Is it necessary for theoretical physics students to take a course in PDE?

[Jamestein Newton]

By PDE. The book written by Walter Alexander Strauss perfect described a typical undergraduate PDE course I have in my mind.

It should at least include:
Laplace equations, waves and diffusions
reflection, boundary problems, Fourier series

The content of the book I mentioned can also be found on
https://www.wiley.com/en-us/Partial+Differential+Equations:+An+Introduction,+2nd+Edition-p-9780470054567

Indeed, Algebraic structures(Lie groups), Differential geometry, Complex analysis, and PDE are all essential for a theoretical physics student. I think such a student should take all the courses I mentioned above. It's the minimum
But what's better? Are there any alternative paths on course choosing?

 

[hutchphd]

To know what is the perfect preparation for future discovery would require one to presage future discovery. Better that one apprehend a sampling of things that are most interesting thereby facilitating deep knowledge that may prove valuable. I fear the rest is a crapshoot. But you will enjoy the experience!

 

[Jamestein Newton]

To know what is the perfect preparation for future discovery would require one to presage future discovery. Better that one apprehend a sampling of things that are most interesting thereby facilitating deep knowledge that may prove valuable. I fear the rest is a crapshoot. But you will enjoy the experience!

I agree with you that students should not be so "calculated" while they should also aim at having a list of subjects to build the solid foundations when they are in undergraduate

 

[Orodruin]

It is not really clear to me what you are asking. Your title states one question, but then you seemingly answer that question in your post:

Algebraic structures(Lie groups), Differential geometry, Complex analysis, and PDE are all essential for a theoretical physics student. I think such a student should take all the courses I mentioned above. It's the minimum

As for:

But what's better? Are there any alternative paths on course choosing?

What do you mean by better?

 

[haushofer]

I never did. And I turned out OK.

 

[Jamestein Newton]

It is not really clear to me what you are asking. Your title states one question, but then you seemingly answer that question in your post:

As for:

What do you mean by better?

Yes I stated my opinion and I was looking for a random discussion

 

[Orodruin]

Do you need to take a course? No.
Are PDE solving skills useful? Yes. Very much so.

 

[gwnorth]

Apparently my son's professors seem to think so since it's covered as part of the mandatory 3rd year Mathematical Physics I course for all Physics majors at his school and is also part of the standard curriculum for Physics majors at other Canadian universities as well.

Mathematical Physics I

Eigenvalue problems, Fourier transforms, special functions, spherical harmonics, partial differential equations, boundary value problems.

 

[Orodruin]

... now if only someone wrote a good book about all of this aimed at physicists ...

 

[vela]

Apparently my son's professors seem to think so since it's covered as part of the mandatory 3rd year Mathematical Physics I course for all Physics majors at his school and is also part of the standard curriculum for Physics majors at other Canadian universities as well.

Mathematical Physics I

Eigenvalue problems, Fourier transforms, special functions, spherical harmonics, partial differential equations, boundary value problems.

It's the same in the US as far as I know. I guess I would take the OP's question to mean "Is it worth taking a course on PDEs aimed at mathematicians?"

 

[MidgetDwarf]

Depends on the students ability and goals. I am a firm believer that when a student enters their 2 to 3rd year of whatever field of study. That they SHOULD have the skills necessary to teach themselves skills needed for coursework/field of study.

SO YES, it would be a good idea. But one can self-learn it.

 

[MathematicalPhysicist]

Depends on the students ability and goals. I am a firm believer that when a student enters their 2 to 3rd year of whatever field of study. That they SHOULD have the skills necessary to teach themselves skills needed for coursework/field of study.

SO YES, it would be a good idea. But one can self-learn it.

Well, you can self-learn all the courses...
But in the end the degree needs certain courses to be taken from a list of courses.

 

[Orodruin]

Well, you can self-learn all the courses...
But in the end the degree needs certain courses to be taken from a list of courses.

I mean, the obvious answer to the question in the thread title is ”if it is mandatory in the degree”. However, I feel like this is not the actual question being asked...

 

[MathematicalPhysicist]

I mean, the obvious answer to the question in the thread title is ”if it is mandatory in the degree”. However, I feel like this is not the actual question being asked...

Yes, I know. The real question is :"Is it helpful for theoretical physicist to know the matter covered in the PDE course?" I guess it cannot hurt; but then again if you don't need it now how would you find time for learning it?

 

[Jamestein Newton]

I mean, the obvious answer to the question in the thread title is ”if it is mandatory in the degree”. However, I feel like this is not the actual question being asked...

In recent days I had an in-depth conversation with a famous researcher who does theoretical physics and is heavily math inclined and he's doing something "both edge-cutting math and edge-cutting physics". He believes that the four most important undergraduate mathematics courses are functional analysis, differential geometry, algebraic topology, and algebraic geometry.

 

[gwnorth]

It might be difficult to fit all those topics into a standard Physics degree as standalone courses, though some topics will be covered either in the requisite math courses or embedded into other Physics courses. I'm also not sure that all those topics would be required at an undergraduate level, even for those students choosing to continue their studies in graduate school. Certainly some could be included as part of the mandatory course work included in the graduate degree once a student has a stronger idea of what specific area of Physics they may wish to focus on.

As much as an undergraduate degree is structured around a major, I believe that that major should provide a broad based grounding in the fundamentals of the subject with some leeway to specialize and focus studies towards areas of specific interest in upper years. Undergraduate studies should allow for some breadth of study both within and outside of the major. Beyond that, deeper specialization might be better left to graduate studies.

