How can I acquire physics and mathematics knowledge effectively?

[DifferentialGalois]

Greetings, I am a 12 year old who is vastly intrigued by the wonders of theoretical physics (experimental physics has not exactly been to my liking) as well the subtle art of mathematics. For the past six months, I have attempted to work my way up to mastering mathematical prerequisites required of basic quantum mechanics. While I have learned some of the conceptual aspects of QM, I understand very scarce amounts of the mathematical formulation of it. The Dirac notation is bearable, but the issues turn up when there begin turning up partial derivatives, partial differential equations, esoteric metrics, topological spaces and so forth. How would I potentially overcome such a barrier? My math repertoire is currently exceedingly limited, consisting of merely 75% of differential calc., 50% of integral calc and mastery of the prerequisites. I have dabbled a bit in the fields of complex analysis and linear algebra, albeit now I fear that by learning excessive theory, I am not gaining much out of it. For instance, there were questions in a national math olympiad past paper that completely stumped me, even though the answers operated on basic mathematical principles such as the pigeonhole principle. Thus, I desperately want to enhance my mathematical problem solving skills, not for the sake of time management, but for the sake of finding innovative and creative methods to solve a problem by applying the theory. I have read a bit on The Art and Craft of Problem Solving by Paul Zeitz, but I feel that it isn't allowing my problem solving (which is exceedingly important in research mathematics) to improve by a vast amount.

As for theoretical physics, I have read up a bit on the underlying basics of special relativity and quantum physics (e.g. Minkowski spacetime diagrams, Bell's inequality, Lorentz and Gallilean transformations, Kochen Specker theorem and the EPR paradox), albeit I honestly don't know what to do now, considering my limited math knowledge. General relativity simply overwhelms me with excessive differential geometry, Griffiths' introductory quantum physics book is just too advanced for me, special relativity provides with a relief but nonetheless, I get perplexed by the most seemingly simple things. I don't know how to go about such.

 

[gleem]

Patience. I know QM, relativity, etc are interesting but you have to have a good grasp of the fundamentals. How is your knowledge of classical mechanics, and electricity/magnetism. You must master these subjects first. They will also give you a map to develop your math skills and show you how the math helps develop the science.

 

[TeethWhitener]

Practice practice practice practice practice. Get math and science books. Do the problems. All of them. If you get stumped, you can ask questions here. You're young, so you have lots of time that you can devote to this project. If this is something you really want to do, now is the best time to make progress on it, before "life" and "responsibility" start to get in the way.

 

[fresh_42]

Here is a list of articles about self study and its obstacles:
https://www.physicsforums.com/threads/self-teaching-gcse-and-a-level-maths.933639/#post-5896947

 

[DifferentialGalois]

The thing is I tend to readily get distracted by the game of chess, which captivates me in the most intriguing of psychological ways. Howbeit, despite playing it on essentially a daily basis, I prefer gaining mathematical and physics knowledge. Would there be an effective strategy so as to minimise my addiction to the game and focus solely on math and physics?

 

[DifferentialGalois]

Classical Mechanics - Relatively sound knowledge of the subject, though gaps when it comes to aspects such as Young's modulus, Hooke's law implications and torsion balance. As for magnetism, I'm quite an amateur with maybe only a decent grasp of electromagnetism. For things such as Ampere's law, Kirchhoff's laws, moving coil galvanometers, Van De Graff generators, I'm nowhere near the standard that would assist me in excelling in physics.

 

[Delta2]

Its a very good thing that you are only 12 and still interested to master mathematics and theoretical physics at the highest level.
There are only three secrets I can tell you: Study, study and more study :). Thousands of hours of study (we don't have problem with time here, you still only 12 so you got all the time ahead of you),will be required for you to master math and theoretical physics. But you need to study properly. Try to get good books, that have not only the theory but many solved examples. When you see an example try to work it out yourself before you read it solved on the book.
And as others have mentioned , you ll need patience and persistence for you to do so many hours of study.

About chess, i also like to play chess, i spend at least 2-3 hours daily on online chess servers. Chess is not only a game or a sport i believe its a science by itself and you ll also need many hours of study if you want to become good at it as well.