Reddit reviews Geometry, Topology and Physics (Graduate Student Series in Physics)
We found 7 Reddit comments about Geometry, Topology and Physics (Graduate Student Series in Physics). Here are the top ones, ranked by their Reddit score.
CRC Press
I'm not too sure about it personally, but several friends have taught from Nakahara, and have a lot of good things to say about it. It's graduate level.
The mathematics necessary for theoretical physics varies based upon what type of theoretical physics you want to work in.
I assume you are a rising senior?
Long term the best book I've seen for an overview of what you want is Geometry, Topology and Physics by Nakahara link
Although this book is really suited for graduate students with extensive mathematical background. But think of this book as a goal!
For you you'll want to read up a good deal on Abstract Algebra. That paves the way for understanding Lie Algebras, Topology etc. And you'll also want to do some analysis at the same time.
I am not a mathematical physicist but representation theory has a lot of applications in physics so I know a good bit of literature if you have more specific questions about books for self-studying some of the courses that people have listed below. (Understand though that you will have to retake them once you get to college).
I've become greatly interested in geometric concepts in physics. I would like some opinions on these text for self study. If there are better options, please share.
For a differential geometry approach for Classical Mechanics:
Saletan?
For a General self study or reference book:
Frankel or Nakahara?
For applications in differential geometry:
Fecko or Burke?
Also, what are good texts for Geometric Electrodynamics that includes spin geometry?
Some of my physics major friends liked Nakahara. If you want to instead just do Riemannian geometry computations like a physicist you can try a general relativity book like Wald or Carroll.
Geometry, Topology, and Physics isn't a complete overview of math (as suggested by the title, it focuses on, well, geometry and topology), but if you're interested in learning about those specific subfields and their application to physics, I'd definitely recommend it.
Let me point you to my friend Nakahara.
Nakamura is ok. I like Bleecker. The classical reference is Kobayashi and Nomizu. Nakamura is advanced undergrad. Bleecker is masters / post grad and K & N is renowned for both it's rigour and difficulty. From taking a brief look over the notes you are currently using any of these books would be fine.
I'm a bit surprised that you've had difficulty finding resources. Maybe it's your search terms? Try looking for principal fibre bundles, differential geometry, geometric analysis... etc...
Oh. Speaking of geometric analysis Josh does an ok job of reviewing fibre bundles / connections. There's a little bit of a connection to physics via Yang-Mills.
https://www.amazon.com/Geometry-Topology-Physics-Graduate-Student/dp/0750306068
https://www.amazon.com/Gauge-Theory-Variational-Principles-Physics/dp/0486445461/ref=sr_1_fkmr0_3?s=books&ie=UTF8&qid=1467948564&sr=1-3-fkmr0&keywords=bleecker+guage
https://www.amazon.com/Foundations-Differential-Geometry-Classics-Library/dp/0471157333/ref=sr_1_1?s=books&ie=UTF8&qid=1467948581&sr=1-1&keywords=kobayashi+and+nomizu
https://www.amazon.com/Riemannian-Geometry-Geometric-Analysis-Universitext/dp/3642212972/ref=sr_1_fkmr1_3?s=books&ie=UTF8&qid=1467948599&sr=1-3-fkmr1&keywords=Josh+geometric+analysis