Are there any materials exploring intermediate levels (of any sub-subject) which give plain English descriptions along side formulas/equations/diagrams/notations?
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1$\begingroup$ possible duplicate of Beginner Physics Resources? $\endgroup$– Mark EichenlaubCommented May 18, 2011 at 11:52
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$\begingroup$ @mark: had hoped, rather desperately, to avoid beginner resources. $\endgroup$– That Realtor Programmer GuyCommented May 18, 2011 at 15:13
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3$\begingroup$ translating conceptualization into rigorous mathematical formulae isn't just some trivial detail; it's an art that develops over years of practice and is sort of the essence of theoretical physics. If you expect to buck learning the basics because it's "dull and nothing new", well, prepare to be disappointed. $\endgroup$– wscCommented May 20, 2011 at 0:11
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2$\begingroup$ @Garet You might think we're all avoiding the question or being unhelpful, but that's really not the way it is. You aren't missing notation; you're missing mathematics. If I tell you $\nabla \times \vec{B}$ is the curl of the magnetic field, I've explained the notation, but I doubt that's going to help you much. Basically, if you want to learn physics, you're going to have to disabuse yourself of the notion that you are already advanced. You aren't, because it's essentially impossible to have an advanced nonmathematical understanding (Faraday aside). What you want is to learn math. $\endgroup$– Mark EichenlaubCommented May 20, 2011 at 1:26
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2$\begingroup$ @Garet In that case, just ask a question about what math you need, or better yet use the search feature to read the previously-asked questions on that topic. Or ask specific math questions on math.stackexchange. Or ask about specific formulae you don't understand here, along with why you don't understand them. Your question is vague and unanswerable right now because you consistently refuse to tell us in a straightforward, comprehensible way what math you already know. I've voted to close as not a real question. $\endgroup$– Mark EichenlaubCommented May 20, 2011 at 11:07
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2 Answers
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Because of the proliferation of notation across multiple physical specialties, I don't know if there is a concise reference. I don't know what level you are at, so I don't know where you feel comfortable.
I would start:
a) with a table of mathematical symbols
then move to:
b) Who is Fourier? as an introduction and desk reference on Fourier Analysis (and there are PHDs I know who keep this on their desk as well, especially once they discover who the lead advisor for the english edition was).
Next are:
c) Quantum Mechanics Demystified by McMahon
d) Relativity Demysitified by McMahon
Do not be fooled by the cover art, granted these are not textbooks, but they will give you the basic training needed to step into more rigorous books.
I would then take time to understand what the Action is and what it means to vary it. One quick reference is:
e) Quantum Field Theory Demystifed by McMahon
Followed by:
f) Quantum Field Theory in a Nutshell by Zee
I would recommend starting with just the first few chapters of Zee before hitting the best kept dirty little secret paper on ArXiv that I have found to date:
g) A Simple Introduction to Particle Physics by Robinson, Bland, Cleaver and Dittman
Garanteed to turn you into a bed wetter.
From here you will have some interesting choices, but for recreation I would spend 4 weeks and watch and take copious notes (quite seriously) on all the lectures:
h) The Fourier Transform and its Applications by Brad Osgood at Stanford
You could probabaly actually just start with this, but it is important to make sure you take it seriously before doing so.
After all that, then I would start in on Supersymmetry, which has its own host of deep dark notation, as discussed in:
i) Supersymmetry Demystified by Labelle
and then you need to tie up everything you know and start in on string theory:
j) String Theory Demystified by McMahon
From here you should be able to read things directly in the arxiv, or dig into more rigorous textbooks.
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$\begingroup$ very sorry, I thought I had accepted this long ago. $\endgroup$ Commented Sep 17, 2012 at 3:04
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$\begingroup$ With respect to McMahon's book, please see the cooperative effort to make errata sheets here $\endgroup$ Commented Jan 31, 2013 at 16:21
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This is series from Stanford university by Leonard Susskind:
http://www.youtube.com/watch?v=hbmf0bB38h0
which introduces and uses tensor notation. This is a fairly high level course with a good introduction (the first 2 or 3 videos!) to various mathematical descriptions.