B What Math do I need to learn best for Classical and Quantum Physics?

[Godzilla-3301]

I am a 14 year old who is very interested in Physics, especially astrophysics, but I don’t know exactly which math I should study in order to learn more in depth of the field. What is the best thing to learn?

 

[fresh_42]

Physics is written in mathematics, a rather specific mathematical dialect to be exact. It is usually taught parallel to the standard courses in physics.

You could begin to learn calculus or linear algebra because these two are the fundamentals of basically everything else.

BUT ...

... there are some serious implications which must be considered:

• If you learn it wrong because you are alone and have no feedback from a teacher, it is very difficult to "unlearn" misconceptions.
• If you learn it right, e.g. because you regularly checked your knowledge here on PF, then you will probably get bored if it is time to learn it at a university. And being bored is a serious danger as it kills curiosity, the most important attitude of all.
• You could get frustrated because things are more difficult than you thought. And frustration is a sad thing. People tend to give up if being frustrated.
• Where do you learn the school stuff, which is in between your current knowledge and the beginning of a calculus textbook?

So unless you're a genius, there are some severe obstacles to be considered. The best recommendation is very likely: Learn as much as you can along with your regular classes at school, especially in math, physics, and chemistry, maybe biology, too, and try to understand those subjects on a deeper level of understanding. Always ask why, read additional texts, e.g. Wikipedia pages, and do your homework.

If you want to know where you are at, you can test your knowledge with the books on https://openstax.org/subjects or have a look at the high school problems in https://www.physicsforums.com/threads/solution-manuals-for-the-math-challenges.977057/. Those problems (all of them) give you an example of where you want to go. Keep in mind that you are not supposed to understand them, yet, so do not get frustrated. They are challenges, and even physicists or mathematicians cannot solve all of them from the spot.

Summary: Be good at school!

 

[Godzilla-3301]

Physics is written in mathematics, a rather specific mathematical dialect to be exact. It is usually taught parallel to the standard courses in physics.

You could begin to learn calculus or linear algebra because these two are the fundamentals of basically everything else.

BUT ...

... there are some serious implications which must be considered:

• If you learn it wrong because you are alone and have no feedback from a teacher, it is very difficult to "unlearn" misconceptions.
• If you learn it right, e.g. because you regularly checked your knowledge here on PF, then you will probably get bored if it is time to learn it at a university. And being bored is a serious danger as it kills curiosity, the most important attitude of all.
• You could get frustrated because things are more difficult than you thought. And frustration is a sad thing. People tend to give up if being frustrated.
• Where do you learn the school stuff, which is in between your current knowledge and the beginning of a calculus textbook?

So unless you're a genius, there are some severe obstacles to be considered. The best recommendation is very likely: Learn as much as you can along with your regular classes at school, especially in math, physics, and chemistry, maybe biology, too, and try to understand those subjects on a deeper level of understanding. Always ask why, read additional texts, e.g. Wikipedia pages, and do your homework.

If you want to know where you are at, you can test your knowledge with the books on https://openstax.org/subjects or have a look at the high school problems in https://www.physicsforums.com/threads/solution-manuals-for-the-math-challenges.977057/. Those problems (all of them) give you an example of where you want to go. Keep in mind that you are not supposed to understand them, yet, so do not get frustrated. They are challenges, and even physicists or mathematicians cannot solve all of them from the spot.

Summary: Be good at school!

Thanks, I will use this advice to heart.

 

[nuuskur]

From what I saw what they learn in QM, a lot of functional analysis is involved. I would say 14 is far too young to get into analysis.

 

[PeroK]

If you are keen, you could take a look at complex numbers. They're important for QM.

Also, probability theory might be interesting.

And, there is nothing to stop you talking a look at Special Relativity.

 

[Mayhem]

• If you learn it right, e.g. because you regularly checked your knowledge here on PF, then you will probably get bored if it is time to learn it at a university. And being bored is a serious danger as it kills curiosity, the most important attitude of all.

Speaking for experience:

I self taught the first semester of university's 1st semester math curriculum during my gap year and basically slept through the course. I didn't even purchase the book. Result: Easy A on exam. A 4 hour exam took 20 minutes to complete. While this is bragging, my message is that it really pays off as I could focus on my other (more difficult) courses. If OP nails down his maths skills, he could focus on the actually interesting things about physics.