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How to Choose the Right Measure for Your Data
The basic structure of any neural net machine learning process consists of a model, an “objective function”, and a way of taking said function’s gradient. An objective function is a way of measuring the performance of a model. Thusly, it is also sometimes called a measure. Measures are often constructed using large sets of data… Continue reading
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Field Theory-Deconstructing Analysis (not redundant, I swear)
Have you ever thought about why we use exactly the techniques we use to prove facts of algebra? Every single one comes down to being a generalizable (at least, somewhat) line of reasoning that takes you from some piece of information, to some other piece of information. It turns out that we can do a… Continue reading
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Numerical Stability; when is a statistical algorithm safe?
When building statistical algorithms, there are many factors which can make something rather unstable in such a way that, if not computed exactly (and we can almost never compute exactly with digitized computataion) it might diverge in a very strange way. When considering what may be considered stable and what may not be, it is… Continue reading
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Intro to Combinatorial Games: Nim
When people first hear about combinatorial games, they are often a little bit intimidated by the name; combinatorics has been a source of trauma for numerous people in school, I’m sure. But despite their name, combinatorial games are actually easy to define and play. A combinatorial game is a game defined by a sequence of… Continue reading
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Investigating an interesting continuous function using discrete methods
Many of you will be familiar with the famous counterexample to the claim that all differentiable functions are continuously so: f(x) = (x^2) sin(1/x), with the point (0,0) When you look for ideas on how to show that this is differentiable at 0, despite the fact that the derivatives do not approach the value of… Continue reading
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One More Proof of the Divergence of the Harmonic Series
All right, you read the title; its time for you to go through this rite of passage of mathematics with me (even if you’ve gone through it a few times before). We’re gonna prove the divergence of the harmonic series. To begin with, I’ll just write out (really only for formality’s sake) what the harmonic… Continue reading
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A Nice Solution To a Very Nice Problem
When you start on learning discrete mathematics, one of the first really interesting ideas you’ll come across (well maybe it won’t be that close to being the first, but you get the point…) is that of even and odd parity permutations. If you haven’t heard of permutations before, they’re basically just ways of scrambling numbers… Continue reading
About Me
I’m a person passionate about science, math, and their applications. I thinks it’s important to try to write about what you learn, in some form ot another, so I’ll be doing that here. Hopefully, some of you reading my posts will find them to be just as helpful and interesting to you as they were for me!
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