It' helpful to distinguish between the general structure of a subject and particular examples of it. For example it's entirely possible to have a good and deep understanding of quantum mechanics without having mastered all the details of Laguerre polynomials or selection rules in the dipole...
This is quite wrong, especially regarding Peskin and Schroeder. That book spends half of its chapters working out tedious calculations relating to QED, QCD and standard model phenomenology. Someone who works on some narrow part of string theory, say topological strings or entanglement entropy...
Strong bump dude.
Anyway, point is do math if you enjoy it. Very few people can become Gausses or Eulers, but just be the best you can be. You might not reach greatness, but you'll still have a career that you'll enjoy and you will have contributions you'll be proud of.
How could one go about "preparing" themselves? What is it that all the physicists/mathematicians who transition into finance/wall street usually do to prepare themselves for such a job?
Yeah it's certainly an interesting thread with lots of good insight from an experienced guy. I would be reconsidering theoretical physics as well had I resonated with what he was saying. But in fact, I've greatly enjoyed the journey so far and while I do find parts of physics to be quite boring...
By the way, it's available for free online as a pdf.
The two "subareas" are not really subareas. They aren't really related and there's no real overlap. The main reason is that the tools used in the "physical mathematics" field would be considered "non-rigorous" by the guys working in the...
I would suggest that your first course of action should be to get familiar with path integrals. That's the most widely used tool at the starting stage. It's what Alvaraz Gaume used for the supersymmetric proof of Atiyah-Singer. It's what Witten used to derive the Jones polynomial from...
You're asking many great questions that I've asked myself and researched over the past couple of years regarding what "mathematical physics" is.
Broadly speaking I would divide "mathematical physics" into two categories.
Firstly there's the type of mathematical physics, where you are trying to...
I understand your struggle, and though I'm less experienced than you, I can relate to the feeling of being stuck with learning prereqs. I think the important piece that you are missing, without which everything seems disconnected, boring and hard to remember is "unification". What I mean is that...
If you want a good discussion of the physics AND math behind QM, start reading Shankar. Now. He starts off with a very nice chapter on the relevant mathematics, followed by a chapters on classical mechanics and the experimental basis of QM. Chapter 4 is then a very enlightening read, since he...
I haven't read that book but it should be alright as long as
1. It covers complex analysis, including contour integrals
2. Fourier series and transforms
3. Greens functions
4. Linear algebra, with emphasis on inner product spaces.
Hassani has a pretty decent coverage of these topics...
Learn math, mainly complex analysis and linear algebra by using Hassani. Learn Lagrangian and Hamiltonian mechanics using Landau. Learn Quantum Mechanics using Shankar or Sakurai. Learn special relativity using Schutz. Then you'll be ready for QFT. Enjoy the ride!
For both HET and CMT, classes that are useful and pretty much mandatory to know are graduate level quantum mechanics (Shankar or Sakurai), quantum field theory, and maybe a math methods course. Other useful classes for HET are general relativity, a particle physics/standard model course, and if...
And they'll be discussing QM in a non-calculus based class? What the f*ck man, please tell me I misunderstood something?
Here's the thing man. If you're interested in physics at all, you should be learning it using calculus. For heaven's sake, physics was why calculus was invented in the first...
Here are some options which might be fun to study and should be within reach given your background. They are also very important topics if you choose to pursue physics.
1. Lagrangian and Hamiltonian Mechanics. This is the foundation for pretty much all of modern physics.
2. Special Relativity...
Always better to learn something earlier than later IMO. In your year without physics classes you can choose to improve your understanding of the physics you studied, or like you said, study more advanced topics on your own.
OP, IMO you shouldn't be focusing on the quest to find/work on a "unified" theory as you probably have a long way to go in terms of knowledge before you can even start learning what efforts have already been made in this direction (though it's a nice goal to have because even a modest attempt at...
If you really want to be working through the more advanced texts, it's important that you are comfortable with the previous material at the level where you can solve a good amount of textbook problems. Susskind's book is fine, but I think it might only give an illusion of understanding unless...
For the Linear Algebra, I would strongly recommend that you either take a proof-based LA class or go through chapters 1,2 (especially 2.6), 4,5,6 of "Linear Algebra" by Friedberg, Insel and Spence. All these would be very useful for QM and GR.
Here's what you have to understand. Pretty much everyone who applies to these schools has a GPA above a 3.8 or 3.9, with a strong curriculum and also would have done a decent amount of research. As a result, letters of recommendations are extremely important. I would say it's a better situation...
Of course you say this as a math-physics double major, but not all physics students are pure math majors as well. Most physics students don't learn about bi and multilinear maps, dual spaces, and the behavior of these objects under linear transformations and it would simply be too distracting to...
I go to a large state school ranked similarly to yours. Here is my take on your questions.
1. This is an issue only for introductory courses, in which pretty much the only way to distinguish yourself is to go to office hours and do well on exams. The more advanced courses you take, the smaller...
Depends on what approach you want to take. I think for a first approach learning it without the linear algebra, (i.e description as multilinear maps) as objects that "transform" in a certain way is probably fine. You'll learn how to do basic computations and the important formulas, which should...
I hated this book because of the immense amount of hand-waving it contains, and the lack of emphasis on the formalism. And since it is usually a first book on QM it gives students the false impression that all QM is about is a series of diconnected methods for solving the Schrodinger equation (I...
I don't know about your other option, but Part III seems like a great opportunity if you are interested in theoretical physics, especially since you have a scholarship. Since the program doesn't start until late September, you have quite some time to self-study what you feel your knowledge...
I just got back a grade for an independent study I did this past spring. I really wasn't expecting this grade (B+) since people get away with A's in reading independent study/independent reasearch/reading courses by doing a lot less work than I had done. I can think of a couple of places where I...
Right now I'm interested in and looking to go into string theory and the related mathematics. I'll be starting my 4th year in the fall and here are the classes I recommend you take:
Physics: Classical mechanics, Stat Mech, E&M, 2 semesters QM are the fundamentals. Then you should take graduate...
I think basic proficiency in proof writing is a great skill to have for a theoretical physicist. You probably won't be doing many proofs in advanced theoretical physics, but things can get quite mathy and I can't imagine proceeding very far with a good understanding unless one has a good amount...