Published September 20, 2011
education , mathematics
Tags: commutative ring theory, differential geometry, education, fall 2011, geometric analysis, graduate school, homological algebra, mathematics, metric spaces, NTNU
Gradient Flows by Luigi Ambrosio
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.
Continue reading ‘First Week of the Fall Term 2011 – Mathematics Graduate School’
Atiyah's Introduction to Commutative Algebra
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.
Continue reading ‘Graduate Student Lectures: Great Learning Opportunities But You’ll Need Preparation’
Atiyah's Introduction to Commutative Algebra
This year, the graduate class format changed dramatically for me. I went from a normal class, filled with students, to classes with at the most 4 students and a professor. Actually, my Complex Analysis II class has only another student enrolled. As such, the format has changed. The professors no longer give 3h-lectures, the students do, each in turn.
Basically, each graduate student will prepare a 3h-lecture¹. In one class, that means that I lecture every 4 weeks. In another, it’s every other week². Preparing the lecture involves going over the textbook and the proofs. Depending on how detailed the proofs are, you’ll need to flesh them out further, and make them understandable, citing the right theorems, propositions, etc. Depending on what book/resources you are using, this might take quite a few hours. It also depends on the overall complexity of the class and the overall sparseness of the authors of the book. Atiyah’s books is very sparse. The proofs are sometimes quite short and they need to be expanded significantly.
Continue reading ‘Mathematics Graduate Class Lecture Format’
It’s good to be back at school. I missed most of last week because I was teaching 30 hours. I didn’t miss much³, but I felt terrible. In the future, I won’t want to miss any school at all. My classmates were actually worried about me, which was kind of nice.
I ran some errands.
Continue reading ‘Back At School’
Great article I found thanks to Andrew. It’s by Danah Boyd on the importance of choosing the right grad school. I know about this and it’s important to choose the right school and the right adviser.
Published October 22, 2009
cycling , education , mathematics
Tags: Algebra, Analysis, azumaya algebra, bicycle, calculus, clifford algebra, cycling, differential manifold, graduate school, graduate studies, holomorphic analysis, mathematics, riemann surfaces, topology, velocite
Morin surface as a sphere, via Wikipedia
Things got abstract very quickly in complex analysis. We are constructing differentiable manifolds in the complex plane, to see the topology of holomorphic domains. It blends together quite a few algebraic notions, as well as some beautiful topology, and it’s extremely interesting. The prof told us that this would fit neatly into a Riemann manifold or Riemann surfaces class.
Why is this so interesting? It explains exactly why derivatives and integrals actually work in the complex plane. Well, that’s not really true. It’s more than that. Applying calculus to complex functions is certainly richer than for real functions. We delve into the differential k-forms and their construction⁷. It’s quite elegant, I have to say. Some of my classmates were a bit dismayed by the abstract nature of this week’s lectures, but it had my full attention⁴.
I also noticed that we started using Berenstein & Gay’s book, Complex Variables¹. We’re about 5 weeks into the semester and we are on page 10 or so⁵. The level of difficulty in this class just went up a notch. Also, the level of complexity went up. That’s why they call it complex analysis!
Continue reading ‘Differentiable Manifolds’