Topics They Don't Seem to Teach in Undergrad

[TomServo]

I've noticed that there are certain topics that physics departments don't seem to teach at the undergrad level, except maybe smaller introductory elective courses here and there. It seems like the emphasis is entirely on making E&M and Quantum specialists at the expense of certain other areas. I'm curious as to why this is the case for the following topics:

General relativity
Anything to do with fluid dynamics (it seems completely possible, judging by the curricula I've looked at, that one could get a BS in physics without ever learning about why things float)
Heat transfer (yes, one thermo class is required at most institutions, but this seems almost like an afterthought)

In short, it seems like mechanical and aerospace engineers study a heck of a lot of physics that physics majors themselves gloss over. Why is this? Or am I completely wrong?

 

[Andy Resnick]

You are not wrong, and I would also add 'optics' to your list. I have no idea why the 'canonical' curriculum is defined the way it is. Although the US does not have an accreditation of physics degrees in particular (except for medical physics via CAMPEP), the IOP (UK) accreditation requirements list a specific set of topics for "Core of Physics" on http://www.iop.org/education/higher_education/accreditation/file_43311.pdf, and the topics you mention are conspicuously absent. That is, General Relativity is not considered part of the 'core of physics' according to the IOP!

For that matter, it's not clear why (in the US) 124 +/- credit hours are needed to get a BS degree- one of the national accreditation agencies simply states:

"3-5-202. Education Requirements. The minimum number of credits required for the bachelor’s degree shall be 120 semester hours, 180 quarter hours, or their equivalent, normally earned over a period of eight semesters, 12 quarters, or their equivalent. Transfer and award of credit for appropriate work at other institutions may be granted."
but does not give a reason for the numbers.

To summarize, the current state of the BS degree in the US is based on fairly arbitrary guidelines. To be sure, since our BS Physics degree does not have an accreditation distinct from our parent institution, we have wide latitude in what subjects to cover (given that we have state guidelines which are designed to allow students to transfer with a minimum of problems). If we wanted to, we could petition the faculty senate to change required courses- and most likely, if we were serious about it, the petition would be granted.

 

[f95toli]

*I studied fluid dynamics as an undergrad. But I studied engineering physics.

*Heat transfer is pretty easy at the "theoretical" level (as long as you don't start worrying about real-world applications, and limit yourself to conduction and radiation) and tends to be covered quite well in various courses. I e.g. solved lots of heat transfer problems in my PDE course (as well as in comp phys and math phys courses)

*GR is very complicated if you do it "properly" and it is very unlikely that you will get the mathematical background as part of you undergrad math courses.
Also, remember that there are few applications of GR outside of cosmology whereas QM and EM are used in just about every field of physics (and quite a few fields of engineering). Or in other words: GR might be interesting but it would be an unnecessary course for nearly everyone.

 

[AlephZero]

I wonder if part of the issue with fluid dynamics is that (notwithstanding the huge advances in the 20th century) there are still large parts of the subject that are semi-empirical. If understanding the general solution of the Navier-Stokes equations are still the subject of a Millennium Prize, there is a very big hole at the core of the subject from a purist's point of view.

Of course engineers just have to get on and make the best practical use of what is already known, but that's the basic difference between physics and engineering.

 

[lisab]

When I was a senior physics major, my university decided to offer a class in gravity to junior/senior undergrads. It was touted as a trial class, a beta-version. I had one look at the syllabus and thought, no thanks...one of the best decisions I made that year!

Turns out, the few intrepid students who did take that class were simply blown away - totally unprepared for that level of work. It didn't help that most were taking E&M and QM at the same time, so they just didn't have much time left to commit to it.

The class wasn't offered again, AFAIK.

So I know it's been discussed by at least one school, to broaden the base of undergrad exposure. But it would almost have to come at the expense of narrowing the traditional E&M and QM material - something most physics departments aren't willing to do.

 

[SophusLies]

Statistics/probability and non-awkward communication skills.

 

[D H]

*General relativity.
As others have noted, the math is a bit on the advanced side even for the typical senior physics major. Some colleges let seniors, with permission, take introductory graduate level courses.

