Originally posted on R196, Hilbert's Hotel:
Just mirroring a post from the other blog. Here is an IPython notebook with an implementation of the linear percepton algorithm. Details will follow in another post and I give a general idea of what it does in the notebook but here is what the picture looks like. Assuming that you have a set of points and you… Continue reading An IPython notebook on the linear perceptron
A friend asked the following question: Describe the contrast between the abstract and the concrete [in mathematics], citing examples. Some have claimed that the notion of abstraction is itself flawed. Argue either for or against this position.” Here’s my take on it. One example comes from modeling random situations, for example when using the Normal distribution. We really like it cause it’s this continuous, unbounded, … Continue reading Abstractions in math
I recommend this great lecture! So many good points about research in there. Continue reading “You and your research”
Originally posted on TIFFANY MARTÍNEZ:
My name is Tiffany Martínez. As a McNair Fellow and student scholar, I’ve presented at national conferences in San Francisco, San Diego, and Miami. I have crafted a critical reflection piece that was published in a peer-reviewed journal managed by the Pell Institute for the Study of Higher Education and Council for Opportunity in Education. I have consistently juggled… Continue reading Academia, Love Me Back
https://www.quora.com/At-what-point-does-mathematics-get-hard There is a point where math gets hard for anybody and everybody. For some it’s high school, for others college, undergraduate or graduate study, or even research-level math, and there most problems are really hard. Do not assume that 90’s in all math classes at high school imply that you won’t find any difficulty with college math. You probably still haven’t been taught math … Continue reading At what point does mathematics get hard?
Consider a matrix . In general, this matrix has rank Now, suppose we wish to column-center the data. We can do this algebraically by using what is known as the centering matrix, where is the matrix where for all . Multiplying with results to the centering of all the columns. The vector of ones is the only independent element in its nullspace and so . … Continue reading Rank of centered data
From: https://www.quora.com/Why-am-I-good-at-mind-calculations-but-bad-at-problem-solving I have this friend who is great at cutting vegetables. You give her whatever you want, she can shred it in seconds. However, when it comes to cooking, she needs to be shown how to combine the vegetables and understand the differences in taste and acidity of each one, etc. Otherwise she can’t progress, she is almost paralyzed by fear. Why doesn’t her … Continue reading Why am I good at mind calculations but bad at problem solving?
This is the second part of the story that I started with the previous post. Wanting to build a quick counterexample, I wondered if I can create a random variable by solving the moment problem with only finite non-zero moments. In the language of the moment problem, my sequence was such that for all greater than some number . That is, only finite elements of … Continue reading But moment picking is tricky too.
Yesterday, while trying to build a counter-example for a research problem, I started playing with the idea of designing a random variable, not by picking a vanilla distribution, but by selecting its moments myself. That is, if I pick the moments myself, can I find a distribution that has them? More formally, if I provide , is there a : probability measure such that … Continue reading Going moment-picking
The following is from an answer I wrote on Quora. The easiest answer is: “You just can’t cram the research.” Let’s figure it out together, assuming you’ve passed your quals, you are done with classes, and you work in the natural sciences, engineering, or computer science. First, you need to pick a good problem, which will take some time, except if your advisor already has … Continue reading “Why isn’t it possible to finish a PhD in less than three years?”
R196, Hilbert's Hotel 