Archive for the 'education' Category



The PhD Illustrated

I found infographic very entertaining. It’s what a PhD is.

My New Daily Routine

Usual art supply suspects: Tombow ABT, Sakura Pigma

For the month of July, my daily routine wasn’t that filled up. I still worked about 8 hours a day, but it was nothing to write home about. Now, for the month of August and probably for the rest of the year, I’ll be following this routine, which includes 35 hours/week of teaching, 10-15 hours/week on writing, 10-20 hours/week on my business, Asterisk*Cycles.

The trick in surviving grueling routines and long days are power naps as well as little pockets of goodness, which are easily wasted if you aren’t careful.

Continue reading ‘My New Daily Routine’

The Girl Who Conned The Ivy League

I expected more from this article, but it was still interesting. Still, I don’t believe that Esther Reed deserved to get 51 months in jail + a $125,000 fine. She’s obviously got some psychiatric issues that she needs to take care off. That doesn’t mean that I approve of identity theft.

The Worst Swearword In the World

Jon Ronson and his 8-year old son on the worst swear word in the English language, and it’s pretty funny. Limone!

I also like the sanitized swear words such as: dang it, fudge, son of a gun.

Back At School

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.

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Paracompact Spaces

Toroid, via Wikivisual

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It’s strange that I was actually researching paracompact topological spaces on Sunday and that we are seeing those types of spaces in my complex analysis class. We just started the Berenstein & Gay Complex Variables¹ book and things are pretty interesting. I actually deduced that we were heading there because of some of the concepts that we are seeing.

A paracompact space is a topological space in which every open cover admits an open locally finite refinement.

Continue reading ‘Paracompact Spaces’

Germs & Sheaves

Hyperbolic triangle, via Wikipedia

Hyperbolic triangle, via Wikipedia

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I spent most of the day reading up on differentiable manifolds, Riemann surfaces, germs, and sheaves. Some of the concepts are extremely interesting since they tie into category theory. This led me to differential geometry. I supposed that differential geometry had more to do with Euclidean geometry, an undergrad class that I didn’t enjoy all that much³, but it’s got a lot more to do with the geometry and structure of differentiable manifolds, which interest me¹.

Since the late nineteenth century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable manifolds.

The study of calculus on differentiable manifolds is known as differential geometry.

Continue reading ‘Germs & Sheaves’

Categorically Yours & Typographical Musings†

Okamis Lamy fountain pens

Okami's Lamy fountain pens

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One of the marks of being a good prof is when they see that students didn’t understand something and go over it again. My algebra prof has made a habit of this, especially when he goes over stuff in class too quickly. This happened last week and left me quite furious. Someone must have mentioned something to the prof², and he went over what we saw in the last hour again. This took an hour out of the three-hour class. I appreciated. I realized that there were some undergrads in our class, who weren’t familiar with some of the more abstract concepts of category theory³. It was an issue. Class was great today. I was drinking my strong milk tea and noting stuff down. We saw direct sums and (co)universal objects. Having proofs done with commutative diagrams is so elegant and simple.

Continue reading ‘Categorically Yours & Typographical Musings†’

Differentiable Manifolds

Morin surface as a sphere, via wikipedia

Morin surface as a sphere, via Wikipedia

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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’

Mathematical Teaching Methods

Snake Lemma, via Wikipedia

Snake Lemma, via Wikipedia

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It seems to me quite logical on how math classes should proceed. The professor presents some theory, with theorems and their demonstration, as well as definitions and propositions, before venturing into a slew of examples. For some reason, this is completely absent from my classes in Taiwan. The examples. I don’t know what these profs are thinking, but examples are paramount for students to understand some of the theory. OK, my complex analysis prof is good. he gives examples and answers questions well¹.

Continue reading ‘Mathematical Teaching Methods’


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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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