Tag: Algebra

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

Giving Lectures & Presentations in Graduate Classes (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…

Categorically Yours & Typographical Musings†
I 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…

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…

Mathematical Algebraic Structures
I I’ve spent about 45 hours on my algebra homework. I still have another 27 problems to finish¹. Naturally, they get harder as you go along. Kind of annoying. I like writing easier ones first and then moving to harder ones a bit later. I like this to happen in each problem set. For some…

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…

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 Linuxbased derivative. I’ve been going to a class where the professor solely relies on using Powerpoint presentations.…

Moleskines and Graduate Texts
I had to get another Moleskine for my Modern Algebra class. I just received the textbook, appropriately called Algebra [Hungerford, Springer Verlag, vol 73], and needed to get back to class quickly. I spent an obscene amount of time waiting at the ESlite at Gongguan to get served. I wanted to get a red Moleskine…