10,838 reputation
21135
bio website math.berkeley.edu/~cawong
location Berkeley, CA
age 25
visits member for 2 years, 8 months
seen 17 hours ago

I am a fourth-year mathematics graduate student at the University of California, Berkeley.

I graduated with a B.S. in Applied and Computational Mathematics from the California Institute of Technology.

My general mathematical interests include applied functional analysis, numerical analysis, harmonic analysis, partial differential equations, numerical linear algebra, and mathematical and computational biology, chemistry, and physics.


1d
comment Constructing a sequence of function with bounded derivative
Do you mean to say that you require $f_n$ to have uniformly bounded third derivative with respect to $n$?
Sep
17
comment Why does the discrete cosine transform compact the information at the “low frequencies”?
The rank of a matrix is the dimension of its column space. For generic values of the entries, an $n \times n$ matrix always has rank $n$. However, it might be very close in value to another $n \times n$ matrix whose rank is much less than $n$. This is the assumption used when one does a compression.
Sep
16
answered Why does the discrete cosine transform compact the information at the “low frequencies”?
Sep
11
reviewed Leave Open I lost my love of math; I'm getting it back. How can I determine if math is actually right for me?
Sep
11
reviewed Close Converting non-continuous angle to 360
Sep
11
comment Questions about weak derivatives
@bartgol, for (3), he is asking whether it is possible, for example, for a function to have a weak 2nd derivative but not a weak 1st derivative.
Aug
30
comment What is an example of a function that is measurable but not strongly measurable?
@Freeze_S, by $\ell^2([0,1])$, what exactly do you mean? I'm assuming this is not the same as $L^2[0,1]$, since that would be separable.
Aug
30
revised What is an example of a function that is measurable but not strongly measurable?
edited title; some additional comments
Aug
30
asked What is an example of a function that is measurable but not strongly measurable?
Aug
23
comment Local inversion theorem (théorème d'inversion local)
Locally invertible is the same thing as bijective (within a neighborhood).
Aug
23
comment Local inversion theorem (théorème d'inversion local)
It sounds like you might have some confusions as to the definitions of "locally invertible" or the concept of $x$ being "isolated". If you review these definitions, then look at my hints, I think you might be able to see how to resolve these issues.
Aug
22
comment Local inversion theorem (théorème d'inversion local)
Right, and what defines a diffeomorphism?
Aug
22
comment Local inversion theorem (théorème d'inversion local)
Your critical point is $x$ such that $f'(x) = 0$. Since $f'$ is invertible, then locally $x$ is the only point such that $f'$ evaluates to $0$.
Aug
22
comment Local inversion theorem (théorème d'inversion local)
Apply the theorem to the derivative of $f$.
Aug
21
reviewed Close Drawing 3D stomach structure in Matlab
Aug
18
comment Approximation of (n^n)^n
That's a good point. I am not an expert on state-of-the-art approximation methods for standard functions. Such methods are pretty well-understood, I'm led to believe, so I guess somebody could add some references to such methods if they have the time.
Aug
18
answered Approximation of (n^n)^n
Aug
8
reviewed Leave Open Exponential function (t)
Aug
8
reviewed Close Weird Calculus problem
Aug
8
answered What type of Banach spaces $X$ does the sum $x + c$ make sense where $x \in X$ and $c \in \mathbb{R}$?