10,579 reputation
21133
bio website math.berkeley.edu/~cawong
location Berkeley, CA
age 25
visits member for 2 years, 7 months
seen 30 mins 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.


Jul
24
comment What is the inverse Fourier transform of $|k|^{-\alpha}$?
But that's the same thing. $x$ and $k$ are interchangeable, up to a sign flip.
Jul
24
comment What is the inverse Fourier transform of $|k|^{-\alpha}$?
Do you need to compute the Fourier transform, or do you just want to know the result? I believe one can find tables of Fourier transforms for functions such as this. Otherwise, the computation is nontrivial, since one needs to understand how to appropriately define $|x|^{-\alpha}$ as a distribution when $\alpha > 1$.
Jul
24
revised How to reverse matrix vector multiplication?
added tag
Jul
24
answered How to reverse matrix vector multiplication?
Jul
22
comment How do people on MSE find closed-form expressions for integrals, infinite products, etc?
This is largely a matter of experience and pattern matching, not a specific and dedicated study to the art of obtaining closed form solutions. Two areas that are particularly conducive to finding these closed-form expressions are differential equations and probability. There are quite a few special functions that arise as families of solutions to particular ODE/PDE or as some explicit probabilistic expression.
Jul
22
awarded  Enlightened
Jul
20
comment Finding the maximum value of $\displaystyle \int_{0}^{1}e^x\log f(x)dx$ when $\displaystyle \int_{0}^{1}f(x)dx=1$
Sorry, I've been away for a day. I've updated my answer; credits to @Did for seeing how to do it first.
Jul
20
revised Finding the maximum value of $\displaystyle \int_{0}^{1}e^x\log f(x)dx$ when $\displaystyle \int_{0}^{1}f(x)dx=1$
added maximizer argument
Jul
20
awarded  real-analysis
Jul
19
awarded  Nice Answer
Jul
19
comment What are the various branches of Vectors?
I agree with most aspects of your post except one. I would never recommend any book by Serge Lang to any beginner. I'm not sure I can forgive you for your crime =P
Jul
19
answered Prove: For any real number a,b : |a - b| >= |a| -|b|
Jul
17
answered Distortion and Norm Stabilization
Jul
17
comment Distortion and Norm Stabilization
It may be useful if you provide the relevant definitions for "distortable" and "stabilizes".
Jul
16
awarded  Good Answer
Jul
16
revised Finding the maximum value of $\displaystyle \int_{0}^{1}e^x\log f(x)dx$ when $\displaystyle \int_{0}^{1}f(x)dx=1$
added a comment since the function is only nonnegative
Jul
16
revised Finding the maximum value of $\displaystyle \int_{0}^{1}e^x\log f(x)dx$ when $\displaystyle \int_{0}^{1}f(x)dx=1$
added a comment since the function is only nonnegative
Jul
16
revised Finding the maximum value of $\displaystyle \int_{0}^{1}e^x\log f(x)dx$ when $\displaystyle \int_{0}^{1}f(x)dx=1$
added 534 characters in body
Jul
16
answered Finding the maximum value of $\displaystyle \int_{0}^{1}e^x\log f(x)dx$ when $\displaystyle \int_{0}^{1}f(x)dx=1$
Jul
13
comment numerical solution of integral equation
This depends on your choice of quadrature (your choice of $t_j, w_j$). Different quadratures yield different orders of accuracy.