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I've realised that the completely unstructured way I've been going about trying to self-teach physics and mathematics isn't going to work - everything overlaps with everything far too much. So I'm looking for help in structuring my teaching. I'm also planning on starting from scratch.
What I know:
High school physics:
Classical mechanics (sans the Lagrangian or Hamiltonian formalisms)
Fundamentals of ray optics
Fundamentals classical of electrostatics and electrodynamics, along with the classical theory of magnetism
Fundamentals of thermodynamics
Fundamentals of waves/acoustics
High school mathematics:
I know how to do calculus, but I don't understand it at the deeper levels. I can solve problems, visualise it clearly, apply it to physical or other systems, and all that. But the higher-level pure mathematical theory of analysis which underlies it, along with both the analytical and geometric sides of topology, is mystifying to me. I've been trying to remedy this lack, but even there, I found too little structure.
I have one fundamental objective - to understand, to the point where I can visualise clearly (is not simultaneously) both in my mind's eye, the theories of relativity and quantum physics. Then, if I'm still interested, I want to go further. But this is the basic requirement.
Now my plan is as follows:
1) Do the maths. Whatever mathematical tools I require to understand these theories and visualise them, I want to acquire them before I try to touch the physics. Mathematics should never be a stumbling block.
2) Study basic relativity.
3) Study basic quantum mechanics.
I want help because I want to know how I can go about doing that. I'm going to study entirely on my own, so book recommendations will be the thing I'll find most useful, preferably of books meant for self-study without the help of a teacher.
I'd like to start from scratch - that is, from the assumption that I know absolutely nothing of relativity or quantum physics whatsoever. Please assume that I know nothing except classical physics. That way, I won't miss anything out, and I'll be learning from introductory material which makes everything explicit.
I'm requesting help and advice in primarily two things:
1) Is my structure or study plan correct? Or is there a better way of going about it?
2) What should the final structure actually be filled with?
What mathematics will I need to learn?
In what order should I try to learn it?
How should I tackle relativity? How should I go about it?
How should I try to understand quantum physics? In what order?
For both of the above, what are the best methods of learning them? What are the best books?
What I know:
High school physics:
Classical mechanics (sans the Lagrangian or Hamiltonian formalisms)
Fundamentals of ray optics
Fundamentals classical of electrostatics and electrodynamics, along with the classical theory of magnetism
Fundamentals of thermodynamics
Fundamentals of waves/acoustics
High school mathematics:
I know how to do calculus, but I don't understand it at the deeper levels. I can solve problems, visualise it clearly, apply it to physical or other systems, and all that. But the higher-level pure mathematical theory of analysis which underlies it, along with both the analytical and geometric sides of topology, is mystifying to me. I've been trying to remedy this lack, but even there, I found too little structure.
I have one fundamental objective - to understand, to the point where I can visualise clearly (is not simultaneously) both in my mind's eye, the theories of relativity and quantum physics. Then, if I'm still interested, I want to go further. But this is the basic requirement.
Now my plan is as follows:
1) Do the maths. Whatever mathematical tools I require to understand these theories and visualise them, I want to acquire them before I try to touch the physics. Mathematics should never be a stumbling block.
2) Study basic relativity.
3) Study basic quantum mechanics.
I want help because I want to know how I can go about doing that. I'm going to study entirely on my own, so book recommendations will be the thing I'll find most useful, preferably of books meant for self-study without the help of a teacher.
I'd like to start from scratch - that is, from the assumption that I know absolutely nothing of relativity or quantum physics whatsoever. Please assume that I know nothing except classical physics. That way, I won't miss anything out, and I'll be learning from introductory material which makes everything explicit.
I'm requesting help and advice in primarily two things:
1) Is my structure or study plan correct? Or is there a better way of going about it?
2) What should the final structure actually be filled with?
What mathematics will I need to learn?
In what order should I try to learn it?
How should I tackle relativity? How should I go about it?
How should I try to understand quantum physics? In what order?
For both of the above, what are the best methods of learning them? What are the best books?
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