The long and winding road that leads to your TOE

[WannabeNewton]

@WannabeNewton I think that it's better to reach the interesting topics quickly using the minimum required background . In electrodynamics , In my opinion , It's better to understand how maxwell equation can be derived from the principle of Einstein relativity by choosing a lagrangian that's lorentz scalar and deriving the equation of motion and then work out the consequences of this equation not to first learn the electric field and solve tons of problems before getting to static magnetic fields

There's a reason why every major university does things in exactly the opposite way that you deem is "better". Deriving Maxwell's equations from a variational principle is trivial and doesn't teach you any physics. Doing 3 and 4 star problems in Purcell's first year electromagnetism text does teach you physics. The OP's goal is to actually learn and get an intuition for things like electrodynamics, not skip ahead to more "advanced" topics with just enough background so as to be able to reproduce technical terms to friends and internet goers.

 

[DiracPool]

Introductory real analysis is also something you need to cover once. The problem with this is that it is practically useless in physics. I don't know any physics where a knowledge of introductory real analysis is very helpful.

Well, with such a persuasive argument I just had to take this class! Lol. I like this guy Francis Su and its one of the few (perhaps only) full video courses I could find online that comes with a syllabus and textbook reference.

http://www.youtube.com/watch?v=sqEyW...07EDAF&index=1

I'm trying to find online courses that I can somehow engage in more than just watching the lecture. I feel a big limiting agent in these online courses, especially math, is that there's no readily apparent problem sets to solve, and essentially no review of the problem sets in the form of fully worked solutions to compare your work against. I'm surprised it's so hard to find this as, has been mentioned here many times, it's important to work your own problems and not just watch the prof work them.

So, I was planning on getting the book for Su's course and work the problems in the book. The problem there is the book is by Rudin and I've heard some bad reviews on that one here in this forum.

http://www.math.hmc.edu/~su/math132/syllabus06.pdf

So what do I do? Should I just go ahead with the Rudin book, just watch the lectures and not get the book? Or is there another alternative?

 

[espen180]

Any book is better than no book. The thing about Rudin is not that it is a bad book! If you manage to get through it, you will have learned a significant amount of analysis. However, his style is very dense and he doesn't spoonfeed the reader. It can take a few readings before you are able to digest the material.

I suppose many people don't like Rudin because they expect math books to read like novels. With Rudin, you really have to work, think a lot, and go slowly. Expect to spend at least one hour per page, on average. I would guess the majority of higher level math books are like this, so it is in your best interest to get used to it.

I remember reading a really dense math book, and it taking me several hours just to digest a single page. It was frustrating, and sometimes it is disheartening to return to the same page for the fourth or fifth time, but it paid off in the end.

 

[WannabeNewton]

So what do I do? Should I just go ahead with the Rudin book, just watch the lectures and not get the book? Or is there another alternative?

If I asked you a very basic calculus question like "prove every convergent sequence in $\mathbb{R}$ is Cauchy and that every Cauchy sequence in $\mathbb{R}$ is bounded" would you immediately be able to do it? If not, jumping into Rudin would be a very bad idea. You should learn proper calculus (like at the level of Spivak) before moving on to proper real analysis. Even then, you might like Carothers better than Rudin.

 

[micromass]

I recommend that you do Spivak first before you tackle Rudin (or similar books).
Other very good introductory books (at the level of Spivak) are Berberian: https://www.amazon.com/dp/0387942173/?tag=pfamazon01-20 and Abbott: https://www.amazon.com/dp/1441928669/?tag=pfamazon01-20

After these books, I suggest you do Carothers or Knapp (or Rudin if you insist).

 

[DiracPool]

@WannabeNewton and Micromass

OK, thanks for the advice. That's going to save me some time, money, and grief.

@espen180

Thanks for your confidence in my abilities, but this old cowboy just aint young enough to cross that river (the river of an hour per page) right now. It's going to take longer, but I'm going to have to head west towards the ridge where the river's shallower and narrower, you know, Spivak pass.