Studying How to self-study physics past High School Level?

[TensorCalculus]

Hello! So I'm a teenage physics enthusiast, who wants to take my knowledge past A-level (or in America I believe this would be high school level) physics.
I've studied multiple textbooks like Young and Freedman's University physics, studied maths from books like mathematical methods for physics and engineering.
I solidified all that by doing lots (like, LOTS) of the practice problems and some Olympiad papers.

I don't really know where to go from here.
I've resorted to surfing the internet, and finding free courses and watching YouTube videos that satisfy my interest, or reading popular science, reading high-school textbooks, and just sitting around.
I'm not entirely sure what books to buy - I fear that if I accidentally skip straight to something too advanced I'll not have strong basics. My teacher told me to just read popular science, but I really enjoy looking at the math behind things and I feel that there are few popular science books (that I've read at least) that satisfy my curiosity.
I do really, really love physics, and want to try and study it further - unfortunately, I'm 13 and have quite a long time till I can study physics in University/College.
Does anyone have any resources they would recommend to me (my interest particularly lies around astronomy and electromagnetism) , or any advice to give?

 

[fresh_42]

Here is a series of articles you might want to read:
https://www.physicsforums.com/insights/early-physics-education-in-high-schools/#toggle-id-1
and
https://www.physicsforums.com/threads/self-teaching-gcse-and-a-level-maths.933639/#post-5896947
for the mathematical part of your endeavour.

If you want to learn physics seriously then there is no way to avoid mathematics. Physicists use mathematics like a language and you have to learn that part of mathematics like you learn a language.

 

[TensorCalculus]

Wow- these guides are so detailed! Thank you so much, I'm sure these will be helpful

 

[Frabjous]

Calculus is the basic language of physics. Put yourself on a path to learn it.

 

[TensorCalculus]

Yes - my calculus doesn't go much past second order differential equations. How much calculus do you suggest I learn before going into any depth into any physics topics? Is there anything calculus wise that might not necessarily be taught in math textbooks but that is useful in physics specifically?

 

[Frabjous]

Yes - my calculus doesn't go much past second order differential equations. How much calculus do you suggest I learn before going into any depth into any physics topics? Is there anything calculus wise that might not necessarily be taught in math textbooks but that is useful in physics specifically?

I interpret this to mean that you know integral and differential calculus and ordinary differential equations. You need to learn vector calculus. You should be able to handle sophomore physics with what you know now.
Next you learn tensor analysis, linear algebra, partial differential equations and complex analysis. With this you should be able to handle undergraduate physics.

 

[PeroK]

Yes - my calculus doesn't go much past second order differential equations. How much calculus do you suggest I learn before going into any depth into any physics topics? Is there anything calculus wise that might not necessarily be taught in math textbooks but that is useful in physics specifically?

Your mathematics and physics ought to develop in parallel. Learn the mathematics you need for the physics you are learning.

 

[fresh_42]

I would use the search key "<course name> for physicists + pdf", e.g. "vector calculus for physicists + pdf". This pattern has the following reasons. The "+pdf" part usually leads to lecture notes on university servers somewhere on the globe. The English name for the courses ensures that you will find scripts in English (or change them to your native language, in case it isn't English). And the "for physicists" part I think is important so you won't run into mathematics but into how physicists use mathematics instead. These are a bit different. As I said, physicists use math as language. The mathematical treatment of subjects is often less concentrated on frames and more on theoretical aspects that shouldn't interest you in the first place. You need coordinates and frames all over physics, and this part of mathematics works more like a language than, for example, pure logic.

 

[TensorCalculus]

I interpret this to mean that you know integral and differential calculus and ordinary differential equations. You need to learn vector calculus. You should be able to handle sophomore physics with what you know now.
Next you learn tensor analysis, linear algebra, partial differential equations and complex analysis. With this you should be able to handle undergraduate physics.

Yes, that's what I know. Thank you very much for the list of things I should learn in maths - that's something I've been really stuck on recently! Especially considering my bad habit of learning the physics first and the maths later, that's probably where this comes in:

Your mathematics and physics ought to develop in parallel. Learn the mathematics you need for the physics you are learning

^Yeah, I really need to get better at doing this. Thanks for the advice

I would use the search key "<course name> for physicists + pdf", e.g. "vector calculus for physicists + pdf".

Ok! I've just tried it and you're right - this works very well!

And the "for physicists" part I think is important so won't run into mathematics but into how physicists use mathematics instead. These are a bit different. As I said, physicists use math as language. The mathematical treatment of subjects is often less concentrated on frames and more on theoretical aspects that shouldn't interest you in the first place. You need coordinates and frames all over physics, and this part of mathematics works more like a language than, for example, pure logic.

