Mathematical Teaching Methods

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.

Parachute Kids

Parachute kids are Asian-born international students who have come to the United States to study unaccompanied by their parents. Usually, they will stay with a family member, like an aunt or grandparent. But sometimes, the parents hire someone to act as their guardian.

Children of rich Asian families sent to live in U.S. suburbs known for good schools and safe streets. Typically, mothers try to split their time between their husbands in Asia and their children in America, often leaving housekeepers in their stead. Parents may feel guilty about spending too little time with their kids and shower them with money and gifts, says May To, executive director of the Asian Youth Center, which has dealt with parachute kids.

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This is quite common in Taiwan. I’ve known quite a few parachute kids that were getting some intensive ESL tutoring in order to be able to speak well in the US or Canada. Typically, a lot of Taiwanese pursue graduate degrees in the US as well, after completing their undergraduate degree in Taiwan. Parents will save for years to make this possible.

While this can be seen as a great opportunity, it can also be trouble for the children that won’t be supervised as assiduously as by their own parents. In some cases, the kids will live alone in apartments paid for by their parents without any supervision. It can also leave them vulnerable to kidnapping, much more than if they were living with their parents.

Researching Trends

Clifford algebra representation

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I met a very helpful second or third-year grad student¹ that really helped me out with finding interesting research assistant positions. There are two for which I will be applying for. One will be for next semester, and the other one will be for next year, running for a whole year from July 2010 to July 2011². There was no way that I would have been able to apply for these this year. Still, it’s going to be interesting. That only leaves me to check out all of the profs with grants at my university to see if they need a RA for this semester. I think that it will most likely in PDEs since NTNU received some major funding on two large PDE projects.

One of my colleagues is an SAT tutor to some senior high school kids. This is paid quite well, something around 3 times what a usual foreign ESL teacher makes in Taiwan³. I’m going to see if I can teach something similar. It would be different from teaching English. The good thing is that I have taught math before, as well as science. What’s really interesting is that I wouldn’t have to work that many hours. I doubt that many hours are available anyway. Two hours would be the same as 6 hours of ESL teaching.

More Math Graduate School Advice

Another post on advice about graduate school. Good and sound advice from Berkeley graduate Noah Snyder.

Rainy Mathematical Days

Lamy Safari fountain pens²

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The rain has finally abated. I love the rain in Canada, but I hate it here. Why? You just get wet all the time. You get wet when you get on the scooter, when you drive around, and when you get off. Rain gear does wonders, but it’s annoying to have to carry it around and wait for it to dry. Also, driving in the rain is a lot more dangerous. I tend to be really careful.

Temperatures have cooled down significantly. It’s no longer 30C, but only 24C³. It’s getting a bit chilly when riding on the scooter. I’ll need to take a scarf.

Using Powerpoint Presentations In Classrooms

My wife teaches university students and she really enjoys using Powerpoint presentations in class³. Most lectures by visiting scholars, as well as research, is usually presented with some kind of presentation. In the math world, it’s usually some Linux-based derivative.

I’ve been going to a class where the professor solely relies on using Powerpoint presentations. I have come to hate them. The reason is that the professor doesn’t understand how much time it takes for students to note down what they see on the slides. Sure, the presentation is made available later on the web, but I like taking notes. That’s how my learning process works. I know that most students work in similar fashion.

The professor shows a theorem, barely explaining it and the rushes through a demonstration. I haven’t even finished noting down the theorem when he’s already midway through the demo. It’s very annoying. The other extremely annoying fact is that the demos, or parts of them, vanish because animation is used in the Powerpoint. Extremely frustrating⁵.

Non-Riemannian Integration

Paul Halmos' Measure Theory from Springer

We started seeing the Riemann-Stieltjes integral today as well as a reminder on rectifiable curves¹. We didn’t see much⁴, but it made me interested in other forms of measure. Appropriately, I bought Halmos’ Measure Theory [vol 18, Springer-Verlag] for $6.18 last week. It’s going to be useful. It was a good idea to spend some money on reference books.

I’m still kind of surprised at the amount of books that I got for $120². Today, my classmates organized a photocopying session. By this, I mean that they will organize to have Measure and Integral by Wheeden photocopied and bound for everyone who wants it. I hopped on the photocopying bandwagon, as this book costs about $70 new³. I can always order it if I like it. It seems that the real analysis professor is basing his course on that book.

I read up on the Daniell integral, Lebesgue integral. I came across this in Henri Lebesgue’s biography on Wikipedia.

Lebesgue integration has the beautiful property that every bounded function defined over a bounded interval with a Riemann integral also has a Lebesgue integral, and for those functions the two integrals agree. But there are many functions with a Lebesgue integral that have no Riemann integral.

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Using Moleskines As Class Notebooks

A3 Moleskines vs standard size

Honestly, it has been my plan to do so since last week, but the price of it all didn’t hit home until I was going around trying to find some Moleskines at ESLite.

