Math

I just now realized how simple math really is at its lowest level.  If you are familiar with sets and functions, and have a decent grasp on logic, then you understand almost all of math(nice job!).  Of course the most fundamental assumptions have been built upon for thousands of years and, as a result, some of the latest constructions are quite complex.  Creating a model and applying the results to real problems is not always easy either.  Still, math can be boiled down to an amazingly simple foundation, and its truly a marvel that it can tell us anything useful about what's going on in this universe.

Project Euler

Last week I was shown a website, http://projecteuler.net, that offers a long list of math problems and challenges the reader to develop an efficient algorithm, which should be able to find the solution in a minute or less. So far, I've gone through the first ten problems and found that they could all be solved with a basic knowledge of algebra and number theory, particularly prime factorization.  A few didn't even require writing an algorithm and were readily solved with a calculator and some scratch paper!  However, a quick glance at the last problems (there are nearly 400 problems total) shows that there are some very challenging problems ahead.  In fact, the first problem has been solved by over 200,000 users while the last problem has been solved by just over 100.

This seems like good way to get practice in various areas of math as well as algorithm design.  So, I plan on working through these as time allows and will post descriptions of my solutions to any problems I find especially interesting.

Introduction

Thanks for stopping by!  I'm a graduate student in operations research(O.R.) with a background in mathematics, computer science, actuarial science, and physics.  This is the place where I'll be posting my random thoughts and updates.

Don't worry if you aren't familiar with operations research!  The field doesn't have great name recognition, especially here in the Midwest.  This is partly because O.R. is very interdisciplinary by nature.  Some universities have their O.R. programs in the industrial engineering department; while other schools put O.R. in the math or business departments.  Adding to the confusion is the fact that O.R. is known colloquially by any number of terms.  Some popular synonyms are 'management science,' 'decision science,' and 'analytics.'

To help cut through the confusion, here is my simplistic one-sentence definition of Operations Research:
An applied branch of mathematics which aims to improve decision-making through the analysis and optimization of systems constrained by at least one resource.

For a more complete description, here is a link to an informational website run by The Institute for Operations Research and the Management Sciences:  http://www.scienceofbetter.org/what/index.htm