I never thought about that - I mean I've heard thing like "maths is the language of the universe" but never about how maths is applied differently in physics, not as an abstract discipline/pure logic but a language. It's a great insight (and one that will definitely come in useful when learning maths for physics), thank you very much!

 

[Muu9]

Read "advice for introductory physics" by Kevin Zhou

For a textbook, look at Halliday Resnick Krane, 5th edition

https://oyc.yale.edu/physics/phys-200

https://compos.web.ox.ac.uk/

 

[TensorCalculus]

Read "advice for introductory physics" by Kevin Zhou

For a textbook, look at Halliday Resnick Krane, 5th edition

https://oyc.yale.edu/physics/phys-200

https://compos.web.ox.ac.uk/

^These are all actually so good, I haven't taken a look at the books yet but the course is so good, and thank you for showing me COMPOS. It looks like something I'd really want to do when it starts next year (unfortunately, I'm only in year 9 right now - and this year's one has already started )

 

[CrysPhys]

@TensorCalculus . As an alternative to creating your own curriculum, why not just follow an established university physics curriculum? E.g. MIT has an extensive catalog of free online physics courses: https://ocw.mit.edu/search/?d=Physics&s=department_course_numbers.sort_coursenum.

Their sequence for undergrad physics majors is given here: https://physics.mit.edu/academic-programs/undergrads/requirements/ (Focused Track is what you should look at). At MIT, all freshman are required to take 8.01 (intro classical mechanics) and 8.02 (intro E&M); so begin there (at MIT, physics courses start with 8). The physics curriculum then picks up from there. The physics courses list co-requisite or pre-requisite math courses. At MIT, math courses start with the number 18. There is also a large catalog of free online math courses: https://ocw.mit.edu/search/?d=Mathematics

 

[Muu9]

@TensorCalculus . As an alternative to creating your own curriculum, why not just follow an established unvversity physics curriculum? E.g. MIT has an extensive catalog of free online physics courses: https://ocw.mit.edu/search/?d=Physics&s=department_course_numbers.sort_coursenum.

Their sequence for undergrad physics majors is given here: https://physics.mit.edu/academic-programs/undergrads/requirements/ (Focused Track is what you should look at). At MIT, all freshman are required o take 8.01 (intro classical mechanics) and 8.02 (intro E&M); so begin there (at MIT, physics courses start with 8). The physics curriculum then picks up from there. The physics courses list co-requisite or pre-requisite math courses. At MIT, math courses start with the number 18. There is also a large catalog of free online math courses: https://ocw.mit.edu/search/?d=Mathematics

In my opinion, the physics 200 and 201 courses from Yale are better than the 8.01 and 8.02 OCW courses.

 

[jtbell]

In the US at least, many physics students learn vector calculus along with intermediate level E&M. Griffiths's widely used E&M textbook starts out with a chapter or two devoted to vector calculus.

 

[TensorCalculus]

@TensorCalculus . As an alternative to creating your own curriculum, why not just follow an established university physics curriculum? E.g. MIT has an extensive catalog of free online physics courses: https://ocw.mit.edu/search/?d=Physics&s=department_course_numbers.sort_coursenum.

I found that a lot of their courses were incomplete but you're right - some of MIT's courses are really good (especially the less niche ones, such as the ones on classical mechanics). I just sometimes don't know which ones to pick, or I'm hesitant because the lectures are very long considering the amount of information they actually seem to convey. Are there any good courses you'd suggest?

In my opinion, the physics 200 and 201 courses from Yale are better than the 8.01 and 8.02 OCW courses.

I haven't seen them yet - apart from the one you showed me - I'll take a look!

In the US at least, many physics students learn vector calculus along with intermediate level E&M. Griffiths's widely used E&M textbook starts out with a chapter or two devoted to vector calculus.

I live in England - do you think they'll still be accessible? I have got a few English textbooks for math but none of them are hugely popular/ highly reccommended

 

[CrysPhys]

I found that a lot of their courses were incomplete but you're right - some of MIT's courses are really good (especially the less niche ones, such as the ones on classical mechanics). I just sometimes don't know which ones to pick, or I'm hesitant because the lectures are very long considering the amount of information they actually seem to convey. Are there any good courses you'd suggest?

I don't know what you mean by incomplete. Subject matter (e.g., classical mechanics) is typically covered iteratively at increasing levels of difficulty over several courses (e.g., intro, intermediate, advanced, grad). My suggestion above was to follow the sequence that a physics major at MIT would take:

Their sequence for undergrad physics majors is given here: https://physics.mit.edu/academic-programs/undergrads/requirements/ (Focused Track is what you should look at). At MIT, all freshman are required to take 8.01 (intro classical mechanics) and 8.02 (intro E&M); so begin there (at MIT, physics courses start with 8). The physics curriculum then picks up from there. The physics courses list co-requisite or pre-requisite math courses. At MIT, math courses start with the number 18. There is also a large catalog of free online math courses: https://ocw.mit.edu/search/?d=Mathematics

 

[Muu9]

In the US at least, many physics students learn vector calculus along with intermediate level E&M. Griffiths's widely used E&M textbook starts out with a chapter or two devoted to vector calculus.

