Saturday, March 29, 2014

"Nature of Math"-- Mathematics is a language the world speaks that humans can understand

           Throughout the semester we have studied numerous mathematicians in MTH 495. We have learned about mathematicians from ancient Greece to China, and have been led through the centuries by great mathematical discoveries. As we learned about these great thinkers, it struck me how much “math” encompasses, and the contrast of this vastness to the small scope the term evokes in the minds of most people today.
            By nature, humans want to understand the world around them. Mathematics is a language the world speaks that humans can understand. Math is the tool that humans use to investigate the nature of the world, though it is rarely taught as so in today’s Western society.
            To many people today, math is seen as numbers, a calculator, and equations. It is seen as a requirement, a monotonous lecture, and as an overrated skill. Math has been parsed off from what it initially was, and, in a sense, what we consider “math” today is more confined that it ever has been.
            Archimedes was a mathematician. He was also a physicist, an engineer, an inventor, and an astronomer. Omar Khayyam was a mathematician, a philosopher, an astronomer, and a poet. Brahmagupta is considered a mathematician and an astronomer, but his texts were composed in elliptic verse, which shows a poetic intellect in the man as well. Rene Descartes was a mathematician, a great philosopher, and a writer. These great men are considered mathematicians, and in that overarching term lay discoveries in optics (Decartes), weaponry (Archimedes), a calendar that is more accurate than the one used today (Omar Khayyam), hydrostatics (Archimedes), and so much more.
            In their day, what were the labels put on these men? Were they identified as contributing to each of the disciplines mentioned above, were all of their discoveries considered mathematical discoveries, or were there few labels used at all? Why do we limit math as it is today, so early on? In grade school and even high school, math is taught separate from astronomy. Separate from the other sciences as well, in most cases. Math might be brought up in a physics class, but rarely is it explained why the formulas work the way they do, why we can put numbers and equations to a natural phenomenon. Perhaps more tragically, in high school I can’t remember more than a handful of times in a math class where any other discipline was brought up to help me understand and appreciate why I was learning what was taught. Students lose interest in math without even gaining the slightest understanding of its importance in the world.
             All of the men I mentioned were mathematicians, but they were also big thinkers who wanted to understand the world. They did this through math, but also though philosophy, physics, and astronomy. These disciplines are ones that frequently come to people’s minds when the question of “What discipline seeks to understand the world, and human’s place in it?” It is a tragedy that math, the foundation of physics and astronomy, and a sister to philosophy, would rarely be unveiled as an answer to many today.

Mathematics is the queen of sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank.”-Carl Friedrich Gauss

Thursday, March 20, 2014

"Doing Math": Biz's Bracketology

I will preface this post by saying that the last time I watched a basketball game for more than ten minutes was when I was 11, with my grandma. I have never been interested in basketball (my family is of short, Polish stock), and have only the faintest idea of what March Madness is. But, I have a competitive nature, and I love applying my math and stats skills and my intuition. So, this year I decided to jump on the bracket bandwagon.
            To determine my bracket I used various sources:
·         FiveThirtyEight’s NCAA Tournament Predictions (accessible at
I relied heavily on this tool, more so than seed, because of the breadth that it covers (from the pre-season rankings, various professionals’ estimates, the power rankings, player injuries, and geography, among many other factors).
·         The Washington Post’s list that contains the number of upsets per round each year (accessible at
This helped me determine how many upsets I should include in my bracket. Some upsets were already statistically determined by FiveThirtyEight’s tool, but others I decided for myself.
·         The tournament results from the past five years
·         Seed
·         My own (slight) biases
Mostly based on living in Michigan, my love for Oregon, and the graduate schools I applied to.
From the past five years I noticed that, usually, around one team from the previous year’s Final Four makes it to the current year’s Final Four. In three out of the last five instances, that team won. In the following table, the underlined teams were in the Final Four the year before:
1 North Carolina (won)
1 Duke (won)
3 Connecticut (won)
1 Kentucky (won)
1 Louisville (won)
2 Michigan State
5 Michigan State
11 Virginia Commonwealth
4 Louisville
4 Michigan
1 Connecticut
5 Butler
8 Butler
2 Ohio State
4 Syracuse
3 Villanova
2 West Virginia
4 Kentucky
2 Kansas
9 Wichita State

This year Louisville, Michigan, and Wichita State are all in the same region, so only one of them can go to the Final Four. Louisville has, from what I’ve read, been mis-seeded because of their easy schedule during the year, and according to FiveThirtyEight they have a 38% chance at getting to the Final Four (against Wichita State and Michigan’s 14%), so I decided to include them. I have Ohio State beating Syracuse in the second round as one of my second round upsets, thus they can’t make it to the Final Four.
            Additionally, as you can see from the table, each time a team has shown up at the Final Four in two consecutive years, it does as well or better than the second year than the first. Thus, although Michigan State and Louisville are seeded the same, and Michigan State does have Tom Izzo, I decided to have Louisville going to the Semi-finals (also, on FiveThirtyEight it shows that Louisville has a much better chance at going to the Semi-finals than State).
            That is as far as I took the insights that I gained from the last fine year’s Final Four history—instead, I took into account Florida’s place as a #1 seed as well as the fact that no team has won the title two years in a row since the 1980s, and gave Louisville a respectable home in second place.
            I used the number of upsets per round over the past few years to guide the number of upsets I would have per round.
Number of upsets
            Since 2009, the number of upsets in round 1 has been 10 four times and 7 once. When FiveThirtyEight projected that a lower seed would beat a higher seed, I would put that in as one of my upsets. My biases accounted for my putting NC State (12) beating Saint Louis (5), even though FiveThirtyEight projects otherwise (I’ll be attending NC State in the fall to obtain a masters in Data Analytics), Harvard ahead of Cincinnati (Harvard has done well the past few years, I looked into applying at Harvard’s statistics program, and FiveThirtyEight has Harvard winning a 42% chance and Cincinnati a 58%--relatively close), George Washington beating Memphis (FTE estimates 55/45 Memphis—but I applied to GW’s Data Analytics program and was accepted), and Stanford over New Mexico (Stanford’s stats program is ranked #1 in the US).
            The number of upsets in round 2 has been between 1 and 6 over the past five years, though mostly the number of upsets is in the higher range. I chose Ohio State over Syracuse almost arbitrarily, but more because I’ve heard of Ohio State and I haven’t heard much about Syracuse. Also, I needed an upset, and FTE estimated that Ohio State has a 40% chance of winning that round verses Syracuse’s 50%--not too much of a difference. So, Ohio State is my upset for this round. Oregon is my other upset, mostly because my family bought a house there this year. I visited Oregon over winter break with my family, and fell in love. I don’t have high hopes for them, but I thought that maybe I could send enough positive vibes their way for them to beat number 2-seeded Wisconsin.
            In round 3 I have a few more upsets than I normally would like—I have three, while the range over the past five years has been between 2 and 3, with the mode being 2. I already explained why I think Louisville will go to the finals—they are one of my upsets. FTE accounted for my putting Duke to beat Michigan, and my home-state bias (as well as Izzo) helped me choose Michigan State as beating Virginia.
            For the Final Four game I have 1 upset—the only time there has been an upset in the last 5 years was in 2009. But I see Louisville as a strong team, and FTE has them at a 1% chance of getting to the finals over Arizona, so I chose to have them beating Arizona.   

            Overall, I have enjoyed making my bracket. I have never thought of myself as wanting to go into sports statistics, but now I can see how people are drawn to it. I can definitely see myself getting into watching sports more often if I view the opportunity as a competition or for me to use my statistical abilities.