6,340 reputation
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bio website mathcs.holycross.edu/~ahwang
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visits member for 1 year, 3 months
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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).
Aug
28
comment Prove this function is a bijection
Sounds like you've answered your question. :) Here's a small linguistic note for future reference: When you write "such that...", you need to give a condition to be imposed on the subject of the sentence. What you have, "$y$ such that $y = 1/x$", isn't completely suitable because you haven't said what $x$ is. What you meant, presumably, is "Let $y$ be a non-zero real number, and let $x = 1/y$. Notice $f(x) = 1/x = y$...."
Aug
25
comment 'Proof ' that $\ln(x)$ converges
@alexqwx: Perhaps it helps to note that your purported argument is equivalent to the common misperception that an infinite series necessarily converges if its terms decrease to zero.
Aug
25
comment If a plane intersects a regular surface at exactly one point, then it is the tangent plane
Point of skepticism: In differentiating, you're assuming equation (1) holds in a neighborhood of $q$, but your hypotheses seem explicitly to say that (1) holds (only) at $q$. (Your time might be better spent studying Professor Lee's proof and filling in any perceived gaps. :)
Aug
22
answered Geometric interpretation of an integral inequality
Aug
19
reviewed Close How to find this integral $\int_{0}^{\infty}\dfrac{f(x)}{g(x)}dx$
Aug
19
reviewed Close Example of a function $u\in L^\infty(0,T,H^1)$ such that $u_t\notin L^\infty(0,T,H^1)$
Aug
19
answered $x\cdot 0 \neq 0$ infinitely many zeroes on a finite interval