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nibotmath methods: the first lecture struck me with the incredible fear that I would be subjected to elementary linear algebra yet again... before I could commit hari-kari, though, the topic moved onto more interesting subjects. right now the professor is 100% redeamed, as the last lecture was a whirlwind tour of complex analysis that I found quite delightful. i 
complex analysis. i (heart) linear algebra just as much as the next person, but one can only be subjected to so many painstaking one-hour lectures on linear independence (for instance) before one must auto-immolate for the greater good.
electromagnetics: i haven't taken an advanced course in E&M and yet I still find it tremendously boring. i believe this is because i haven't been asked to do problems yet. (!) also maybe because it's a lot of tedious math to derive things that aren't particularly spectacular. unlike, say, condensed matter physics. i solid state! p.s. I promise to be the guy wearing the "I statmech" t-shirt next semester!
quantum mechanics: this class makes me want to cry. you would think that when prof. H saw the big tears rolling down my cheeks, he would have just stopped with the two-week long overview of linear algebra. you might have thought he wouldn't have lectured today on the various experiments that showed that classical mechanics couldn't be the whole story (the ultraviolet catastrophe [someone name a band that!], rutherford and his silly bread pudding model, the photoelectric effect...), a story that i have already written in fancy handwriting with a mechanical pencil in a quadrile composition book, a story that, IIRC, was given on the first day of undergraduate QM.
add anger to the sobbing when the homework assignments are handed out. we're asked to prove something that's patently untrue. (And the grader's patronizing tone: "You assumed that when Dr. H said, ``Show that the basis B must be of the form X, that there must be only one." Well, that's what "the" means!) and then we have propositions like "Consider the operator Omega = sigma_1 dot sigma_2 where sigma_1 and sigma_2 are independent sets of Pauli matricies," and I'm left utterly baffled at how one takes a dot product of a set. we decipher that it's an allusion to the dot product with a healthy dose of tensor product thrown in for good measure:
Now to prove that "U = 1 + i(L dot n) sin ψ + (L dot n)^2 (cos ψ - 1)" is unitary, where "L dot n" is a linear combination of angular momentum operators, with no motivation whatsoever.. all the while vaguely annoyed at this dot product between a set of operators and a coordinate vector...
complex analysis. i (heart) linear algebra just as much as the next person, but one can only be subjected to so many painstaking one-hour lectures on linear independence (for instance) before one must auto-immolate for the greater good.electromagnetics: i haven't taken an advanced course in E&M and yet I still find it tremendously boring. i believe this is because i haven't been asked to do problems yet. (!) also maybe because it's a lot of tedious math to derive things that aren't particularly spectacular. unlike, say, condensed matter physics. i
solid state! p.s. I promise to be the guy wearing the "I statmech" t-shirt next semester!quantum mechanics: this class makes me want to cry. you would think that when prof. H saw the big tears rolling down my cheeks, he would have just stopped with the two-week long overview of linear algebra. you might have thought he wouldn't have lectured today on the various experiments that showed that classical mechanics couldn't be the whole story (the ultraviolet catastrophe [someone name a band that!], rutherford and his silly bread pudding model, the photoelectric effect...), a story that i have already written in fancy handwriting with a mechanical pencil in a quadrile composition book, a story that, IIRC, was given on the first day of undergraduate QM.
add anger to the sobbing when the homework assignments are handed out. we're asked to prove something that's patently untrue. (And the grader's patronizing tone: "You assumed that when Dr. H said, ``Show that the basis B must be of the form X, that there must be only one." Well, that's what "the" means!) and then we have propositions like "Consider the operator Omega = sigma_1 dot sigma_2 where sigma_1 and sigma_2 are independent sets of Pauli matricies," and I'm left utterly baffled at how one takes a dot product of a set. we decipher that it's an allusion to the dot product with a healthy dose of tensor product thrown in for good measure:
Now to prove that "U = 1 + i(L dot n) sin ψ + (L dot n)^2 (cos ψ - 1)" is unitary, where "L dot n" is a linear combination of angular momentum operators, with no motivation whatsoever.. all the while vaguely annoyed at this dot product between a set of operators and a coordinate vector...
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no subject
Date: 2004-09-23 11:04 pm (UTC)no subject
Date: 2004-09-24 08:01 pm (UTC)a better example of my complaint, though, is that the assignment said "Find the equation P(Ω)=0, where P(Ω) is a polynomial in Ω." Of course there are potentially zillions of such polynomials, but what he really means is to find a polynomial from the defining characteristics of Ω...
really I'm just complaining.. it would be nice if the problems were better posed.
no subject
Date: 2004-09-23 11:10 pm (UTC)no subject
Date: 2004-09-23 11:51 pm (UTC)I need to teach myself Elementary Algebra over winter break so I can qualify for Intermediate Algebra next semester and take Statistics at Laney next summer, presuming Cal will let me in on the Essential Skills Requirements via SAT score. You are apparently a Math God, so such simple concepts are surely a joke to you. Please come back to California and be my tutor over free lunches at Naan and Curry.
Your friend,
Erin
ps -- Okay, okay, so that won't happen, but can you recommend a good book or website or something that'll somehow help me place into the intermediate class in only four weeks of study? I'm desperate here.
no subject
Date: 2004-09-23 11:59 pm (UTC)::cries::
no subject
Date: 2004-09-24 12:08 am (UTC)no subject
Date: 2004-09-24 07:57 pm (UTC)in a lot of ways it's quite helpful, but it's also a little distracting.
no subject
Date: 2004-09-24 04:38 am (UTC)We have an analytic functions test in math physics today to add to the fun.
no subject
Date: 2004-09-24 08:02 pm (UTC)no subject
Date: 2004-09-25 04:49 pm (UTC)But it really is a dot product. And all he means by mutually commuting "sets" is that for each particle it has a complete set of three Pauli matricies (one for each direction x,y,z).
The key is that the sigma_hat's he has here are vectors. But the components of those vectors in cartesian coords are each a tensor product of two matricies (one for each particle). The thing that's confusing is: for sigma_1, the second set of matricies in each tensor product is the identity matrix. And for sigma_2, the first set is all the identity. So when you dot product them together, you just get three tensor products added, like he has written there. What happens is profs get sloppy and instead of writing a product of two operators, they often just write one operator with the implication that it's tensor producted with the identity operator for the other particle(s).
Don't know if any of that made sense, but hopefully a bit moreso than what he has written in the problem set!