*Fluid dynamics.
Yep. Undergrad physics education here pretty much stops at Halliday & Resnik. Physics majors don't have to know what a shock wave is, which is pretty shocking.

*Heat transfer.
And thermo in general. Halliday & Resnik again is about as far many physics majors get in studying thermo. Statistical physics is offered at the undergrad level in many schools but it is optional.

In short, it seems like mechanical and aerospace engineers study a heck of a lot of physics that physics majors themselves gloss over. Why is this? Or am I completely wrong?

It's because the primary goal of undergraduate physics is to educate students so they have a good chance of getting admitted to some graduate physics program. Most graduate physics programs focus on solid state physics, particle physics, or optics. Each of these requires a solid quantum and E&M background, so that's what they teach.

 

[Dembadon]

It probably varies by institution. At mine, "Modern Optics and Photonics (after EM & Quantum prereq)" is required, as well as probability and statistics, but Special and General Relativity are not.

 

[Nabeshin]

I don't really understand the approach that 'GR is too mathy, we cannot teach it to undergraduates.' It seems to me absolutely unacceptable that an undergraduate go through his education and be called a physics major without having learned, at least at a basic level, GR. I see no reason why courses based on Hartle or Schutz shouldn't be required just as much as a course in QM at the undergraduate level. Obviously all physics subjects have many layers of understanding, but strangely many people seem to think that if you're not going to teach GR with a full introduction to differential geometry then it's not even worth teaching.

Nonsense.

 

[Angry Citizen]

Also, remember that there are few applications of GR outside of cosmology

Pardon? GR is the reason why we have GPS satellites that work. And that's just one area that I'm aware of where GR made an enormous impact outside of cosmology. God only knows where else it's been important.

 

[Mépris]

Halliday & Resnik again is about as far many physics majors[/B] get in studying thermo. Statistical physics is offered at the undergrad level in many schools but it is optional.

Seriously? That Fundamentals of Physics textbook? So, it's in grad school that students learn the meat of physics - during those two years of the MS course? :S

 

[quantum13]

*General relativity.
As others have noted, the math is a bit on the advanced side even for the typical senior physics major. Some colleges let seniors, with permission, take introductory graduate level courses.

What kind of math is needed for to understand general relativity? I don't understand the big difference between a senior undergrad and a first year grad student. Do grad students take those advanced math courses concurrently with GR or is it assumed they have more time to study?

 

[D H]

Also, remember that there are few applications of GR outside of cosmology

Pardon? GR is the reason why we have GPS satellites that work. And that's just one area that I'm aware of where GR made an enormous impact outside of cosmology. God only knows where else it's been important.

f95toli said very few. You named one. That qualifies as "very few." I'll name one more: high-precision planetary ephemerides over millennia or longer. Now name one more.

Of both those named applications, you don't have to understand general relativity as a taught as a subject to be able to understand the subject application. A weak field approximation as a given works just fine. Besides, physicists don't work on GPS for the most part. It is a solved problem as far as physicists are concerned.It is important to remember that the primary purpose of an undergrad physics program is to prepare students for a graduate physics program. Television programs such as Nova make it appear that cosmology is the only thing that PhD physicists do. The reality is that very few PhD physicists work in this area.

Seriously? That Fundamentals of Physics textbook?

I was thinking more of Halliday & Resnick Physics rather than the dumbed-down Fundamentals of Physics, but yes. A typical undergrad physics has eight or so required physics classes for juniors and seniors, and even fewer if the physics department happens to in a college that offers a bachelors of arts degree as opposed to a bachelors of science. The junior level statistical mechanics course is optional in a some undergrad physics programs, about a third from browsing at various schools. If it is offered at all, the follow-on senior level statistical physics course is optional in a solid majority of such programs.

So, it's in grad school that students learn the meat of physics - during those two years of the MS course? :S

That's true for many subject areas, not just physics. The freshman and sophomore years give a smattering across a broad range of subjects. Juniors and seniors relearn those subjects and build upon them. Then when you get to grad school you find that even the hard subjects you took as a junior and senior were but a simple facade to what is really going on.

