Math for Physics | Learn to Interpret the Physical World

[LouArnold]

I have a degree in electrical engineering, but of some years ago.
For my own simple enjoyment, I wanted to learn the math of physics - specifically for cosmology. Key to my interest is the interpretation of the math in the physical world. In summary, what is the track in math topics?

 

[FunkyDwarf]

Calculus and lots of it.

 

[LouArnold]

Calculus and lots of it.

Haha. That's a rather obvious answer, considering my degree. I'm sure that there is a more concise list. There has to be some one or some book that conveys what the math means in terms of a physical reality.

But considering that there has not been another answer to this, perhaps the question is poor. Explaining why or how its poor would be a help.

For those who at least looked at it - thanks. And to FunkyDwarf, a special thanks for responding.

 

[phreak]

You won't need to use too much calculus (in the usual sense), actually, unless you think of the study of differentiable manifolds as generalization of calculus (in all honesty, it probably is, although I don't think many mathematicians think of it this way). A somewhat advanced introduction to the mathematics of cosmology is in Frankel's Geometry of Physics. The approach is very physics-oriented. If you wanted a more pure mathematics-oriented introduction, I would suggest Lee's Introduction to Smooth Manifolds or Jost's Riemannian Geometry and Geometric Analysis. All texts I mentioned are advanced in the sense that if you don't have a good pure mathematical background, you won't know what's going on, so if you never took such mathematically rigorous classes as Real/Complex Analysis or Topology as an EE major, you would need to go back and independently study these topics before looking into the books I suggested.

 

[LouArnold]

You won't need to use too much calculus (in the usual sense), actually, unless you think of the study of differentiable manifolds as generalization of calculus (in all honesty, it probably is, although I don't think many mathematicians think of it this way). A somewhat advanced introduction to the mathematics of cosmology is in Frankel's Geometry of Physics. The approach is very physics-oriented. If you wanted a more pure mathematics-oriented introduction, I would suggest Lee's Introduction to Smooth Manifolds or Jost's Riemannian Geometry and Geometric Analysis. All texts I mentioned are advanced in the sense that if you don't have a good pure mathematical background, you won't know what's going on, so if you never took such mathematically rigorous classes as Real/Complex Analysis or Topology as an EE major, you would need to go back and independently study these topics before looking into the books I suggested.

Thanks, that makes sense. My background is in applied math, as befits engineers. But we covered Complex Analysis, but not topology or anything in the greater sense of pure math.
Perhaps I have too far to go to be realistically capable of catching up to most Masters level physics students.

 

[Kaizer6]

Hi LouArnold, I have a book that pretty well sums up what you want to know, it's called mathematics for physics and physicists by Walter Appel. It basically tell you the mathematical tools required to understand physical principles. :D