Archive for the 'mathematics' Category



Nick Werle on Asimov and Psychohistory

I’ve always imagined that pyshohistory might be achievable at some point in time, since I’m a mathematician and a lover of science-fiction. Foundation as always been a favorite of mine and I’ve read it countless times. Nick Werle compares it to macroeconomics of a certain kind.

June 13 to 19 2011

Beginning of clear days

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.

Continue reading ‘June 13 to 19 2011′

Graduate Student Lectures: Great Learning Opportunities But You’ll Need Preparation

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’

Doing A Graduate Degree In Taiwan

NTNU Main building on Heping Dong Rd.

I just read Fili’s most recent post about his stint at a Taiwanese university (I couldn’t tell which from the post). Having been an international student at NTNU, in the graduate program of Mathematics since ’09, I have different things to report. Granted, I am studying in sciences at the graduate level, so the classes are ultimately very small. I have 4 students in one class and 2 in another.

Still, there are some important points to remember when you think about doing a graduate program in Taiwan.

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Mathematics Graduate Class Lecture Format

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.

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Algebra and Scaffolding

Giving Lectures & Presentations in Graduate Classes (Commutative Algebra)†

Introduction to Commutative Algebra

Last Thursday, I gave my first lecture in a graduate  class of mathematics. There were three other students in that class, and the professor. All of the students were graduate students in Algebra. I was the sole person in Analysis. At first, this intimate setting was pretty daunting. I hadn’t taken the class last semester and the prof obviously didn’t like me being part of it¹.

Continue reading ‘Giving Lectures & Presentations in Graduate Classes (Commutative Algebra)†’


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ranjitwithkinginbehand.jpgI'm Range, your host. On the menu, photos, art, stories, entertainment and reviews. Links, maths, education and social issues. I'm in Quebec (Canada) or Taiwan (R.O.C.). Follow me on Twitter.

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