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bio website mathcs.holycross.edu/~ahwang
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visits member for 1 year, 5 months
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1h
comment Blackboard bold, Bold, Fraktur, and Reserved Variable.
@achillehui: Thank you for that information. Perhaps \Reals is a safer choice? I'm happy to edit my answer if it seems worthwhile to do so.
1d
answered Blackboard bold, Bold, Fraktur, and Reserved Variable.
Dec
9
awarded  Caucus
Nov
9
comment Can ratios really be manipulated as fractions?
@Bede: The usages I've seen, come to think of it, are in older (pre-1923) works. Your interpretation seems to be widespread nowadays (e.g., when giving odds). (+1 to your question, and to Meelo's answer.)
Nov
8
answered Can ratios really be manipulated as fractions?
Oct
29
comment Intuitively understanding Riemann surfaces
@Wooster: You're welcome; glad the picture was helpful. :)
Oct
28
answered Intuitively understanding Riemann surfaces
Oct
11
comment Is the Projective Real Plane Compact?
Can you think of a compact space $S$ and a continuous surjection from $S$ to the projective plane...? :)
Oct
10
answered Why do we need min to choose $\delta$?
Sep
30
awarded  Explainer
Sep
15
comment 3D graph of a function - its projection onto xy plane?
What do you mean by "the projection of a function"? (Perhaps the projection of the graph?) And when you say "a function with three variables", do you mean "$w = f(x, y, z)$" (i.e., a function of three variables) or "$z = f(x, y)$"? If the latter (as I suspect), the projection is just the domain of $f$....
Sep
4
comment Prove that $V = \ker(\phi) \oplus \text{image}(\phi)$
My comment was careless: If $\phi$ has nilpotent Jordan blocks, then the corresponding blocks of $\phi^{n}$ are zero. From this (and a bit of work), your desired conclusion follows.
Sep
4
comment When convolution of two functions has compact support?
Do you have an example of a non-negative, continuous, integrable $f$ and a compactly-supported, non-negative, continuous function $\phi$ with unit integral such that the support of their convolution is compact?
Sep
4
comment Prove that $V = \ker(\phi) \oplus \text{image}(\phi)$
It will help to notice (using Jordan canonical form, say) that $\phi^{n}$ is diagonalizable.
Aug
30
comment Can you graph equations with a negative discriminant? And how do you plot complex numbers both on a 2D complex plane and a 4D complex plane?
Welcome to MSE! I've added mathematical markup to your question; please feel free to edit if I've misconstrued anything. As stated, it's difficult to tell exactly what you're asking: Do you merely want to plot complex numbers? Do you want to visualize the graph of a complex polynomial (a surface in four-dimensional space)? Something else...?
Aug
30
revised Can you graph equations with a negative discriminant? And how do you plot complex numbers both on a 2D complex plane and a 4D complex plane?
Added LaTeX, changed tags
Aug
30
comment How do I solve $x^5 +x^3+x = y$ for $x$?
FWIW, your question title (invert $y = x^{5} + x^{3} + x = f(x)$) does not match the question body (find $f^{-1}(3)$, which is much easier). It's possible this mismatch has caused some confusion.
Aug
30
revised What does this Perspective-projection matrix in 2D do?
Tweaked LaTeX
Aug
30
comment What does this Perspective-projection matrix in 2D do?
You've noticed that the matrix $P'$ reduces to $P$ when $\theta = 0$? (Often a matrix defines a mapping on column vectors by multiplication on the left, but for your two matrices this doesn't seem to accomplish any "standard" projection in computer graphics.)
Aug
30
comment The derivative of $z=x^2+xy+ y^2$
You're conflating "implicit derivatives" (your understanding) and "partial derivatives" (the video you saw).