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  • 30 votes cast
Dec
10
comment Elliptic Curves and Points at Infinity
@xdfm Yes, they are. You can imagine my surprise when I missed thanksgiving week and we jumped infinite fractions to discussing elliptic curves.
Dec
10
comment Elliptic Curves and Points at Infinity
If I'm understanding you correctly, the "infinity" comes when we try to map this point back into k^n, over which the polynomial is defined? In other words, if we homogenize a polynomial (and Z is the added dimension), then all points in the vanishing locus with Z = 0 are points at infinity? In the end, isn't our goal to analyse the polynomial itself (and not the homogenized version)? So it makes sense to "normalize" with respect to Z.
Dec
10
asked Elliptic Curves and Points at Infinity
Dec
8
comment how to read a mathematical paper?
Introduction, Conclusion, pictures/equations, and then the text if it actually is what I need.
Dec
3
comment what is product of delta function with itself?
On a related note, does anyone know what the convolution of two delta functions is? Mathematica is telling me that $\delta(x-x_1)$ convolved with $\delta(x-x_2)$ is $\delta(x- x_1 - x_2)$, somehow doesn't seem believable.
Dec
3
awarded  Talkative
Dec
1
comment $e$ to 50 billion decimal places
It becomes even more incredulous when you realize that you only need 55 digits of pi to draw a circle with the radius of the universe to the accuracy of the radius of a hydrogen atom.
Nov
24
comment Methods to see if a polynomial is irreducible
I'm not able to access the first link you posted
Nov
23
comment Why would I want to multiply two polynomials?
@J.M. You are right that the actual solution involves a single polynomial. But if you are doing Laguerre polynomials by hand they are (well, can be) defined through a recursion relation and thus require you to multiply polynomials together.
Nov
23
answered Why would I want to multiply two polynomials?
Nov
23
comment Converting an explicitly defined function to a recursive one
Recursion (n) - See: Recursion
Nov
19
awarded  Nice Question
Nov
15
comment A root? Or two roots?
I was under the impression that those are just two ways of saying the same thing.
Nov
12
comment Can the phase of a function be extracted from only its absolute value and its Fourier transform's absolute value?
Just curious. How would one even define the phase of a constant function?
Nov
12
comment Making meaning of mathematical “bridges”
Personally I find the "full" version of the formula ($e^{i\theta} = \cos{\theta} + i\sin{\theta}$) of which this "identity" is a special case to be much more beautiful and revealing
Nov
9
comment What's so “natural” about the base of natural logarithms?
I would think that very few function are eigenvectors of the Derivative operator. In fact, I'd be curious to know if there are any others besides the exponentials and even some sums of sinusoidals/hyperbolics.
Nov
5
comment Is It True that We Can Never Be Sure of Validity of a Mathematical Proof?
The only solution is to train more quality mathematicians so that our peer-review process can be more comprehensive and accurate. On the serious side, results that are very specialized (like the proof of fermat's last theorem) can spend a long time in review before they are published for this very reason.
Nov
5
answered Which one result in mathematics has surprised you the most?
Nov
4
comment Is speed an important quality in a mathematician?
@mike too true unfortunately. I've lost many points on exams that had I had more time to think I would have solved completely. There must be some middle ground between the free for all of a take home exam (there are not very many questions you can ask on an undergraduate exam that won't be proven in some book) and the stressful race of a sit-in exam.
Nov
4
comment Is speed an important quality in a mathematician?
It sure helps on mathematics exams!