Need guidance as to what to do next, high school student

[bigerst]

Hello I am a grade 12 student looking to be a physicist. the school course is hardly satisfactory so I did a hell of a lot of self study, I'm wondering in which direction i should head next.
I did high school physics in grade 9, calculus in grade 10, first yr uni physics g11, and intro to real analysis, i finished 1/2 of john taylor's classical mechanics, now almost done griffith's electrodynamics, and i read most of Boas' methods in physical sciences.
So now I am just confused, in which direction should i head (excuse me for the vague question, please read on) i also enjoy math, especially rigorous math (and phycists tend to be very sloppy) so i read trench's introduction to real analysis, and is reading pugh's real analysis, however i seeem to have hard time with the vector calculus presented in such abstract manner, and lesbeguese theory is a hell of a theory to me. so I am just wondering, are there suitable math books (the ones that do legitimate proofs instead of shuffling it under the carpet) suitable for my current level? intro to complex analysis maybe? tensor analysis? ( i had a look at rudin's book and it gives me nightmares) or more rigours books on mathematical physics? ( i really like calculus and analysis, maybe i should wait to mature a bit before returning to Pugh?) also heading onto university would it still help for me to read so much on my own time or focus more on the curriculum? I am looking to be a theoretical/ mathematical phyicist.
thanks

Bigerst

 

[ModusPwnd]

If you really have mastered undergrad physics material (griffiths, boas, etc) then what you are lacking is research. You should head to your nearest university and find a research group to volunteer with. Its not unheard of for advanced high school students to do research at a university.

However, did you just read the books or did you actually do work? If you just read through them without doing problems I would suggest you go back and try some problems and try to reproduce some of the theorem's without looking at the book. Blazing through books is easy. Working out the ideas takes a long time. There is a reason that most people take 4 years to study the material you have already read.

 

[bigerst]

thanks for the reply
that's pretty much what I am facing right now, i wouldn't say i mastered all of the content for i am well aware it is going to take a year or so for those material to sink in and become part of my arsenal, for i can see a gap between myself and really recreating and advancing what i have learned. however i wouldn't say the opposite either, for i can do most of the problems in grffiths (ok i admit, i read it 5 times) and Boas (this is slightly easier). so right now I am in a kind of awkward situation, I'm waiting for my physics maturity to catch up, I am just uncertain what to do at this stage.

Thanks

bigerst

 

[Vanadium 50]

I'm wondering in which direction i should head next

You should work on your English. Nobody has ever run into trouble in science because their English was too good.

 

[Matrix0]

Dear high school student,

It is great to hear that you have a passion for physics and mathematics and have taken the initiative to do self-study. I can understand your confusion about the next steps to take in your academic journey. My first suggestion would be to talk to your high school physics teacher or a guidance counselor about your interests and ask for their advice on courses or extracurricular activities that could further your knowledge and skills in physics and mathematics.

In terms of your current level, it seems like you have a strong foundation in calculus and introductory physics. To continue on the path of becoming a theoretical/mathematical physicist, I would recommend focusing on developing your mathematical skills further. Complex analysis and tensor analysis are both important topics in theoretical physics, so I would suggest exploring those areas.

However, it is important to also have a well-rounded understanding of physics, so I would also recommend taking courses in other areas such as quantum mechanics, thermodynamics, and statistical mechanics. These will provide you with a solid understanding of the fundamental principles of physics and how they can be applied to different areas.

In terms of suitable math books, I would suggest looking into textbooks used in university-level physics and mathematics courses. These will often have a more rigorous approach and will provide you with the necessary proofs and mathematical techniques. It is also important to practice problem-solving and critical thinking skills, so I would recommend working through practice problems and seeking help from professors or tutors if needed.

As for your question about whether to focus on self-study or the curriculum, I would say that both are important. While the curriculum will provide you with a structured learning path, self-study allows you to explore topics that interest you and go beyond the curriculum. It is also a great way to prepare for university-level courses.

Overall, my advice would be to continue exploring your interests in physics and mathematics, seek guidance from experienced teachers, and challenge yourself with new concepts and problems. With dedication and hard work, I have no doubt that you will succeed in your goal of becoming a theoretical/mathematical physicist. Best of luck on your journey!