- #1
DiracPool
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- 516
I am hoping to get some guidance in this thread from those who have traveled the path before me. For the past couple of years I have been on a tear to educate myself in mathematical physics for a variety of reasons I won't bore you with here (some personal, some professional). In any case, to make a long story short I want to get to a point where I can speak and write intelligently on popular cosmology (TOE) models, L-CDM, string, LQG/LQC, Quantum field theory, etc. I don't know if I'll ever get there or how close I'll get, but shoot for a star and hit a bird, shoot for a bird and hit a rock, right?
To put it simply, I'm kind of looking to do what Lenny Susskind is trying to put together with his "theoretical minimum" campaign. In fact, at one point I got real excited about this thinking, hey, I can get where I want to go with some one-stop shopping at Lenny's. Just watch all his classes on you tube and there you go. Unfortunetely, it wasn't so easy. In fact, I personally got very little out of his lectures other than a great deal of entertainment. He is a master showman and a master at his craft. However, for me watching him lecture is like watching performance art. It's like watching an episode of Iron Chef America. I can see how the iron chef is preparing his meal and get caught up in the excitement, but at the end of the day I have no idea why he picked the ingredients he did or used the proportions he did, so I learned almost nothing about how to prepare those dishes--evidenced by the fact that I get nowhere when I attempt to tackle the problem myself.
Other than the Susskind lectures, I have been hard at work rekindling my math skills which have laid dormant for two decades and this is where I could use some advise. I started at the beginning with general math, algebra, geomerty, trig, matrix algebra, calculus 1,2, and 3, and differential equations, and now I'm kind of stuck. I'm stuck because this is the traditional basic progression of maths classes that I am aware of, and I don't know where to go from here to get to my quest for theoretical minimum, or TOE, street-cred. There seems to be a hundred different areas of study, and I don't know 1) which ones are necessary to get me TOE street-cred, and 2) what order I need to learn these mathematical disciplines.
To put it simply, what in your opinion is the essential maths that you feel a student needs to learn and in what order in their attempt to begin to understand contemporary TOE models. I know its best to learn and know all of them, but the idea is to get an idea of a sane and doable curriculum. RIght now, I'm standing at a crossroads with 100 different roads to take and I have no idea how to proceed. Here's a short list of the roadsigns--unitary groups, differential geometry, Lie algebra, Spinors, Legendre polynomials, Fourier analysis, Laplace transforms, tensor calculus, Special unitary groups, Cauchy integrals, Christoffel symbols, The residue theorem, gauge theory, Phasors, yada yada yada, I could go on for a while here.
So right now I'm stuck, I don't know which of these I need to study, or in what order. I'm looking for a workable path here, a way to organize my approach here. It would be great if they had a TOE service pack instruction kit. Service pack one is to study this, this and that in this order. Then move on to service pack 2, etc.
I know this is as much of an art as a science, as far as what to study and how to go about it, but that's kind of what I'm looking for, what your personal path or approach was and what you would recommend to those following behind.
BTW, here's some background music while you're thinking it over:
https://www.youtube.com/watch?v=x6AuKENgmLQ
To put it simply, I'm kind of looking to do what Lenny Susskind is trying to put together with his "theoretical minimum" campaign. In fact, at one point I got real excited about this thinking, hey, I can get where I want to go with some one-stop shopping at Lenny's. Just watch all his classes on you tube and there you go. Unfortunetely, it wasn't so easy. In fact, I personally got very little out of his lectures other than a great deal of entertainment. He is a master showman and a master at his craft. However, for me watching him lecture is like watching performance art. It's like watching an episode of Iron Chef America. I can see how the iron chef is preparing his meal and get caught up in the excitement, but at the end of the day I have no idea why he picked the ingredients he did or used the proportions he did, so I learned almost nothing about how to prepare those dishes--evidenced by the fact that I get nowhere when I attempt to tackle the problem myself.
Other than the Susskind lectures, I have been hard at work rekindling my math skills which have laid dormant for two decades and this is where I could use some advise. I started at the beginning with general math, algebra, geomerty, trig, matrix algebra, calculus 1,2, and 3, and differential equations, and now I'm kind of stuck. I'm stuck because this is the traditional basic progression of maths classes that I am aware of, and I don't know where to go from here to get to my quest for theoretical minimum, or TOE, street-cred. There seems to be a hundred different areas of study, and I don't know 1) which ones are necessary to get me TOE street-cred, and 2) what order I need to learn these mathematical disciplines.
To put it simply, what in your opinion is the essential maths that you feel a student needs to learn and in what order in their attempt to begin to understand contemporary TOE models. I know its best to learn and know all of them, but the idea is to get an idea of a sane and doable curriculum. RIght now, I'm standing at a crossroads with 100 different roads to take and I have no idea how to proceed. Here's a short list of the roadsigns--unitary groups, differential geometry, Lie algebra, Spinors, Legendre polynomials, Fourier analysis, Laplace transforms, tensor calculus, Special unitary groups, Cauchy integrals, Christoffel symbols, The residue theorem, gauge theory, Phasors, yada yada yada, I could go on for a while here.
So right now I'm stuck, I don't know which of these I need to study, or in what order. I'm looking for a workable path here, a way to organize my approach here. It would be great if they had a TOE service pack instruction kit. Service pack one is to study this, this and that in this order. Then move on to service pack 2, etc.
I know this is as much of an art as a science, as far as what to study and how to go about it, but that's kind of what I'm looking for, what your personal path or approach was and what you would recommend to those following behind.
BTW, here's some background music while you're thinking it over:
https://www.youtube.com/watch?v=x6AuKENgmLQ
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