I just recently sorted out how to run MPI jobs on google compute cloud instances. For my own memory’s sake and also in the remote possibility that this could be useful to anyone I give an overview of the steps I took.
I have recently encountered several significant bugs in C codes with a common source: variable length arrays (VLAs). The bug ultimately arises from assumptions made years ago about how big a VLA could get, which would later be violated - leading to undefined behavior in C. The tricky part about this kind of bug is that there is no way within C to check for successful allocation of a VLA; incorrect VLA construction simply is undefined behavior leading usually to crashing code.
I came across an International Mathematical Olympiad problem from 1978 which I had the feeling I would be able to solve quickly. The problem is stated as follows:
I have successfully defended my PhD thesis “Accelerated Plane-wave Discontinuous Galerkin Methods for Heterogeneous Scattering Problems,” and today submitted my committee’s signatures. Hopefully now I will have a little more time to pursue some personal projects :)
In a previous post I gave a nice proof that there are infinitely many prime numbers. The proof however is somewhat nonconstructive because by way of a contradiction argument I sneak around issues of actually constructing a new prime not in a prespecified finite list, which would be the “constructive” manner of proving this same fact.
Here is the YouTube video of my JuliaCon presentation on the implementation of finite element methods in Julia. I had a great time at the conference and was really impressed with all of the presentations. I’m really glad so many people have come together to make this a reality.
In a recent post I showed that there are infinitely many prime numbers. A little stronger fact than this is that the sum of the reciprocals of prime numbers diverges, which I attempted to concisely explain in this Quora response. I have always wanted to find a simple proof of this fact, but so far I have not been successful. Euler’s proof to date appears to me to be the most straightforward argument. However at the time of writing this post, this Wikipedia entry lists Euler’s proof and calls its steps a sequence of audacious leaps of logic.
(Note: I have updated this post to reflect that the origin of this argument was Euler, although it was unknown to me when I first posted this)
I decided to try my hand at various technologies of the web. Whether I have been a failure I will let you decide. The experience has however left me fairly confident that I should keep the majority of my focus on mathematics and scientific computation.