate and integrate when $x \neq n \pi$ of course the constant solutions $x = n\pi$ are exceptional in this problem. For the case of a vector $x$ I have no idea what $\sin(x)$ would mean.