On Mathematics
I have a very awkward relationship with math. Most of my peers love it to pieces. They constantly suggest that I learn more and more of it. There are constant cheers that Math makes universe go around and the world is so beautiful with mathematician goggles. The problem is that it is not how I view math.
My view of the subject is utilitarian. I do my own thing. I am a computer scientists. I enjoy going out and writing interesting algorithms. There is certain challenge to exploring ways of modeling processes. The nature of the computation is equally frustrating and illuminating. Sometimes I run into problems representing certain aspects of the problem. The issue is usually tied to some mathematical concept that I do not know. That is the state of mathematics and me. When I am in a jam I call up math to help me out. It is strictly a tool in my set of skills.
Recently, I have been reaching into that toolbox more often than I want to. The problem is I really do not know what math is useful and which is not. I voluntarily took up to multivariable calculus. There was this underlying assumption that I would be as a computer scientist using math that uses arbitrary numbers of variables. What I forgot was that computer science uses discrete mathematics. Calculus is the mathematics of continuous systems! So while what I had just learned was very handy for mechanical engineers and physicists, it was useless to me.
Combinatorics does not come as often as the college classes make it out to be. It just has the habit of occuring just when you do not expect it. Mostly I run into it when I am employing some Bayesian learning algorithm. Geometry and graph theory are the math fields I will run into most often. Graph theory is used essentially everywhere. It is the ultimate generalization of all data structures. Most reinforcement learning algorithms require a substantial knowledge of graphs. Neural networks is all about fancy graphs. The things are everywhere.
Geometry I run into a lot due to working on projects that interface with the world. The programs in your cellphone need to some heavy duty triangulation to figure based on the locations and distances of various cellular towers where the hell you are. Geometry is the only thing that will help in that class of problems. This includes such headaches like what area does a collection of cellular towers provide coverage for. Also this is not the geometry you are taught in grammar school. This geometry will use trigonometry, and it will employ a set of procedures so repetitive that you will memorize the C function that does it, convex hull I am looking at you.
Dealing with those fields of mathematics has been annoying but acceptable. Lately, I have been running into a lot of projects that require heavy use of number theory. Number theory is the stuff of higher mathematics classes. The is the stuff of 300 and 400 level math undergraduate math courses. Saying "number theory is a strange subfield of mathematics" is about as tautological as saying circles are round. Alice in Wonderland was written by a logician that studied number theory. I do not want to get near this thing. Mathematics has given me such sharp and powerful tools. Understanding the concepts undelying my problem requires the most twisted tools in the box.
So I downloaded some pdfs and started reading. The notation alone almost overtook me. The structures they introduce are so specific and exact. They are constrained in the exactly the ways the object I am going to work with will be. This thought is comforting since most people will not have an immediate use for this stuff. I am digging since I know I need to use it. I read through a few chapters and did some exercises for myself. Then the nightmares started.
The nightmares mostly consist of me inside of these structures, and I can not get out of them. I am not assaulted with the notation and barrages of equations. It is not that the equations themselves that scratches at my face. As they fly by I try to read them and understand what they mean. Unfortunately, due to the biological natures of dreams/nightmares I can not. The frustration hurts me physically in this nightmare. That is the most generalized I can make it. They really differ otherwise. With my luck, tonight I will be murdered by an n-element ordered set.
My view of the subject is utilitarian. I do my own thing. I am a computer scientists. I enjoy going out and writing interesting algorithms. There is certain challenge to exploring ways of modeling processes. The nature of the computation is equally frustrating and illuminating. Sometimes I run into problems representing certain aspects of the problem. The issue is usually tied to some mathematical concept that I do not know. That is the state of mathematics and me. When I am in a jam I call up math to help me out. It is strictly a tool in my set of skills.
Recently, I have been reaching into that toolbox more often than I want to. The problem is I really do not know what math is useful and which is not. I voluntarily took up to multivariable calculus. There was this underlying assumption that I would be as a computer scientist using math that uses arbitrary numbers of variables. What I forgot was that computer science uses discrete mathematics. Calculus is the mathematics of continuous systems! So while what I had just learned was very handy for mechanical engineers and physicists, it was useless to me.
Combinatorics does not come as often as the college classes make it out to be. It just has the habit of occuring just when you do not expect it. Mostly I run into it when I am employing some Bayesian learning algorithm. Geometry and graph theory are the math fields I will run into most often. Graph theory is used essentially everywhere. It is the ultimate generalization of all data structures. Most reinforcement learning algorithms require a substantial knowledge of graphs. Neural networks is all about fancy graphs. The things are everywhere.
Geometry I run into a lot due to working on projects that interface with the world. The programs in your cellphone need to some heavy duty triangulation to figure based on the locations and distances of various cellular towers where the hell you are. Geometry is the only thing that will help in that class of problems. This includes such headaches like what area does a collection of cellular towers provide coverage for. Also this is not the geometry you are taught in grammar school. This geometry will use trigonometry, and it will employ a set of procedures so repetitive that you will memorize the C function that does it, convex hull I am looking at you.
Dealing with those fields of mathematics has been annoying but acceptable. Lately, I have been running into a lot of projects that require heavy use of number theory. Number theory is the stuff of higher mathematics classes. The is the stuff of 300 and 400 level math undergraduate math courses. Saying "number theory is a strange subfield of mathematics" is about as tautological as saying circles are round. Alice in Wonderland was written by a logician that studied number theory. I do not want to get near this thing. Mathematics has given me such sharp and powerful tools. Understanding the concepts undelying my problem requires the most twisted tools in the box.
So I downloaded some pdfs and started reading. The notation alone almost overtook me. The structures they introduce are so specific and exact. They are constrained in the exactly the ways the object I am going to work with will be. This thought is comforting since most people will not have an immediate use for this stuff. I am digging since I know I need to use it. I read through a few chapters and did some exercises for myself. Then the nightmares started.
The nightmares mostly consist of me inside of these structures, and I can not get out of them. I am not assaulted with the notation and barrages of equations. It is not that the equations themselves that scratches at my face. As they fly by I try to read them and understand what they mean. Unfortunately, due to the biological natures of dreams/nightmares I can not. The frustration hurts me physically in this nightmare. That is the most generalized I can make it. They really differ otherwise. With my luck, tonight I will be murdered by an n-element ordered set.
posted by James Ridley at 12:08 AM
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