## Posts Tagged 'topology'

### Patterns of Flocks of Starlings Mathematically Behave How Magnets Would Move

Starlings, a small to medium-sized passerine bird in the family Sturnidae, achieve extraordinary coordination in flight and they behave mathematically as metals being magnetized. A new study published its findings in the journal Proceedings of the National Academy of Sciences.

### Differentiable Manifolds

Morin surface as a sphere, via Wikipedia

I

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!

### 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.

### Depanning and Charging Math

Two of my classes this semester include specific periods where graduate students come to answer questions about the exercises we have to complete. We call these classes a charge or a dépannage. This semester, both of these guys aren’t very good. The department decided to give these teaching hours to new graduate students, who don’t really have any idea on how to teach. Last year, I had two really great students who were great in class. This semester, it’s pretty paltry. The reason is that the department wanted to give these new students a chance, even though the professors had requested specific students, which would have been really good.

Thankfully, the student for Analysis III (metric spaces, compact spaces, topology, etc) is still decent. We shall call him S. Even though S is hard to understand, he does explain the problems and is willing to help us out. Since my linguistic ability is quite adaptable, I have no problems understanding him. He seems to have a good grasp of the subject matter and I actually enjoy going to those classes. By far, Analysis III is my favorite math class. It’s probably the class that I like the most out of all of the classes I’ve ever taken. I dream of Analysis, of open boules and series that converge towards their limits and are excluded from these boules.

Our other graduate student is a bit of a joke. Nope, that’s probably saying too much. We shall refer to him as Y. Y isn’t that bad, but out of 17 students, 3 elected to stay for this period. Then again, the same number stayed for the other period with the other student, but the quality definitely went down.

Still, it’s possible to learn. The one thing is that he makes a lot of mistakes on the black board on stuff that he’s supposed to get right, which is kind of annoying. Strangely enough, I did manage to learn something. Elo learned something as well, even though the graduate student frustrated her.

### Le Système Est Lent

I’ve heard this sentence repeated over and over to me. Basically, it implies that the network is slow to respond to queries.

Well.

School has started.

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