A specific example: special relativity. Some aspects of special relativity are so simple that it can be taught in part in high school physics. You'll revist these simpler aspects of special relativity as a freshman or sophomore. Then you'll relearn it at least twice as a junior and senior. It is one of many subjects covered in the upper level undergrad classical mechanics class, it is taught once again in the junior level E&M class, and if you take a high energy physics class you'll hit the subject for a third time. And then as a grad student you'll hit the subject at least twice more. Somewhere along the way you'll derive the relativistic form of Maxwell's equations.

What kind of math is needed for to understand general relativity?

Differential geometry.

I don't understand the big difference between a senior undergrad and a first year grad student.

The big difference is in the diversity of classes, the difficulty of those classes, and the assumed background. Undergrads in the US have to take quite a few classes completely outside of their specialty. How many depends on whether the physics department offers a bachelor of arts versus a bachelor of science degree. Grad school students are completely immersed in their subject matter; they have very few if any required outside classes.

Grad school classes are considerably more challenging than are undergrad classes. Some of your undergrad classmates will not apply to or will not be accepted in a graduate program. The instructors can and do make those grad courses much more intense because they are teaching to the cream of the crop.

And finally, differential geometry almost universally is not a required subject for undergrad physics majors. It is often taught as a part of the graduate level class on general relativity.

Do grad students take those advanced math courses concurrently with GR or is it assumed they have more time to study?

Most undergrads have several unstated minors such as studies of the opposite sex. Grad students can only audit these subjects. They are spending too much time studying.

 

[Andy Resnick]

<snip>

It is important to remember that the primary purpose of an undergrad physics program is to prepare students for a graduate physics program. <snip>

That's part of the problem with Physics degrees- on one hand, we explicitly tell prospective students that a BS degree in Physics is not designed to help them get a job, but we also tell students that a BS degree in physics gives them all kinds of skills that employers want (e.g. problem-solving).

In truth, teaching more thermo, fluids, and optics would likely help undergrads to use their degrees.

 

[D H]

That's part of the problem with Physics degrees- on one hand, we explicitly tell prospective students that a BS degree in Physics is not designed to help them get a job, but we also tell students that a BS degree in physics gives them all kinds of skills that employers want (e.g. problem-solving).

In truth, teaching more thermo, fluids, and optics would likely help undergrads to use their degrees.

I agree. It would also help those who want a physics undergraduate degree but an engineering graduate degree. Hearkening way back to the original post,

n short, it seems like mechanical and aerospace engineers study a heck of a lot of physics that physics majors themselves gloss over.

That is exactly right. Mechanical and aerospace engineers are better versed in classical mechanics, fluid mechanics, and thermodynamics than are most physics majors. This can hurt those who want the broad-based learning and problem solving skills that an undergraduate physics degree offers but want the specialized skills that a graduate engineering degree offers.

 

[Mororvia]

My undergraduate physics (BS) requirements were as follows:
Physics Laboratory for Scientists I and II
Thermodynamics and Modern Physics (sort of a survey course)
Classical Mechanics I
Thermal and Statistical Physics
Electronics
Advanced Laboratory
Quantum Mechanics I
Electricity and Magnetism I

Outside of the first two lines above, most of these were at the junior/senior type of level. Physics majors also had to complete the introductory mechanics and E&M lecture courses experienced by many science/engineering majors, as well as the typical calculus sequence plus 2 more math courses at the junior/senior level. These were usually linear algebra and PDEs.

There was still a good amount of electives to choose from even after completing the university requirements in english, history, etc. Many people took optics, electronics, nuclear physics and solid state as well as more advanced courses in classical and quantum mechanics and E&M. One could even take courses in the engineering department, though you kind of had to fight to get in.

 

[Andy Resnick]

I've been trying to think of alternate approaches to the BS Physics degree; approaches that serve a larger number of students better than the current curriculum. The two I've come up with so far are:

1) get rid of the 3 or 4- credit hour course and replace them with more focused 1- or 2-credit hour courses. This could offer more options to the student, and keep the overall level of content high. Seriously, why spend 8+ credit hours on Physics I and II, only to cover those topics *again* at the 300/400 level? If it's a question of mathematical sophistication, then it's not an issue with the Physics- the Physics department could offer a "mathematical methods for Physicists" class that properly prepares the students.

