What should the Mathematics requirements be for a Physics degree

[stefan r]

@stefan r and @symbolipoint -- let's please stay on-topic for the OP's question. Thanks.

What should the Mathematics requirements for Physics degree really be?...

My answer was very much on topic: 3 years calculus and linear algebra. More requirements diminish the "degree".

You are, of course, welcome to disagree. My being wrong does not imply that I am talking about the wrong subject. Natural science professors tend to think their majors should be bigger. Humanities professors usually state the opposite position. This argument really happens at colleges and universities.

The original post also had this question:

Why then, are these not listed as the official requirements for the degree?

Listing off lots of possible math courses does not answer that question at all.

Physics and Mathematics professors at colleges and universities try to add more mathematics requirements. Professors from other departments block those proposals. Reasons are stated more eloquently than I am likely to be capable of.

 

[Mark44]

@stefan r, your post #27 was off-topic, and was the reason @berkeman listed your name. The title of this thread is "What should the Mathematics requirements be for a Physics degree" -- (emphasis added).

English/writing so that they can write decent papers. Economics/business and maybe political sci so they can run a lab. History/social sci so they know when they are why. Psychology and communications also to run a lab. Some phys ed because brains need food and exercise and also because this is easy to work into a schedule.

Also, what does "History/social sci so they know when they are why" mean?

 

[symbolipoint]

@stefan r, your post #27 was off-topic, and was the reason @berkeman listed your name. The title of this thread is "What should the Mathematics requirements be for a Physics degree" -- (emphasis added).

Also, what does "History/social sci so they know when they are why" mean?

Right. berkman does have a point. This point can be made better if done as a separate topic. Some departments and universities seem to like to ADD a separate WRITING course supposedly suited to a particular major field. My belief is that such a separate course should not be needed, since the major field's program should have some significant report-writing as part of more than one of the major-field's courses. A very significant routine lab exercise in some phys sci courses is the writing of formal lab reports. Any student can easily adapt to these. Note that one of the "humanities" areas is the courses which emphasise modern foreign languages; which definitely bring up instruction about both CULTURE & HISTORY, and also the workings of the LANGUAGE. The student will then develop some precise language translation, which is much like what we do mathematically anyway in our physical sciences. When "we" do this, it is between a described or representable physical situation and mathematical expressions and equations.

 

[bhobba]

I only did a very basic statistics course at first year level yet as an applied physicist, I would have benefited from far more depth in statistics.

Yes - I originally only did the minimum required which believe it or not were 4 subjects - Mathematical Statistics !A, 1B, 2A, 2B. Didnt like it much personally, but the lecturer for the advanced subjects was great - I even remember his name - Dr Ogalvie. I really liked him so, not because I liked stats much, but purely because I liked him , I did 3A and 3B. Turned out to be a very good choice not only for physics but for computing later on - they wanted all these statistical reports etc and it was great to know the background behind them. Not to 3A and 3B level, but it was very useful in understanding QM and it's probability bit such as exactly what does the Heisenberg Uncertainty Principe mean. - you need to know and understand variance for that one.

Thanks
Bill

 

[Charles Link]

Besides having courses in advanced calculus, differential equations, and complex variables as an undergraduate physics major, I also had a course in Probability Theory given by the Mathematics Department. One of the most useful things about probability theory is the concept of the distribution function, $F(x)=P(X \leq x)$ compared with probability density function $f(x)=F'(x)$. This concept is very useful in a number of places, including particle scattering, where a section (area ) on the target $\sigma$ maps into a solid angle $\Omega$. (Thereby concepts like the differential scattering cross section $\frac{ d \sigma}{d \Omega}$ are much more readily understood). And I do think in this area, the mathematicians generally have at least a slight edge over most physicists in presenting material such as this. $\\$ The mathematical concepts presented in the Probability course have also been very useful in understanding things such as the Planck spectral function for blackbody radiation, as well as the Maxwell/Gaussian type distribution (density) functions of particle velocities. The Probability course also covered the Standard Normal Distribution function, including how to normalize a function of the Gaussian form. The various probability concepts, including binomial trials, etc., and discrete distributions were also very good things to have learned. I would recommend that anyone who is serious about their physics education have such a course as soon as possible after the basic calculus sequence. Whether such a course should be made a requirement I think would depend somewhat on the academic ranking of the university. I think a really top notch program could do well to have such a course be part of their graduation requirements. $\\$ Editing: And although it might start to be a somewhat heavy load from the math department if the advanced calculus, differential equations, and complex variables courses were required, I think it could be advantageous to have them be required. I still am of the opinion that a course in Linear Response Theory and Fourier transforms should be a requirement as mentioned in post 26. I had one additional course from the mathematics department as an undergraduate, besides those mentioned above, and that was Linear Algebra and Matrices. That, IMO, was the least important of all of these courses. A course in Linear Response Theory and Fourier Transforms would have been much more beneficial than the Linear Algebra and Matrices course.

 

[Jenab2]

Linear algebra, probability and statistics, Fourier and Laplace transforms, vector calculus, and partial differential equations.

 

[AgentSmith]

It depends on how your physics courses are organized. There are bits of math needed here and there that can be fit into a physics course. But you need a minimum of ODE, Linear Algebra, some PDE, some tensor analysis. Its possible to take ODE and linear algebra, then a two semester course in physical mathematics involving PDE, vector analysis. complex analysis, tensors, abstract algebra. A separate and serious sequence in experimental methods & data analysis should be required.
In my opinion, to which I give considerable weight, an applied mathematics degree with a year of intense physics work is also feasible. It just depends. There is no single answer, beyond the minimum most people take anyway.