I'm not sure Griffiths would be appropriate for OP - I would recommend HRK and/or Fundamentals of Physics by Shankar instead, and maybe Purcell for greater depth.

 

[Muu9]

I don't know what you mean by incomplete. Subject matter (e.g., classical mechanics) is typically covered iteratively at increasing levels of difficulty over several courses (e.g., intro, intermediate, advanced, grad). My suggestion above was to follow the sequence that a physics major at MIT would take:

One issue with this is that the courses a physics major would take (8.012, 8.022 etc) often don't include both lectures and assignments, the way the OCW scholar courses do.

 

[Muu9]

I found that a lot of their courses were incomplete but you're right - some of MIT's courses are really good (especially the less niche ones, such as the ones on classical mechanics). I just sometimes don't know which ones to pick, or I'm hesitant because the lectures are very long considering the amount of information they actually seem to convey. Are there any good courses you'd suggest?

I haven't seen them yet - apart from the one you showed me - I'll take a look!

I live in England - do you think they'll still be accessible? I have got a few English textbooks for math but none of them are hugely popular/ highly reccommended

https://www.bookfinder.com/my/preferences/ - set your destination and use it to find cheap used books. You can also get ebooks anywhere (but keep in mind discussing piracy options like shadow libraries is against physicsforums rules)

 

[CrysPhys]

One issue with this is that the courses a physics major would take (8.012, 8.022 etc) often don't include both lectures and assignments, the way the OCW scholar courses do.

Not sure what your point is. For some of the courses, there are different versions (8.01_ for intro classical mechanics, 8.02_ for intro E&M), ...). For someone studying via OCW, rather than on campus, they would still follow the same sequence, using the versions available online. [ETA: Obviously, OCW students would need to skip required labs, which are not available online.]

 

[TensorCalculus]

Their sequence for undergrad physics majors is given here: https://physics.mit.edu/academic-programs/undergrads/requirements/ (Focused Track is what you should look at). At MIT, all freshman are required to take 8.01 (intro classical mechanics) and 8.02 (intro E&M); so begin there (at MIT, physics courses start with 8). The physics curriculum then picks up from there. The physics courses list co-requisite or pre-requisite math courses. At MIT, math courses start with the number 18. There is also a large catalog of free online math courses: https://ocw.mit.edu/search/?d=Mathematics

(sorry, didn't see this before somehow) - I never considered taking a course on math, for some reason - and you're right, the catalog is quite large.

I don't know what you mean by incomplete. Subject matter (e.g., classical mechanics) is typically covered iteratively at increasing levels of difficulty over several courses (e.g., intro, intermediate, advanced, grad)

Some of the courses only have lecture notes that cover half the syllabus, then for the rest it says something like lecture notes not available, or some courses only have question sets which is obviously not very useful if you don't know the material to begin with. Most are quite good though.

https://www.bookfinder.com/my/preferences/ - set your destination and use it to find cheap used books. You can also get ebooks anywhere (but keep in mind discussing piracy options like shadow libraries is against physicsforums rules)

oh wow - yeah. I used to just buy second hand books off ebay but this is actually so good!

Not sure what your point is. For some of the courses, there are different versions (8.01_ for intro classical mechanics, 8.02_ for intro E&M), ...). For someone studying via OCW, rather than on campus, they would still follow the same sequence, using the versions available online. [ETA: Obviously, OCW students would need to skip required labs, which are not available online.]

Do they also have required math courses to take alongside these? Looking at some of the classical mechanics courses, it doesn't seem like they'd be able to cover all the content with just the math they learn pre-uni (so A-level or Equivalent), especially once you get onto things like Lagrangian/Hamiltonian Mechanics, which show up in mechanics 2.

 

[Muu9]

(sorry, didn't see this before somehow) - I never considered taking a course on math, for some reason - and you're right, the catalog is quite large.

Some of the courses only have lecture notes that cover half the syllabus, then for the rest it says something like lecture notes not available, or some courses only have question sets which is obviously not very useful if you don't know the material to begin with. Most are quite good though.

oh wow - yeah. I used to just buy second hand books off ebay but this is actually so good!

Do they also have required math courses to take alongside these? Looking at some of the classical mechanics courses, it doesn't seem like they'd be able to cover all the content with just the math they learn pre-uni (so A-level or Equivalent), especially once you get onto things like Lagrangian/Hamiltonian Mechanics, which show up in mechanics 2.

