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 Posted: Fri Apr 04, 2008 8:46 am
Ah, I see. The class I dropped was all on abstract measure and integration theory and stuff like that. I felt like I understood the material, but the problems were just so hard, I couldn't get my head around them.
On an unrelated note, I saw a kewl talk yesterday. It was on "Cohomological hierarchy in a space of weakly invariant Lagrangians of classical mechanics." I didn't understand a lot of the technical stuff, but the main thrust of it was:
If you have a Lagrangian that is weakly invariant under some Lie algebra G, then you can get nice spectral sequences of the cochain groups related to the manifold the Lagrangian acts on. Lots of neat physical effects, spec. Noether charge, Dirac monopoles, and the Aharonov-Bohm effect, relate to nontrivial elements in the various homology groups.
Damn, I need to find more stuff on mathematical physics...
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Posted: Fri Apr 04, 2008 10:09 pm
Last Tuesday in my "Real Analysis" class, we derived the existence of covalent bonds from the Spectral Theorem and Schodinger's equation. Next week, we're going to derive something about particle scattering, probably basic gas dynamics or something.
Mathematical physics is hilarious, because so much of it is just "so, this deep, fundamental result in physics is just kind of a footnote application of this mathematical theorem."
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Posted: Sat Apr 05, 2008 9:43 am
Why is Mathematica so SPENSIVE!?!
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Posted: Sat Apr 05, 2008 4:41 pm
Morberticus Why is Mathematica so SPENSIVE!?! I have no freaking clue. I was pissed 'cos if you bought a laptop through the school (none of which I particularly liked) the year *after* I got a new laptop, it came with Mathematica. Layra: That sounds pretty awesome. But how in the world did you come across that in class?
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Posted: Sun Apr 06, 2008 1:48 pm
Swordmaster Dragon Morberticus Why is Mathematica so SPENSIVE!?! I have no freaking clue. I was pissed 'cos if you bought a laptop through the school (none of which I particularly liked) the year *after* I got a new laptop, it came with Mathematica. !! Do you have to be a student there? Do they ship overseas?
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Posted: Mon Apr 07, 2008 6:07 pm
Swordmaster Dragon Morberticus Why is Mathematica so SPENSIVE!?! I have no freaking clue. I was pissed 'cos if you bought a laptop through the school (none of which I particularly liked) the year *after* I got a new laptop, it came with Mathematica. Layra: That sounds pretty awesome. But how in the world did you come across that in class? So we were looking at approximation methods for guessing the eigenvalues of operators by restricting to subspaces of the Hilbert space and minimizing a certain form over the subspace. At this point, Prof. Sternberg decided to give us an example of how to apply mathematics to the real world, because he loves mathematical physics. In the case of the operator being the quantum Hamiltonian and the Hilbert space being the space of wavefunctions for two hydrogen atoms, we assume that all particles were point particles and that the nuclei are a fixed distance r apart. We picked our subspace to be the space spanned by the tensor product of the ground states of each atom with each electron associated with a nucleus and the tensor product of the ground states of each atom with the opposite arrangement of electrons. We ended up with the minimum energy state to be the sum of the basis vectors, giving us an entanglement with a fixed length between the atoms and the sharing of electrons.
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Posted: Thu Apr 10, 2008 8:37 am
I've gotten so used to TeX that I'm writing my CS notes in LaTeX, even though I know that it will never compile.
Also, I love the hammer.
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Posted: Thu Apr 10, 2008 1:52 pm
Next tuesday I have to decide what maths modules I want to be officially examined in. This requires interaction with the maths department. crying crying crying
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Posted: Thu Apr 10, 2008 5:45 pm
Layra: Much awesomeness. Morberticus: Much non-awesomeness, I suppose. I can see how interacting extensively with math professors could be wearing on the body.
I have to choose classes for next semester soon. I *know* I'm taking real analysis again, and I'm damn sure I want to take the grad course in relativity. I'm thinking of "Philosophy of Physics" as my BS humanities course, and I might wanna take the grad course in QFT. But there's also a class in low-dimensional topology, taught by my current seminar professor, and a class in low-dim topology and gauge theory taught by some big-wig. There's also a class in algebraic topology, if I didn't want to just teach myself and pretend I know something.
There's too much maths and physics in the world. Why do so many of them have to be so bloody interesting?
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Posted: Fri Apr 11, 2008 2:28 pm
Swordmaster Dragon Layra: Much awesomeness. Morberticus: Much non-awesomeness, I suppose. I can see how interacting extensively with math professors could be wearing on the body. I have to choose classes for next semester soon. I *know* I'm taking real analysis again, and I'm damn sure I want to take the grad course in relativity. I'm thinking of "Philosophy of Physics" as my BS humanities course, and I might wanna take the grad course in QFT. But there's also a class in low-dimensional topology, taught by my current seminar professor, and a class in low-dim topology and gauge theory taught by some big-wig. There's also a class in algebraic topology, if I didn't want to just teach myself and pretend I know something. There's too much maths and physics in the world. Why do so many of them have to be so bloody interesting? I'd recommend against Philosophy of Physics, although there might be some redemption there. In general, however, such classes tend to be so watered down and the other students so inane that you'll be tearing your hair out by week three. Unless you're going to be, say, reading Popper and Kuhn in depth, most classes of that form tend to be both over-general and incorrect with regards to actual physical theory.
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Posted: Fri Apr 11, 2008 5:00 pm
Can you find official course material on the Philosophy of Physics module? This will sound obvious, and I'm sure it has already occurred to you, but browsing through lecture notes of previous students, or specified Textbooks, or even just module blurbs is useful.
