Frouel said:
I have a few questions concerning learning mathematics and physics.
1. How to learn abstract definitions?
It's sometimes easier to learn them by heart just to get used to them, than heading for comprehension. E.g. the ##\varepsilon-\delta## definition of continuity. It is easier than to deduce it from its meaning everytime it is used.
Must I do learn it by heart?
How else do you learn physical laws? Newton, thermodynamics, etc. The alternative would be to learn the according underlying differential equation systems. This would be by heart, too, and far too difficult to derive the laws from that.
How to understand and apply them correctly?
By practice. Theorems, exercises, and again exercises. There is no shortcut to practice.
2. What type of subjects you learn in theoretical physics include mathematics. I need subjects with all years of study.
This list would be a bit long, wouldn't it? Just go through our forums, especially the homework forums. The short answer is coordinate systems, linear algebra, manifolds, calculus and differential equations on the mathematical side. They are all over the physical place. But you don't start with such a heavy load. You learn them piece by piece on your way as needed.
3. How to learn on your own?
Now this is definitely an individual question. Different people have different strengths and weaknesses. Some have a photographic memory, others need visual stimulations, some learn best alone, others in groups. This question is one for your teachers who know you better.
How to hasten to learn science?
With a lot of discipline, always being curious and asking "why", and checking - for example here on PF - whether what you have learned is correct, or must be corrected, esp. if you learn on your own.
4. Where I can find help If I am not a student?
Here, where you are. We basically offer free tutorials. All what is needed from your side is seriousness and some efforts, so that we can see, where you got stuck.
5. Do you have any good tips what avoid or what do, learn physics?
Avoid abstract algebra at the beginning and elaborated fields like quantum field theory and general relativity. Do learn calculus and differential equations.