 

[symbolipoint]

Yes, I know. The real question is :"Is it helpful for theoretical physicist to know the matter covered in the PDE course?" I guess it cannot hurt; but then again if you don't need it now how would you find time for learning it?

Not just the post quoted above, but the whole topic now reminds me of the typical Algebra 1 question which students often enough ask: "When will I use this?"

 

[Jamestein Newton]

It might be difficult to fit all those topics into a standard Physics degree as standalone courses

If we are telling Algebraic structures(Lie groups), Differential geometry, Complex analysis, and PDE. I have seen many physics students able to take all those courses.

 

[gwnorth]

If we are telling Algebraic structures(Lie groups), Differential geometry, Complex analysis, and PDE. I have seen many physics students able to take all those courses.

Presumably if it was felt that all of those topics were absolutely necessary to the fundamental learning of Physics at an undergraduate level they would already be mandatory to the degree, and in my experience, both Complex Analysis and PDE are. Beyond that, the question then becomes are there additional topics that would be of value, and the answer to that will depend on the individual goals of the student. That's why electives exist.

 

[Jamestein Newton]

Presumably if it was felt that all of those topics were absolutely necessary to the fundamental learning of Physics at an undergraduate level they would already be mandatory to the degree, and in my experience, both Complex Analysis and PDE are. Beyond that, the question then becomes are there additional topics that would be of value, and the answer to that will depend on the individual goals of the student. That's why electives exist.

Yes and in the original post I mentioned they are "the minimum requirements" for theoretical students. Though there are different kinds of theoretical students but you know.

The target we are discussing so long are "theoretical students".

For complex analysis and PDE they are used among the core courses "mechanics, EM, QM, stat mech". They are just fundamental. Elective for all students but necessary for general theoretical students

Even you don't see a student taken Complex Analysis, PDE. You'll normally see it in a course on "mathematical methods"

Fun fact: in some country like some of the German, and almost all china physics students(they have to follow most of the curriculum set by the Ministry of Education. Courses even have same names among different schools) take "analysis, abstract algebra, probability theory in their first year. pde in later years"

 

[gwnorth]

I think you've misunderstood me. I stated that Complex Analysis and PDE are core requirements of undergrad Physics degrees.

 

[symbolipoint]

I think you've misunderstood me. I stated that Complex Analysis and PDE are core requirements of undergrad Physics degrees.

Is this a change from about 30 years ago? I remember seeing the officially listed course requirements as something like Calculus 1,2,3, and some combination-course of differential equations & linear algebra; but no others. That did not mean students who were aware enough wouldn't also enroll in more Mathematics course - only that they were required to at least enroll in the officially listed required courses.

 

[vela]

Is this a change from about 30 years ago? I remember seeing the officially listed course requirements as something like Calculus 1,2,3, and some combination-course of differential equations & linear algebra; but no others. That did not mean students who were aware enough wouldn't also enroll in more Mathematics course - only that they were required to at least enroll in the officially listed required courses.

Typically, physics majors are required to take a math methods course, which covers topics like PDEs and complex analysis. In hindsight, I'd say a course on probability and statistics would have been useful.

The OP, I presume, is asking if it's worth taking a course on PDEs in addition to the traditional math methods course. (If not, I don't really see the point of the question.) As far as additional math courses go, I'd say a course on differential geometry would be good if you're planning to go into GR, but that probably means taking a year of real analysis first to satisfy prerequisites.

 

[gwnorth]

Probability and statistics are covered as part of the Mathematical Physics II course at my son's university.

Some universities do have their Physics majors take standalone dedicated math courses in the relevant topics rather than as part of mathematical methods courses specifically designed for Physics majors. I imagine that the main reason for this is that it reduces cost and administration since the courses would be of interest to a wider population of students. The question is does it result in better learning outcomes? The advantage of combining the requisite topics into mathematical methods courses is that you can pare down the number of required courses from 4 or more to 2, freeing up more space for electives.

 

[Orodruin]

I wish I had had a statistics and probability course given by a physics department rather than the pure math course that was offered in my curriculum. The math course took a very abstract approach and I strongly doubt many people that passed the course could perform anything to the level of basic data analysis.

 

[vela]

Some universities do have their Physics majors take standalone dedicated math courses in the relevant topics rather than as part of mathematical methods courses specifically designed for Physics majors. I imagine that the main reason for this is that it reduces cost and administration since the courses would be of interest to a wider population of students. The question is does it result in better learning outcomes? The advantage of combining the requisite topics into mathematical methods courses is that you can pare down the number of required courses from 4 or more to 2, freeing up more space for electives.

At my undergrad university, the math methods course was also listed as a math course, which all of the math majors avoided like the plague. I think we also had the option of taking separate math courses in lieu of the math methods course, but as you noted, it does take more time to cover the same topics if you went that route.

 

[gwnorth]

At my son's school the Math Methods courses are also offered through the math department so anyone with the requisite prerequisites can take them, but Math Methods I in addition to requiring 2nd year Calc III and Intro to Differential Equations as prerequisites, also recommends previous credit in the 2nd year Physics Mechanics course. This makes it less likely that non-Physics students will register for it. Instead they are more likely to take the 3rd year standalone Partial Differential Equations math course for which it is an antirequisite. Math Methods 2 requires completion of Math Methods I making it even less likely that non-Physics students will register for it. Instead they take the standalone 3rd year Complex Analysis I.