Recommendations for study materials to prepare for undergrad Physics

[rajsekharnath]

TL;DR Summary: Here I am asking for some opinions and recommendations for mathematically rigorous books that should be taken as an interested physics student. I know the question is quite subjective but any insightful answer is appreciated.

I am willing to join undergraduate physics classes this august, being specific I want to know what level of mathematical rigour I need to outperform in the "physics", like should I take some courses(self-study) on the mathematics generally math majors take?

For example few days ago I came across Vector Analysis in the first chapter of Griffith's Electrodynamics book, then willing to know more on that topic I got to know about the book Vector Calculus by Susan Jane Colley, I studied some of the former chapters of that book and enjoyed the mathematics.So basically my question is do I need to do the same for the other mathematical topics required for physics like linear algebra, variational calculus, complex analysis, tensor analysis, differential geometry and so on?

My main interest is in physics although I enjoy the mathematics also and want to know about the math in some more depth than ordinary folks. Finally to conclude, will studying the mathematics with that much rigour will even benefit me? Like will it give me an extra edge later in my post-graduate studies and my career?

Also recommendations of books for the above mentioned math topics for the level of rigour I am asking for will be beneficiary

 

[Choppy]

Developing a solid foundation in mathematics is certainly going to be an advantage to you in studying physics, however, I would argue that you don't have to overboard in terms of preparation if you haven't started your undergraduate courses yet.

If you're about to start undergraduate physics, I would suggest that you look up the textbooks that you're going to be using in your classes and start working your way through those. If you somehow get through those, then go for the advanced stuff. Read up on the material that you're really interested in, the stuff that drives you. If that happens to be vector calculus, then great!

Just keep in mind that there are a lot of other dimensions to having a successful career in physics as well... things like the ability to organize, sustain, and bring to completion a long-term project , writing skills, collaboration skills, programming skills, presentation skills, etc. And it's just as important to develop those.

 

[hutchphd]

I would echo @Choppy: I think your idea to prepare maths is a good one, and right now you have the luxury of time to "follow your nose". Generally the subjects you will most need to know are vectors and vector calculus, rudimentary linear algebra, and differential equations and so those should be your basics. But if you get interested in, say, variational methods, then spend some time there. You have the internet and the luxury of time. Soon your life will be less luxurious!

 

[Vanadium 50]

August is what, six or seven weeks away? It's not realistic to cover "books" in that time. It's also not necessary to handle math at the level needed for Griffiths as a freshman.

I would a) review what you learned in high school, and try to improve the areas where you are weakest, and b) get ready to live on your own. Can you balance a checkbook? Make a budget? Navigate the subway? Do you have the right attire for college, which may have a very different climate than home? (Edmonton is not Honolulu!) This trips students up more than being "only" 18 months ahead in math and not 24.

 

[jtbell]

If you're about to start undergraduate physics, I would suggest that you look up the textbooks that you're going to be using in your classes and start working your way through those.

For example few days ago I came across Vector Analysis in the first chapter of Griffith's Electrodynamics book

In the US, undergraduates don't start out with Griffiths. We don't get to that level until second or third year. Maybe it's different where you are.

 

[rajsekharnath]

In the US, undergraduates don't start out with Griffiths. We don't get to that level until second or third year. Maybe it's different where you are.

@jtbell I am from India

 

[rajsekharnath]

Developing a solid foundation in mathematics is certainly going to be an advantage to you in studying physics, however, I would argue that you don't have to overboard in terms of preparation if you haven't started your undergraduate courses yet.

If you're about to start undergraduate physics, I would suggest that you look up the textbooks that you're going to be using in your classes and start working your way through those. If you somehow get through those, then go for the advanced stuff. Read up on the material that you're really interested in, the stuff that drives you. If that happens to be vector calculus, then great!

Just keep in mind that there are a lot of other dimensions to having a successful career in physics as well... things like the ability to organize, sustain, and bring to completion a long-term project , writing skills, collaboration skills, programming skills, presentation skills, etc. And it's just as important to develop those.

That was quite insightful, thank you.

 

[PeroK]

You could work your way through Paul's online maths notes:

https://tutorial.math.lamar.edu/

That would probably be time well spent.