For the math:
https://ocw.mit.edu/courses/18-01sc-single-variable-calculus-fall-2010/
https://ocw.mit.edu/courses/18-02sc-multivariable-calculus-fall-2010/
For introductory physics, Kevin Zhou recommends Phys 200/201 from Yale over MIT's 8.01SC and 8.02SC: https://knzhou.github.io/writing/Advice.pdf

 

[TensorCalculus]

For the math:
https://ocw.mit.edu/courses/18-01sc-single-variable-calculus-fall-2010/
https://ocw.mit.edu/courses/18-02sc-multivariable-calculus-fall-2010/
For introductory physics, Kevin Zhou recommends Phys 200/201 from Yale over MIT's 8.01SC and 8.02SC: https://knzhou.github.io/writing/Advice.pdf

Yes - this looks really good (and the courses seem to have a lot of resources too which is nice). What's better about the Yale courses in comparison to the MIT ones for physics, do you know? (also - I know I've said this multiple times but thank you all so much for the help - I've been stuck for so long and this has all really helped me)

 

[Muu9]

Yes - this looks really good (and the courses seem to have a lot of resources too which is nice). What's better about the Yale courses in comparison to the MIT ones for physics, do you know? (also - I know I've said this multiple times but thank you all so much for the help - I've been stuck for so long and this has all really helped me)

You can check out both to compare, but I feel the Yale course is more engaging - the OCW mechanics course give Khan Academy vibes. There also no e&m or thermo course with all the features that the OCW mechanics course does.

 

[Homelilly]

Read "advice for introductory physics" by Kevin Zhou

For a textbook, look at Halliday Resnick Krane, 5th edition

https://oyc.yale.edu/physics/phys-200

https://compos.web.ox.ac.uk/

Do you know if the except students from US? I see that only UK students apply, but in the tuition fees, they mention about non-UK students. Thanks for help!

 

[WWGD]

You can check out both to compare, but I feel the Yale course is more engaging - the OCW mechanics course give Khan Academy vibes. There also no e&m or thermo course with all the features that the OCW mechanics course does.

What are " Khan Academy vibes"? I've heard of them but I haven't seen any of their videos.

 

[Muu9]

What are " Khan Academy vibes"? I've heard of them but I haven't seen any of their videos.

Basically they're short clips of a man talking to a screen:

While the Yale courses are full lectures: https://oyc.yale.edu/physics/phys-200/lecture-5

 

[TensorCalculus]

You can check out both to compare, but I feel the Yale course is more engaging - the OCW mechanics course give Khan Academy vibes. There also no e&m or thermo course with all the features that the OCW mechanics course does.

Oh - ok. That makes sense, and I do really need to get a good thermo course (I literally know like ideal gases things (eg. maxwell boltzmann distribution, ideal gas law) and entropy and that's it haha)

Do you know if the except students from US? I see that only UK students apply, but in the tuition fees, they mention about non-UK students. Thanks for help!

yeah I did take a look at the fees because I have friends internationally and was going to tell them about it. They allow international/privately educated students in for a fee of £25 a week (when it is live)

 

[Muu9]

This is a good book on thermodynamics: https://www.amazon.com/Block-Histor...hermodynamics/dp/0198851553?tag=pfamazon01-20
OYC physics 200 also covers thermodynamics

 

[Klystron]

Does anyone have any resources they would recommend to me (my interest particularly lies around astronomy and electromagnetism) , or any advice to give?

Electromagnetism (EM) also has a practical physical side of great value to understanding modern physics. Cognizant of safety rules, if you are able, set up a work area perhaps shared with likeminded serious people, and explore electronic devices and simple projects.

I was thirteen 60 years ago so my examples are dated but you can find modern inexpensive equivalents. I operated a HAM radio transmitter/receiver built with my sister from a kit. We both learned Morse code that came in handy in computer science. I rewired a stereo FM receiver for quadraphonic (4 speaker), added audio from an old B&W television, then designed and built a remote control from a few parts. I helped repair electric appliances and learned how toasters, refrigerators, and TVs operated.

If hands-on physics appeals to you, PF has a a do-it-yourself (DIY) forum with many modern projects. Always underfunded as a teen, consider surplus and second-hand equipment. I imagine local RAF and Royal Navy bases encourage young scientists with workshops, surplus EM gear and old textbooks and manuals. As a teen in Silicon Valley (Santa Clara County, CA) I attended science fairs, open houses and workshops at SRI International and NASA Ames Research Center, later working at both as an adult software engineer. UK contains many research centers.

Astronomy and cosmology teach us so much about the Universe. I shared a basic reflector telescope with my sister, sketching moons while she photographed using a home made adaptor. We also attended shows at our local planetarium and visited Wilson observatory a top Mount Lick. Consider Isaac Newton experimented with Optics while co-inventing Calculus.