Exploring essential math courses for undergraduate physics majors

[Immanuel Can]

After this coming semester I will have Vector Calc, Intro to ODEs, and Intro to Linear Algebra under my belt. What math essentials for undergrad physics will there be left for me to do? The department at my uni doesn't have any requirements after these(LinAlg actually isn't a requirement at all), other than a 200 level math methods class. There are 400 level DE and LinAlg classes but I think they are proof based.

 

[bcrowell]

None. Take Shakespeare and Chinese history.

 

[id the sloth]

PDEs, Probability, and a complex variables course should be useful but not too necessary. Physics courses where I go tend to teach you the math as you need it, but they may not be as effective as they want to be. It really depends on the professor. Special functions may come in handy if you have a course in them, you run into them as solutions to PDEs in physics courses. Some schools offer a course on Mathematical Physics too. If you are willing to self study I recommend the book "Mathematical Methods for the Physical Sciences" by Mary Boas. It covers pretty much all the math you will need as an undergraduate. It's not very rigorous book, but it is a pretty good one for physics students. Plenty of physical examples, solutions in the back (not too all problems however), and it tries to build off physical intuition.

As for classes that would be useful, Boas on covers analytic methods, so a course on Numerical Analysis, Scientific Computing, or Computational Physics should be helpful. There will often be times in practice where you cannot get an analytical solution to differential equations, when you want to analyze data, or run a simulation which is what is typically taught in these kind of courses.

That is really all I can think of, hope it helps.

 

[Immanuel Can]

PDEs, Probability, and a complex variables course should be useful but not too necessary. Physics courses where I go tend to teach you the math as you need it, but they may not be as effective as they want to be. It really depends on the professor. Special functions may come in handy if you have a course in them, you run into them as solutions to PDEs in physics courses. Some schools offer a course on Mathematical Physics too. If you are willing to self study I recommend the book "Mathematical Methods for the Physical Sciences" by Mary Boas. It covers pretty much all the math you will need as an undergraduate. It's not very rigorous book, but it is a pretty good one for physics students. Plenty of physical examples, solutions in the back (not too all problems however), and it tries to build off physical intuition.

As for classes that would be useful, Boas on covers analytic methods, so a course on Numerical Analysis, Scientific Computing, or Computational Physics should be helpful. There will often be times in practice where you cannot get an analytical solution to differential equations, when you want to analyze data, or run a simulation which is what is typically taught in these kind of courses.

That is really all I can think of, hope it helps.

Thanks Ill check that book out. Is it at all similar to this one?

https://www.amazon.com/dp/0486600564/?tag=pfamazon01-20

I came across that one at a used bookstore for like 5$ and picked it up. At my uni all physics majors have to take a scientific computing and computational physics course, so I'm good on that.

 

[jasonRF]

PDEs, Probability, and a complex variables course should be useful but not too necessary.

I agree with id the sloth on these topics and that it isn't 100% crucial you take them, unless you really enjoy math, in which case you should take what sounds like fun (I took all three of those classes and really enjoyed them). Also, it sounds lilke you are probably a 2nd year student? There isn't really a rush if that is the case. You can always decide to add a course or two later on in your schooling as you figure out what your next step might be. If you eventually decide you want to go to grad school, talk with your advisor about what he/she would recommend. If you eventually decide you want to go into industry, I would recommend a calculus based probability theory class, but again you have time to decide these things and if you don't take such a course it would typically not be a gigantic deal breaker for most potential employers.

If you want to self study some of this, a free book that covers basic mathematical methods for physics is:
http://www.physics.miami.edu/~nearing/mathmethods/
I think it is quite good.

Best wishes,

jason

 

[Immanuel Can]

None. Take Shakespeare and Chinese history.

How about Shakespeare on Chinese history?

I agree with id the sloth on these topics and that it isn't 100% crucial you take them, unless you really enjoy math, in which case you should take what sounds like fun (I took all three of those classes and really enjoyed them). Also, it sounds lilke you are probably a 2nd year student? There isn't really a rush if that is the case. You can always decide to add a course or two later on in your schooling as you figure out what your next step might be. If you eventually decide you want to go to grad school, talk with your advisor about what he/she would recommend. If you eventually decide you want to go into industry, I would recommend a calculus based probability theory class, but again you have time to decide these things and if you don't take such a course it would typically not be a gigantic deal breaker for most potential employers.

If you want to self study some of this, a free book that covers basic mathematical methods for physics is:
http://www.physics.miami.edu/~nearing/mathmethods/
I think it is quite good.

Best wishes,

jason

Thanks for that link. I'll definitely work through some of that.

 

[id the sloth]

Thanks Ill check that book out. Is it at all similar to this one?

https://www.amazon.com/dp/0486600564/?tag=pfamazon01-20

I came across that one at a used bookstore for like 5$ and picked it up. At my uni all physics majors have to take a scientific computing and computational physics course, so I'm good on that.

Judging by this review:

https://www.amazon.com/dp/0486600564/?tag=pfamazon01-20

"Regarding the choice of topics, the book lacks a decent presentation of the special functions of mathematical physics, analytic functions, and integral equations, and nothing is said about Hilbert space (even if only to put orthogonal polynomials into a more unifying perspective...), generalized functions, Green's functions, continuous groups, etc."

It covers plenty of material (a steal for 5 bucks!) but not all. It should be helpful :)

 

[niklaus]

I'd do the proof based Linear Algebra class, you can never know too much LinAlg.

 

[id the sloth]

I'd do the proof based Linear Algebra class, you can never know too much LinAlg.

I think it's a good idea too. Introductory linear algebra focuses on column vectors and such. My friend took a proof based one and it generalizes everything, like treating functions as vectors. It's very useful for quantum mechanics and solving differential equations. I wouldn't say it was necessary though, I learned the advanced linear algebra I needed in quantum mechanics.