After asking around to see what was available, I finally bought a Plain Soft Notebook – Extra Large (19×25cm), which is almost 8.5×11″, standard school sized paper. I was going to buy one for each class, but they are just so expensive here, about twice the price in the US. I think I’ll get them online. There’s no point in wasting that much money on these. I’ll try looking around to see if I can buy them cheaper, but I doubt it. Actually, you can get one like that for $13 on Amazon. The list price is $20. I paid $25.

Update: I just started using the Folio A4 Plain Notebook and it’s a joy to use. No bleeding from fountain pens or ink, the 100 g/m2 really makes a difference. The Plain Soft Notebook’s paper is noticeably of a lesser quality. The price difference easily justifies the purchase of the A4 Folio instead. The Folio A4 Sketchbook has got 160 g/m2 and the Folio A4 Watercolor has got 200 g/m2. The last two have noticeably less pages, 96 and 60 respectively, whereas the plain notebook has 176.⁴

Failing At Buying Class Books

I tried and failed at trying to get Complex Variables by Berenstein & Gay in Springer Verlag today. I didn’t really know where to go and none of the places I went to had any books. I should have just gone back to the one that my classmate showed me.

I checked online and the original hardcover of this book retails for about $100. I wonder how much it will cost here. I’ve learned that counter fitting is rife in the universities, as students are pretty poor. They can’t pay for books. Usually, they will borrow the book from a library, drop it off at a copy shop and have them copy it as well as bind it. The results are good but I prefer buying originals, as I see these books as reference for later things.

The other side of this is that there are actually real looking counterfeit books that are available here. They have been printed here and are extremely cheap. I paid $13 for Principles of Mathematical Analysis by Walter Rudin. It’s a counterfeit book, but looks pretty good. I don’t mind that. The other was is actually an original from Springer Verlag. It’s Topology by Klaus Jänich. I paid $22 for this one.

The bad part was that none of those books were actually class books. Oh well, I was looking for Measure and Integral by Wheeden and Zygmund and Real and Complex Analysis by Rudin.

While I was at ESLite, I saw Dan Brown’s latest book, The Lost Symbol. At the last moment, before leaving the library, I bought it. It was only $20. I almost bought Day Watch by Sergey Lukyanenko and Vladimir Vasilyev. I saw Twilight Watch right beside it, but then I decided that I still had to read Night Watch again before starting out on those books.

I also struck out on getting Kafka on the Shore by Murakami and more Palahniuk novels. I could spend hours in book stores and art supply stores.

For some reason, I escaped the rain. I have been using my scooter as a locker. It’s much more convenient to put my motorcycle jacket in my scooter. However, it’s already packed to the rafters with my rain gear, that I absolutely need, and an umbrella. I’ve gotten tired of always getting wet. Strangely enough, if I compact it enough, the jacket fits in pretty snugly into the compartment.

Graduate Trash and First Impressions

Apparently, a few months ago, there was trash all over the graduate student area at NTNU. It was so bad that the professors and staff talked about how to clean up your own trash for about 20 minutes today. It was kind of funny. Charlotte told me that most graduate students are babied and really don’t know what is going on. She told me that a student had left her with actual mice because of teh amount of trash that she had left there without cleaning up.

I also learned that I have a sort of office. It’s a communal office that I share with other students. This means that I can easily stash my bike there. That’s a relief. Charlotte told me that they have a lot of free space on the 4th floor. That made me want to request other office space, but I won’t. I don’t mind being around other students, it’s going to be fun.

The staff and older PhD students are all very nice, as well as the new students who aren’t too shy. Shida specializes in the education of mathematics and the history of math. Those aren’t my areas of interest, but I’ve been told that I’ll have an easier time studying there than at NTU.

The big thing are the qualifying exams that everyone has to sit in order to get into PhD programs in US universities. Charlotte is taking hers in about a month. I will take them next year in May. There is a chance that if I do well in those exams, I could get a “passage au doctorat”, which means that I’d get a M.Sc and PhD instead of just a PhD by just doing about 3 years. That’s pretty exciting, but that means that this year, it will get intense.

There are quite a few interesting classes. Above all, it’s Real Analysis and Complex Analysis that I will focus on, as Functional Analysis isn’t taught this year. I’ll have to take a Modern Algebra class as well in order to prepare fully for the exams. All the professors that I’ve talked with assured me that this should be my goal. This will make admission into a US university easier as well.

In more mundane tasks, I’ve secured a locker for myself as well. They have given me the access card and I still have one paper to fill in for them.

My wife ended up doing a lot of extra work for professors. This is totally of on top of what she has to do with her classes. It drains a lot of her time. I was curious to find out if this was the same in math. Charlotte assures me that this isn’t the case. She has been studying for her PhD for two years and she never does anything extra. Well she does, but it’s usually small things.

I’m really happy that I’ll be studying there with Charlotte nearby. She’s French and I love the fact that I can speak French with her all the time. I’ve only met a few French-speakers in Taiwan and I’ve never really been in contact with them for long amounts of time.

BTW, Charlotte is studying Mathematical Education and she is translating Sanskrit math problems into English.