This. Townsend is a great book to learn QM for at the undergraduate level. It really is a baby Sakurai in many ways. Making the transition between these books was natural for me. The formalism presented and the mathematics demanded are fair and just right for an average physics major. It's...
If you're just beginning to study these subject then I recommend, as always, "a Modern Approach to Quantum Mechanics" by Townsend and "Gravity: An Introduction to Einstein's General Theory of Relativity" by Hartle. For the QM, you need linear algebra and series solutions to diff eqs. For GR...
I also recommend Hartle as a starting point in learning GR; that is if you're an undergrad or wish to start learning the theory without learning the full-fledged diff geo behind it first. I thought it was a great book, very intuitive and easy to follow. Personally, I took a GR course as a junior...
For diff. geo it depends at what level they decide to teach it. A class out of do Carmo would probably be tougher for somebody coming from (mostly) physics, it was for me. However it was extremely interesting and well worth the hard work. Intro to real analysis and diff geo are not in the same...
I would ask an adviser from the physics department if they can override the pre-req of physics 3 and try to take some junior classes. If they cannot, take advantage of this opportunity to take more math classes (pde's, complex analysis, etc). Knowing the mathematical language ahead of time will...
From what you've said about the research opportunities and the availability of classes, I'd simply say: transfer.
I was in a similar situation with my first uni lacking research and many electives. I transferred after my second year and was able to do about a year and a half of research and...
Look at a copy of Shankar's Principles of Quantum Mechanics. He reviews Lagrangian/Hamiltonian mechanics in chapter 2 I believe and constantly discusses the connection between these subjects and QM throughout the book.
Seeing that you haven't had any physics other than the introductory sequence, I recommend that you pick up a modern physics textbook and get acquainted with quantum from there first. These books usually follow a more "historical" approach to QM and use basic wave mechanics; reading through...
If you're concentrating on undergraduate physics only, then it may be so. However, graduate level topics in physics, and even some at the undergraduate level, require knowledge of mathematics beyond these areas as homeomorphic nicely put it. For example, half of the book "Mathematics for...
Dover books certainly look very appealing. I own three Dover math books, "An Introduction to Topology" by Mendelson, "A book of Abstract Algebra" by Pinter, and "Introduction to Partial Differential Equations with Applications" by Zachmanoglou and Thoe. Of these, I can only really comment on the...
Broccoli21,
I heavily suggest that you take Statistical Mechanics as soon as possible, especially if you've completed thermodynamics and (at least) quantum mechanics 1. Abstract algebra really is a beautiful subject and will show up (especially group theory) in advanced physics courses...
Quantum Mechanics II
Solid State Physics
Nonlinear Dynamics (Grad)
Complex Analysis
+ Research project in the grad course
Last semester as an undergrad!
Just as in other disciplines, concepts become abstracted the further you go into them. As a senior undergrad I can tell you that the classes get more interesting both mathematically and physically. The range of topics one tackles become more broad and the techniques become more rigorous (or at...
The simple answer is : VERY DIFFERENT. I see the introductory physics courses to be more about problem-solving than anything else. Upper level stuff is way more interesting and even the "applied" courses, like Electronics, have a good amount of theory. Don't give up now, take a couple of upper...