2) Introduce a 'classical field theory' sequence (2 4-hour classes, for example) that covers continuum mechanics (including fluids), thermodynamics, and general relativity. Electromagnetism could also be included to some degree, but the sequence would replace courses covering thermo, modern, etc.

Again, I want to emphasize that the 'standard' curriculum is a lot more arbitrary than you think, and there isn't a set of rules about what subjects an accredited curriculum has to contain.

 

[twofish-quant]

I've noticed that there are certain topics that physics departments don't seem to teach at the undergrad level, except maybe smaller introductory elective courses here and there.

There are, and there are reasons that certain topics are left out of the core physics program.

General relativity

This tends to get left out because there are large parts of physics in which it's irrelevant.

Anything to do with fluid dynamics (it seems completely possible, judging by the curricula I've looked at, that one could get a BS in physics without ever learning about why things float)
Heat transfer (yes, one thermo class is required at most institutions, but this seems almost like an afterthought)

The reason that tends to get left out is that much of "real world" heat transfer and fluid dynamics turns out to be both empirical and domain specific.

In short, it seems like mechanical and aerospace engineers study a heck of a lot of physics that physics majors themselves gloss over. Why is this? Or am I completely wrong?

It's the knapsack principle. In order to teach one thing, you have to toss something out. Mechanical and aerospace engineers have to deal with heat and fluid transfers, but they don't usually end up studying quantum mechanics at anything more than superficial levels.

 

[D H]

It's the knapsack principle. In order to teach one thing, you have to toss something out.

Exactly. That undergrad knapsack only holds 120 to 130 semester hours, and the physics department only gets to fill a portion of the knapsack. A physics department will adjust the contents of its portion of the knapsack in response to how typical grad school value the courses in that typical undergrad knapsack. If year after year grad schools tend to prefer students who have taken solid state physics over those who haven't, eventually that will make physics of solids a mandatory course. If physics grad schools regularly accept students who don't even have enough fluid mechanics to explain how things float, well eventually that will make fluid mechanics an optional course (if it is offered at all by the physics department).

Fortunately, there are 20 or so technical hours in that knapsack that are completely up to the student. A student who wants to take fluid mechanics or advanced thermodynamics because that student's goal is to pursue a graduate career in engineering can usually find a way to do so.

 

[mal4mac]

I don't really understand the approach that 'GR is too mathy, we cannot teach it to undergraduates.' It seems to me absolutely unacceptable that an undergraduate go through his education and be called a physics major without having learned, at least at a basic level, GR. I see no reason why courses based on Hartle or Schutz shouldn't be required just as much as a course in QM at the undergraduate level. Obviously all physics subjects have many layers of understanding, but strangely many people seem to think that if you're not going to teach GR with a full introduction to differential geometry then it's not even worth teaching.

Nonsense.

I agree. Hartle has written a paper discussing this:

http://arxiv.org/abs/gr-qc/0506075

And why not string theory? You could use a textbook like "A First Course in String Theory" by
Barton Zwiebach.

It's doing a disservice to physics students not teaching them the rudiments of these topics. Even if they don't go on to become physics researchers, they may become physics teachers and pupils are likely to ask, "What's string theory then...". Or they may become science journalists and be asked to write something on these popular topics. And they need some background for dinner party conversations! And... most importantly... they deserve to be taken near to the frontier of the subject if it as at all possible - and Zwiebach and Hartle have shown that it is.

School students should look carefully at the advanced courses offered in Colleges they are thinking of applying to, to see if GR, string theory and other "cutting edge" topics are actually offered - if they want to do these! And check at interview if there are any barriers to doing these courses - I read that at Cambridge only the top 30 students get to do certain "sexy" topics like these - the rest are filtered into solid state, medical physics, etc - anything directly useful to the current military-industrial-state complex, which hasn't much use for strings or GR (yet...)

 

[Mépris]

Is it possible for one to take the more advanced variant of these courses (say, classical mechanics) straight away?

