Looking back at my schooling (I have an engineering degree) I think that the best advice I can give is to start with the basics, and go from there.
Many times I saw either myself or my peers stuck on a concept because we had forgotten or misunderstood some key concept from a year or two before.
I'd make sure your math background is good. You should learn calculus and differential equations for sure to understand physics. Statistics and
linear algebra would help for certain areas, like quantum mechanics or optics, but calc/DE are key to almost everything in physics. Other concepts
that would help greatly are trigonometry, geometry, and complex numbers, but fortunately those last three aren't too hard, at least compared to the
other stuff I mentioned.
Regarding the nonmathematical books about physics, I see nothing wrong with those and I enjoy that sort of thing, but those alone aren't really
enough to truly understand physics. They are most useful probably for learning little-known scientific facts or getting an understanding of just what
branches of science are actually out there.
I took electrical engineering in school, and just to give you an idea of what I did, here's a list of some of the courses I took, the ones that
concern subjects you seem to be interested in. It'll give you an idea what kind of stuff is out there and a rough idea how much math and such is
needed to understand them.
4x Calculus courses, 1x Linear Algebra, 1x Differential Equations, 1x Statistics & Probability
2x Inorganic Chemistry courses
1x Statics course (the basic civil engineering course, the physics of stuff like beams, bridges, friction, and such)
2x Mechanics courses (basic mechanical engineering course, physics of moving things, like thrown objects or colliding objects)
4x Physics courses (subjects included waves, optics, electromagnetism)
-Many electric circuits courses (since this was my major, I had tons, but for a general knowledge you won't need nearly so much)
2x Power Engineering/Motors (more useful if you like practical applications or want to build stuff, otherwise you can probably skip it)
2x Nanotechnology courses
2x Communications courses (stuff like radio, TV, waveguides)
1x Thermodynamics course (we covered the first two laws of thermodynamics, though there are 3, plus the '0th law')
I did other stuff too, like biomedical engineering, controls systems, signal processing, computer programming, and I took as much history as I could
for credit, just because I like that stuff, but these are subjects that, depending on your interest in them, you could avoid if all you want is pure
A few things I want to learn more about (to give you more ideas
-almost anything in biology, as I know virtually nothing here
Regarding the math, you really can't get too much of it, if you want to understand physics well. Many times when looking up higher level physics I
am still seeing math that is unfamiliar to me, and it makes it really hard to figure out what the heck is going on sometimes. To give you an idea,
most people who take physics degrees will, by the end of their program, almost have a math degree as well just because they need that much math to
learn physics properly.
If you have certain areas you want to focus on, I'll try to suggest the topics I think would help the most.
is a course list for the university I went to. I
am putting it here because you can go to the physics courses and get an idea of what kind of stuff there is out there to learn. They also will tell
you what kind of math you need to understand it. (since they won't let you take something like electromagnetics without calculus first, for
I don't know how good these are, but MIT has some *free* online course materials here
a bunch of subjects, including physics.
The only other thing I have to say is that the more you learn about this stuff, the easier it is to learn more, or at least that's what I found. For
instance, my first year of university I found extremely frustrating because I was still learning the basics, but once I had those down, it became a
lot easier to understand more stuff. So, basically, don't get discouraged if the first few books (like the two you mentioned in your opening post)
are really hard for you to understand at the time.