Learning Advanced Topics in Physics: A Step-by-Step Guide

[Spectrum47]

Hello,

I have a question about learning advanced topics in physics. To start, I am currently working through introductory calculus and physics (calculus-based), and I will eventually get into linear algrebra. However, I do not know what to do in order to learn, say, introductory quantum physics or the next level of physics that is available for me. This is a hobby more or less so I have no curriculum to follow.

In other words, what mathematical material (vector calculus, differential calculus, etc.) is required for learning advanced topics in physics? And, can this be explained in a step-by-step manner or do I need to choose several topics in different subjects (random)?

Thank you.

 

[diazona]

Once you've got linear algebra and some basic multivariable calculus covered, you should be reasonably well prepared to learn quantum mechanics. In fact, multivariable calculus, differential equations, and linear algebra (and a basic familiarity with complex numbers) are more or less all you need to know for most of the topics that are covered in a typical college curriculum for physics majors.

For more advanced (graduate-level) specialized physics topics, you might need to know more specialized math topics like complex analysis, group theory, or differential geometry, but don't worry about that now.

 

[Naty1]

A lot depends on what you want to learn/study,the depth of understanding you seek, what you mean by "advanced" and your ability to learn on your own. If you want to be able to work specific mathematical solutions in many areas of "advanced" physics, you need the math; but if you seek only concepts you can learn a great deal without all the mathematics.

I'm retired and decided about six or eight years ago to renew my interest and reading in physics...I spent summers on my boat and could read four or so hours of physics daily...and relax and really enjoy it...I have some graduate level mathematics and electrical engineering along with undergraduate nuclear reactor theory (nuclear physics) and general physics from many years ago... Just the beginnings of relativity...interestingly, the information theory I studied in graduate school for engineering gave me a lot of insights into information theory in physics, entropy, and things like the holographic principle, black hole horizons, and at least the ability to understand some of the information based theories of our universe.

I started by buying/studying books like Hawking Theory of time, Kaku's Hyperspace, Green's Fabric of the Cosmos, Einstein's Relativity and maybe 15 or 20 others...somewhere along the line I did begin to study some graduate level mathematics, but found it far less interesting than the theoretical conclusions the above experts drew from even more advanced math... I also found substantial disagreements about what the math meant among he various authors...so I decided I'd do better by comparing expert opinions of the math rather than under taking years of math studies on my own and then trying to compare my independent conclusions with those of experts.

So maybe a way to proceed is to read some of the books yourself, see what theories are of special interest, then perhaps study some underlying math. And read posts here and see which interest you. One thing for sure: you'll have a lot of thinking to do whichever way you proceed. It's easy to look at a formula like F=Ma and think you understand it...then you'll read insights from great physicsts who REALLY do understand it...that's often amazing. And reading about, for example, Einstein's struggles with his college friend and once fellow student Marcel Grossman to pin down the math needed for General Relativity is equally fascinating...They went round in circles for maybe five years or so!

Hope the above gives you some ideas on possible approaches, good luck.

 

[Spectrum47]

To start, I apologize for putting this in the wrong forum and am glad to see that it was moved to the right place.

Thanks diazona, and I think I'll look into those topics then. But, what topics are covered for a college curriculum in physics? I'm just curious as I want to look into those as well.

To Naty1: I just want to understand the math behind introductory topics in advanced physics (anything higher than an introduction to physics itself). I'll look into those books as well as they sound very interesting, though, thank you. So far I've only subscribed to certain science-based magazines. I'm not going to go that far ahead and say that I'd like to be able to understand graduate-level physics because I know that the math required to know it will take more time to learn and I might as well have changed my major.

 

[jtbell]

But, what topics are covered for a college curriculum in physics?

Most colleges and universities list the requirements for their physics degree on their web site. Generally, there is a "core" group of required courses (above the introductory courses) that usually includes classical mechanics, E&M, thermodynamics and QM. Courses beyond those are electives that the student choses to fit his/her interests.