Recent content by Huqinpku

https://www.amazon.com/dp/0679776311/?tag=pfamazon01-20 has almost everything you mentioned. Be warned, it is a hard book even for someone who has a PhD.

I second xepma's suggestion. If this is your first programming language, start with python. btw, why do you decide that you need to learn c++?

It looks like this book is a good fit to you: Peter Szekeres - A Course in Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry https://www.amazon.com/dp/0521829607/?tag=pfamazon01-20 I'm currently studying this book. It covers the mathematics for both quantum...

There's no one book covers all topics while providing lots of solved examples. Try Schaum's Outline series.

The first 2 or 3 chapters of Loomis and Sternberg "Advanced Calculus" is a more difficult version of Linear Algebra. It is free online at http://www.math.harvard.edu/~shlomo/