Physics & Math Major Guide | Leon Pierre

[LeonPierreX]

Hello, My name is Leon Pierre, and I am a physics major . I want to double major both in physics and math. My main goal is to be a mathematical physicists , who works in the fields dealing with electromagnetism and quantum mechanics. I am trying to figure out which topics of mathematics am I to study. Anyone can help and guide me ? I really appreciate it Thank you :)

 

[bhobba]

Hi Leon

This really belongs in the academic guidance section and the mods probably will move it there.

I actually did a degree in applied math, not physics, and self taught myself physics, so I feel from experience I can point you in the direction of the math I studied that was useful in that endeavour.

First, if you want to study math and call yourself a mathematician of some sort, eg a mathematical physicist etc, then you must do your epsilonics which is colloquial for mathematical analysis ie the rigorous study of calculus. No need to go really deep into it but you need to know things like the pinching theorem, what being dense means etc. That's so you can understand proofs like the following:
https://www.physicsforums.com/showthread.php?t=758125

Aside from that I would say:
Linear Algebra
Multivariable Calculus
Group Theory
Complex Analysis
Advanced Ordinary Differential Equations
Partial Differential Equations
Hilbert Spaces
Probability and Statistics (the deep theory isn't required - ok if you do it - but an understanding of the basic axioms and statistical inference - they would be courses like Probability and Statistics for Scientists and Engineers)

By self study, better if there is a course in it, but there usually isnt, knowledge of Distribution Theory:
https://www.amazon.com/dp/0521558905/?tag=pfamazon01-20

Its simply the best way to understand Fourier theory, but even aside from that it allows you to get a grasp of the dreaded Dirac Delta function used a lot in QM.

Thanks
Bill

 

[LeonPierreX]

Thank You Bill :) I really appreciate it .

 

[Matterwave]

Bill's list is quite good, but I feel it focuses on the needs of quantum mechanics. You said you also want to do electromagnetism, well, there's actually a few different formulations that require different mathematical knowledge. For an ordinary physicist the regular integral and differential formulations of maxwells equations only require multivariable calculus and vector calculus. In addition the in medium equations and such requires very similar mathematics. These areas Bill has already listed. I do want to mention though that there are additional formulations of the maxwells equations in the language of tensors (the Faraday tensor) and differential forms that would require knowledge of differential geometry and the calculus of differential forms. For a normal physicist these additional formulations are not super necessary and can be skipped. The normal formulations serve all practical and calculational needs quite nicely. But if you want to know more deeply the mathematical and geometrical structure of electromagnetism, then you need to learn this as well.

 

[bhobba]

For a normal physicist these additional formulations are not super necessary and can be skipped. The normal formulations serve all practical and calculational needs quite nicely. But if you want to know more deeply the mathematical and geometrical structure of electromagnetism, then you need to learn this as well.

That's true.

But I can't resist mentioning a book that does all this, and much more beside:
http://matrixeditions.com/UnifiedApproach4th.html

It covers, in an integrated whole:
Basic Analysis
Differential Forms
Linear Algebra
Vector Calculus
Lebesque Integration and Measure Theory - needed for understanding Hilbert Spaces.
Even a good bit of rigorous probability theory in the proper context of measure theory.

I have the third edition - absolutely superb.

Get one for your library - you will not regret it.

Their book on functional anaysis (that's Hilbert spaces and such) is also by reputation excellent:
http://matrixeditions.com/FunctionalAnalysisVol1.html

But haven't got a copy myself, so can't directly speak to it, but have been meaning to get a copy for a while.

Think I will do it now while I remember.

With both those books you will have covered a good deal of what you need to know.

Added Later:
Just ordered it - like I said been meaning to do it for a while.

Thanks
Bill

 

[LeonPierreX]

This is awesome :) I really appreciated guys. I was bit confuse on how to approach on what to study, but you guys simplified it for me . Thank you :)

 

[LeonPierreX]

I have another question. And this is for those who take physics seriously. I want some few pointers on how to approach problems when working on one . What do you do when you are stuck and don't fully comprehend the problem ? ( For Experts and those who are serious.) Anyone

 

[Rocket50]

I have another question. And this is for those who take physics seriously. I want some few pointers on how to approach problems when working on one . What do you do when you are stuck and don't fully comprehend the problem ? ( For Experts and those who are serious.) Anyone

Ask on here for how to start the problem or look online at the first few lines of the solution? Maybe also try to go through the section again.

 

[LeonPierreX]

Thanks . I somewhat understand. This is not a homework problem. I'm working on some problems just for practice. Thanks I really appreciate it .

 

[jtbell]

Even though it's not a class assignment, we consider such questions (asking for help on specific exercises) to be "homework" which need to be posted in the homework help forums. I moved your question and Rocket50's answer into a new thread titled "Relative Velocity Problem" in the "Introductory Physics Homework forum:"

https://www.physicsforums.com/showthread.php?t=771410

 

[LeonPierreX]

Alright. Will do. And thanks for the links .