Bleargh, my masters not only straddles departments (Maths and Physics), it also straddles colleges (Physics modules like QFT and General Rel are done in Trinity College Dublin, Maths modules are done in Maynooth University). And while I'm pretty familiar with what the physics modules entail, the Maths ones are giving me a headache. Apparently I've been given 'free reign' over the Maths department (what lectures I can go to), but official examinations are obviously part of the masters, and that's where the difficulty sets in. Some modules sound completely alien to me (Galois theory?) Others have intimidating roman numerals at the end (Real Analysis II, Algebraic Number theory XVII) which imply previous module prerequisites. If I don't stray too far from the fields I've been exposed to in my mathematical methods modules I should hopefully be fine. This means picking some undergrad courses, like Complex Analysis, Algebraic Topology, Point set Topology (and Homotopy), and at least two graduate modules (Functional analysis and Complex Dynamical Systems). But there are others like 'Measure and Integral' and 'Commutative Algebra' which sound pretty interesting. Argh *tosses coin*
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Posted: Sat Apr 12, 2008 7:55 am
Morberticus, it sounds like you could get a lot of information by talking to math undergrads, grads, and dep reps. A lot of math sounds intimidating and really isn't. Galois theory, for example, is the study of fields which allow solutions to polynomial equations. (Example: if you make a field by attaching i*Sqrt(2) to the rational numbers, you can solve -x^2 = 2. Surprise, surprise). Commutative algebra can be kinda kewl. Algebras are related to rings, fields, modules, vector spaces, etc. I had a class on non-commutative algebra which happened to be pretty interesting (though wicked hard, at least at the time). Just talk to people, see what the first couple days of class are like, the usual.
Layra & Morberticus: I wouldn't be taking Philosophy of Physics for a grade anyway, unless it turned out that I had to drop or PDF QFT. (Ah, acronyms). The sample reading list has David Albert's "Quantum Mechanics and Experience" and Einstein's "Relativity: The Special and General Theory." Statements like "This course will involve technical details of geometry and physics" and "Problem sets are 15% of the grade" somewhat reassure me of its validity.
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Posted: Mon Apr 14, 2008 10:33 am
Swordmaster Dragon Morberticus, it sounds like you could get a lot of information by talking to math undergrads, grads, and dep reps. A lot of math sounds intimidating and really isn't. Galois theory, for example, is the study of fields which allow solutions to polynomial equations. (Example: if you make a field by attaching i*Sqrt(2) to the rational numbers, you can solve -x^2 = 2. Surprise, surprise). Commutative algebra can be kinda kewl. Algebras are related to rings, fields, modules, vector spaces, etc. I had a class on non-commutative algebra which happened to be pretty interesting (though wicked hard, at least at the time). Just talk to people, see what the first couple days of class are like, the usual. Layra & Morberticus: I wouldn't be taking Philosophy of Physics for a grade anyway, unless it turned out that I had to drop or PDF QFT. (Ah, acronyms). The sample reading list has David Albert's "Quantum Mechanics and Experience" and Einstein's "Relativity: The Special and General Theory." Statements like "This course will involve technical details of geometry and physics" and "Problem sets are 15% of the grade" somewhat reassure me of its validity. yar, I'm discussing my options with the maths dept tomorrow . I'd love to dabble in a bunch of modules but it's getting to the stage now where I need to actually start focusing on where I want to specifically lend my efforts in terms of research and whatnot. Since my undergrad degree is half experimental physics, people have been suggesting I focus primarily on mathematical modelling and computational physics, which I enjoy a lot. Wish me luck anyway.
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Posted: Mon Apr 14, 2008 10:44 am
Morberticus yar, I'm discussing my options with the maths dept tomorrow . I'd love to dabble in a bunch of modules but it's getting to the stage now where I need to actually start focusing on where I want to specifically lend my efforts in terms of research and whatnot. Since my undergrad degree is half experimental physics, people have been suggesting I focus primarily on mathematical modelling and computational physics, which I enjoy a lot. Wish me luck anyway. What are you now, a pirate? And does it count as wishing you luck if you command me to do it? I'm tired, and in a bit of a silly mood. Next week I get to lecture on homology groups and the Alexander invariant for knots to a bunch of peers who, while interested in topology, have no formal training in it, algebra, or knot theory. Fun!
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Posted: Wed Apr 16, 2008 8:15 am
Swordmaster Dragon Morberticus yar, I'm discussing my options with the maths dept tomorrow . I'd love to dabble in a bunch of modules but it's getting to the stage now where I need to actually start focusing on where I want to specifically lend my efforts in terms of research and whatnot. Since my undergrad degree is half experimental physics, people have been suggesting I focus primarily on mathematical modelling and computational physics, which I enjoy a lot. Wish me luck anyway. What are you now, a pirate? And does it count as wishing you luck if you command me to do it? I'm tired, and in a bit of a silly mood. Next week I get to lecture on homology groups and the Alexander invariant for knots to a bunch of peers who, while interested in topology, have no formal training in it, algebra, or knot theory. Fun! Heh... well I can't really offer specific advice on the topic, but I find that encouraging questions and avoiding powerpoint presentations are the keys. My most succesful talks are ones where I never touch a powerpoint slide (unless they're used for basic illustrations only) and keep the talk brief with considerable time allocated to Q+A. Had a talk with maths dept. I'm doing undergrad modules on group theory and point set topology, and postgrad modules in Algebraic topology and Functional analysis (The rest of my modules are physics modules, such as QFT, Research Project on Chaos theory, Solid State Physics etc..... matey.
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