The long and winding road that leads to your TOE

[BruceW]

@nabil0 - nice selection of books there. I'll check them out too :)

 

[WannabeNewton]

Hope you don't mind. Lol

Haha, not at all friend. I would have to second what espen said and echo that you shouldn't make Hartle your final textbook on GR but it is a good start. It places physics before math, something Wald rarely does ;)

You don't need any math higher than the level of boas mathematical methods to be able to read an introductory book on quantum field theory .Here are some example of the most important mathematical tools that you will need : contour integration , green functions , special functions and group theory

I strongly feel that doing the bare minimum just to get to the advanced topics in a hurry will only leave you tripping incessantly as you try to learn. Saying Boas is all that is needed in order to do Peskin is quite out there.

 

[Lavabug]

I agree here. You need to study a theoretical Linear Algebra text now. It will be very useful in physics and mathematics.

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 (or at least: significantly more helpful than just knowing the relevant calculus). .

Depends on how rigorously the book uses calculus... Some numerical methods/analysis (of extreme importance in physics) books use very rigorous methods which are not understandable if you haven't gone through something like Spivak or Apostol before. Knowing proof-based mathematics is really essential to read and do exercises from almost any good physics book too (ie: Cohen.Tannoudji's quantum mechanics).

 

[nabil0]

@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 .I think it will be boring this way .Also , learning the advanced formalism can greatly simplify problems .For example, Using lagrangians can greatly simplify problems in mechanics e.g problems in spherical co-ordinates

 

[BruceW]

yeah. there is a grey area in choosing how much you want to stay on the less advanced physics problems, where I think it is OK to 'skip' a little. Using your example, it is probably not necessary to do loads of problems using Newton's laws in polar coordinates before you start learning about how to use Lagrangians instead of forces. But on the other side, I think WannabeNewton is saying that it is counter-productive to have not done any problems using Newton's laws in polar coordinates, before you go on to Lagrangians.

 

[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.