I may be wrong. Its been a while since I learned the basics.
I believe a member on this forum, Mathwonk, wrote some notes explaining Galois Theory first and filling in the blanks.
I can be wrong.
In anycase, check out his algebra notes.
If you want something easier but well written, to get...
Geez. The hardcover is pricey.
BUt it is quality. A friend of myne owns a copy and I skimmed through it. Lots of cool stuff. Will buy a paperback soon. i think the op is better served by Boas due to background information listed.
Having a pure math background. The section on tensors was gold...
If you can find a copy of Alonso and Finn Physics at the library. Its a great book but expensive. I would supplement the class book with this one.
If you can find Alonso and Finn: Fundamental University Physics Volume 1, which is even better but more harder to find. Than use that one in...
It doesn't shy away from the mathematics. Griffiths does. While still being explanatory. It overlaps with the more sophisticated Sakurai.
Griffiths goes to great lengths to hide the mathematics.
Since you have the math for it. Give Townsend or this one a look.
https://www.amazon.com/Quantum-Mechanics-Paradigms-David-McIntyre/dp/1009310615?tag=pfamazon01-20
I dislike Griffiths quantum mechanics book. I am partial to his EM book.
If you are struggling with the mathematics of Griffiths, then you do not meet the math prerequisites. It is probably the most math hand wavy QM there is. Are you sure its the math and not having the physics chops?
Ie., jumping from say an intro mechanics understanding to an upper division QM book?
Simmons is probably the easiest intro to Topology. It starts with metric spaces, then the second half of the book is an intro to functional analysis (think of this as calculus on infinite dimensional vector spaces).
The standard is Munkres, it’s a bit more difficult than Simmons, but still...
Depends on who the book is intended for.
Say for a student first learning geometry or someone who has done a bit more math, but not really upper division mathematics,
Then the Geometry book by Edwin E. Moise/Downs: Geometry is an excellent textbook. It does not contain the dreaded two column...
For probability, I found Hossein to be an excellent text.
For polynomial curve fitting, have a look at numerical methods books.
I took two classes in numerical (Did pure math), and I do not have any recommendations. We used a run of the mill book for numerical. Decent, but I’m not familiar...
For the topics in the course.
Chain rule, chain rule, chain rule... (most important)
From ODE:cauchy-euler method, UC method, variation of parameters.
It doesnt hurt to have familiarity with laplace/inverse laplace transforms.
I found them doable but challenging for, say 1/3 of the problems in each each section.
Granted , I do not use solution manuals. So experience can vary if you plan to look at solutions.
Other book worth mentioning, is the one by Bleeker.
Haberman is also widely used, and is considered to be...