Tag: Analysis

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

Algebra and Scaffolding
I like to say that algebra is the scaffolding that lets us do calculus in different structures. — range (@djrange) March 31, 2011

Great Lost Finale Coverage
I’ve been reading some great coverage on the Lost finale. Since I watched it yesterday, I can now read up on it. First and foremost is the great article over at Wired. The article has a bit of everything, but none of the answers that we’re looking for. Today, I was intrigued by this article…

Differentiable Manifolds
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…

Measure Theory and Disposable Teachers
I I’ve been working hard this week at learning more about measure theory. It’s a really interesting research subject and there are quite a few things that I didn’t know about it. In class, we are currently seeing the Lebesgue measure and topics. I’ve read up on the Borel, Haar, Radon, and Daniell measures. I’ve…

Rainy Mathematical Days
I 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…

GTM Hungerford’s Algebra vol 73†
For some reason, our Algebra prof gave us 40 problems to solve. They are all in the first chapter and review comprehensively what I’ve learned in past algebra and algebraic structures classes. Still, 40 exercises, that’s a lot. Seeing as Hungerford’s book is pretty much a reference for graduate students in algebra, I was looking…

More Cheap Graduate Texts
So I went back to the book store³ and went through all of their books⁴. I couldn’t order Measure and Integral by Wheeden because it was just too expensive for my taste. Instead, I bought Principles of Real Analysis by Charalambos Aliprantis. I paid $30 for the hardcover 3rd edition, which is out of print…

Compactification and Metrisation
Some great notes from Dr. Terence Tao’s lecture on compacity and metric spaces. Metric spaces are sets with a measure of distance between each of its elements. Compact spaces are spaces in which each sequence (xn) admits a converging subsequence. This is called the BolzanoWeierstrass property and such compact spaces are called sequencially compact. There…