A new claim could imply that a proof of one of the most important conjectures in number theory has been solved, which would be an astounding achievement. Mathematician Shinichi Mochizuki of Kyoto University in Japan has released a 500-page proof of the abc conjecture that proposes a relationship between whole numbers (related to the Diophantine equations).
Many coin collectors start their numismatic collections with pennies, and trying to get pennies from every year within a given range. This process, while seemingly daunting, is straightforward and will take about 684 pennies to find all of the pennies from 1959 to 1997, since they are still in circulation.
Students tend to take far from optimal ways to assimilate information, especially when it comes to exams. Scientists Tim Novikoff, Jon Kleinbert, and Steve Strogatz decided to take a mathematical approach to the way that students learn, in order to find the most effective way to succeed.
While most people think that ZIP codes were originally created randomly, there is actually an order to the US mail system. Since it turns out that it has a branching structure, it implies that it has a fractal dimension. Samuel Arbesman of Wired’s Social Dimension used the ZIPScribbles images created by Robert Kosara to calculate the fractal dimension of the US ZIP code system.
While you might just need a pencil and your brain to fill in this week’s Sudoku puzzle, an Irish mathematician used millions of hours of supercomputing time in order to solve an important open problem in the mathematics of Sudoku; the game that was initially popularized in Japan and involves filling up a 9×9 grid with the numbers 1 to 9 according to certain rules.
It’s the second week of school, but with a bank holiday last Monday (09/12/11), graduate school started up slowly. It will take until next week until everyone is finally registered to all of their classes. It took me a while to do so as well, because they changed up the system from a program that you installed on your computer to an online version. The online version is better, but you need to know where to go. I finally registered to my classes last Tuesday. I have three this semester:
Topics in Geometric Analysis: This class is with my thesis advisor and we will be exploring gradient flows in metric spaces. We will be using Luigi Ambrosio’s book of the same title. It promises to be an interesting class. Although, it’s not exactly what I’d like to do in my thesis, it’s getting there. I’d like more measure theory, but luckily, my advisor is doing research in the field. There are six students in the class, but only 4 were registered on Monday. I don’t know if the other two will be registering, my guess is yes. Two of my classmates are the other graduate students of my advisor. We are all going to a workshop in Hsinchu in Differential Geometry on Saturday. Since I work most Saturdays, it’s not really a problem getting up. It will be a break from the norm, and I have a keen interest in Differential Geometry.
I had some excess photos this week, so I’m posting them here. It was good week, somewhat busy and wet, as usual. Next week is the last week of school, but I’m immediately starting a paid math research project with my advisor, which is kind of cool. We’ll be exploring Sobolev spaces and the elasticity of some equations, numerically modeled in MATLAB.
One of the main things that graduate students need to cope with in the sciences is giving lectures. For some, they give lectures to undergrads. Others give lectures in their classes. In my case, since I am not fluent in Mandarin, I can’t serve as TA, which is what most of my classmates have to do. However, in both of my classes, we have to give lectures. This is very different from giving a 30 min to 1h presentation. Students have to assimilate new subject matter and present it to the class, while the prof is watching. In both of my classes⁴, there aren’t that many students³.
This can be quite challenging because you need to prepare fully before you give a 3h lecture. While you give the lecture, the prof will ask you questions about the new topics and proofs, to see if you have understood it. He/She will ask to see if the other students have understood as well. In my case, in my Commutative Algebra class, most, if not all, of the explanations are in Mandarin, but I usually get what’s being explained since I tend to prepare the topics even when I don’t have to give the lecture.