Starting graduate school; advice on deeper understanding?

[ajtcal]

(PREAMBLE: skip to the third paragraph if desired)

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I am currently a physics student about to begin my graduate studies. I will be attending a top-5 school, so I am quite fortunate in that regard. However, having spent time there doing summer research (QCD), I am fully aware of the high standards that will be imposed on me and the fact that I will be working much harder than ever before.

It is my goal to acquire a deeper understanding of my field than I currently have, and that is the basis of my question. I want to re-learn (so to speak) the physics and math that I already do know so that I can have a better foundation for understanding the deeper topics that I will need later on in my research. Therefore, I am considering a program of study to complete during my first two years. I will have a fellowship and I have a very easy-going adviser, so other than a few classes and further work on research (continuing from my summer term), I should be able to devote a good deal of time to these studies.

--------------------------------------------------------------------------------------------------------My intention is to solidify the topics I learned during my undergraduate years during the first year, and then approach more involved foundational topics during my second year.

I present a list of the math and physics topics I propose to study, the sequence in which I will study them, and the textbooks I will start with. I plan to spend a month or two on each book and then about a month doing extensive related problems. From previous experience, I think I should be able to manage about 10 pages in about three hours to really mull things over. I guess this translates into about six hours of study per day, so I should have a decent amount of time left over for classes and research. For any upper-level graduate students, postdocs, or higher, could you please comment on whether my sequence is sound and if you have any comments on the books I plan to use?FIRST YEAR

PHYSICS
Classical Mechanics (Mechanics, Landau and Lifschitz) - I did this this summer
Statistical Mechanics (Fundamentals of Statistical and Thermal Physics, Reif)
E&M (Classical Theory of Fields, L&L)
QM (Quantum Mechanics: Non-relativistic Theory, L&L)
Relativity (Gravitation, Misner, Thorne, and Wheeler)

MATH

Real and Complex Analysis (Modern Analysis, Watson and Whittaker)
ODEs (Ordinary Differential Equations, Arnold)
PDEs (I might just reuse my undergrad book unless someone has any good recommendations?)
Algebra (Abstract Algebra, Herstein)
Set Theory & Logic (Recommendations? I only want a brief overview)
Probability and Statistics (Recommendations? Also a brief overview)
Combinatorics (Recommendations? Brief overview)SECOND YEAR

PHYSICS

QFT (Quantum Field Theory, Ryder)
Particle Physics (Recommendations?)
Nuclear Physics (Introductory Nuclear Physics, Krane)
Plasma Physics (Recommendations?)MATH

Topology (Recommendations?)
Tensors (Tensors, Lovelock and Rund)
Lie Algebras (Lie Groups, Lie Algebras, and Some of Their Applications, Gilmore)
Differential Geometry (Manifolds and Differential Geometry, Lee)
Algebraic Geometry (Algebraic Geometry, Hartshorne)--------------------------------------------------------------------------------------------------------

I realize there are already flaws (differential geometry after relativity), but I have to do my qualification exam at the end of first year. Also, I imagine some people will say that there is no need (nor possibly enough time) to read all of these books. However, unlike most of the beginning students, I will already have a research program well under way, and I was told that, provided it goes reasonably well, I won’t have to take very many classes (maybe just one or two a semester, provided I am enrolled in a research class).

Anyways, my hope is that someone (or someones) could share their thoughts on my plan. Some of the topics (especially second-year math) seem somewhat hodge-podge and arbitrary, and might not be the best order in which I could learn the topics. If I’m missing anything glaringly obvious, or if you have any suggestions for topics to study in my third year and beyond, I would also appreciate that. My primary goal is to learn these topics quite deeply so that I can really know what I’m doing in the second half of my degree.

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I just re-read this post and realize it sounds kind of naive/pretentious, but that wasn't my intention! Hopefully you guys will look beyond that and give some good advice.

Cheers,
James

 

[micromass]

I'm sorry, but your plan is insane. I really don't know what you're trying to accomplish by such a study.

First of all, grad school is not the place for a general education. It is the place to start focussing on a narrow part of physics or math. You're thinking to study very general and very useless (for you) thing.

Seriously? Algebraic geometry? Why would you study that?? And why pick the book by Hartshorne which is awfully difficult.
Combinatorics?
Logic and set theory??

If you do succeed in learning all these things (which I doubt), you will end up with a big gap. Other grad students will already have obtained very specialized knowledge and can be ready to do good research. You will have a very general, but superficial knowledge. You don't want that.

And I don't know what grad school or what advisor would even allow you to waste your time on all these topics.

 

[ajtcal]

Thank you for your reply.

Being that I have to study for my qualifying exam, the material in my first year is not useless, and regardless, I have to take these courses to meet the degree requirements. I figure it would be best to have a thorough understanding of these by reading the books I propose.

The material I'm considering studying afterwards is more arbitrary, and in all likelihood, it won't necessarily directly relate to what I end up researching. However, it has been my experience in my previous studies that there is almost always a deeper understanding to the material presented. Generally, it means looking deeper into the math. That is the motivation for the question: I would like advice on the sequence of physics and math books/courses that give a logical and thorough basis in the more advanced topics. Although I consider my undergraduate basis to be good, I think it could be a lot more thorough.

The material I was thinking of studying after I finish the general courses (as well as the more obscure math; i.e. set theory) was suggested by a variety of grad students and postdocs I worked with. However, every person has a different take on which courses to study and the order to study them in. That is why I am posting it on physics forums.

I also appreciate your point of ensuring that research is given priority. Several people I have talked to say that it would be better to read papers and brush up on weaker topics as needed rather than start off as generally as I was thinking. However, other people say that it is a good idea to spend the first year or two making sure your background is as solid as possible (in order to prepare for quals and to make life easier later on).

Again, I haven't even started grad school yet, so I only have hearsay to go by, but I was surprised that you consider this plan to be so far out of left field.

 

[micromass]

May I ask what math and physics classes you already took in undergrad??

 

[ajtcal]

I double majored in physics and math.

Physics:

In addition to the standard courses (introductory classes, CM, E&M, QM, Stat Mech), I did a graduate class in CM, a grad class in quantum (which went through about half of Sakurai), a grad class in E&M (Jackson), an introductory particle physics course, and an upper-division plasma course.

Math:

Four calculus classes, three linear algebra classes, two analysis classes, two abstract algebra classes, two ODEs classes, one PDEs class, two math methods for physicist classes, an introductory topology class, and number theory.


I'm not worried about being unprepared for grad school (having already done three summer research terms and a thesis), I just would like confirmation or criticism on my proposed course of study. I've heard quals at my school are pretty rigorous, so that's why I'd want to really go over everything again.

But more to the point, I want to do everything I can to have a good foundation. I've read pages by Baez and T'Hooft on this topic, and would appreciate insight from other people who may have done the same thing.