I took it for granted that every physics program had a "Maths for Physicist" kind of course, only that in the US, one could skip this and do the "pure math" variant of this course sequence.

That's part of the problem with Physics degrees- on one hand, we explicitly tell prospective students that a BS degree in Physics is not designed to help them get a job, but we also tell students that a BS degree in physics gives them all kinds of skills that employers want (e.g. problem-solving).

In truth, teaching more thermo, fluids, and optics would likely help undergrads to use their degrees.

Is this not what the Engineering Physics degree is for? Physics + a concentration on a few applied aspects of it? I've seen programs with concentrations on renewable energy, medical physics or with EE courses thrown in.

 

[Andy Resnick]

On a whim, I pulled out my (ahem) 1987 course catalog, compared it to what is the current catalog, and the results are telling. As you may expect, there are changes across the board for all science and engineering majors. However, Physics *by far* has the fewest changes. What better way to communicate to prospective students that Physics is a dead subject?

There could be many reasons for this: engineering programs have always had to be responsive to the changing requirements in industry; among the sciences, Physics students have traditionally considered industrial employment as a secondary option. It would also be incorrect to claim that Biology and Chemistry have somehow undergone more significant changes in their disciplines than Physics, and so their curricula need to reflect those larger changes. Physics has grown just as much (if not more) than the other sciences.

To be fair, my undergrad program now has many fewer required classes and many more electives- this follows my first idea, to offer a wider variety of subjects to the student. This places a higher burden both on the student and advisor to make sure the students ends up with a coherent educational plan- something that has always been done in the case of a minor (or major with a particular concentration).

 

[Angry Citizen]

And why not string theory?

I think it sets an awful precedent to teach theories for which there exists no experimental evidence. Indeed, even its theoretical basis is questionable. As a research topic it is fair game; but as an undergraduate class? You might as well be teaching Intelligent Design.

 

[TomServo]

Is physics at the stage where, like engineering once did, it needs to split? Has it gotten too big, with E&M, quantum, fluid mechanics, thermodynamics, computational, solid state, optical, laser, plasma, astro, classical, relativistic, etc, that saying "I'm a physics major" is more of an umbrella term than an actual major, like saying "I'm an engineering major" means you aren't majoring in "engineering" but a certain kind of engineering?

I mean, from a certain pov, we have a de facto split already, with aerospace and mechanical engineers studying certain areas of physics to a much, much greater extent than most bona fide physicists. From that pov, you could regard aerospace and mechanical engineering majors as experimental physicists in the areas of fluid mechanics, thermodynamics, etc, could you not?

The only way I can see bringing back fluid mechanics, thermodynamics, and at least giving them their due attention on an undergrad-level of understanding for a BS without making the physics BS a six-year degree, is to ditch virtually all GECs to make way for the classes. FWIW, I'm all in favor of ditching virtually all GECs. I would love to be able to at least have the option of trading one more English or art history class to get a better understanding of how water works its mojo.

I have one more question about this:

The reason that tends to get left out is that much of "real world" heat transfer and fluid dynamics turns out to be both empirical and domain specific.

I'm a second-year undergrad so I'm not quite sure what you're saying here. I mean, I understand "empirical" and I think I grasp "domain specific" but could you expand on this? Are you saying that heat transfer and fluid mechanics has too much turbulence or too many atoms or something to be modeled mathematically in a solvable way, so all solutions for a given problem are derived numerically? And if so, since it's still physics, why not at least talk about it?

 

[twofish-quant]

It's doing a disservice to physics students not teaching them the rudiments of these topics.

The problem is that you have to take something out Among the list of things that a physics researcher must know, string theory is pretty low on the list.

Even if they don't go on to become physics researchers, they may become physics teachers and pupils are likely to ask, "What's string theory then...".

Then, answer "I don't really know".

 

[twofish-quant]

Exactly. That undergrad knapsack only holds 120 to 130 semester hours, and the physics department only gets to fill a portion of the knapsack.

And if you increase the science/physics component of the course, then what gets hit are the humanities, which are going to help the student after he gets his Ph.D. and is trying to stay sane looking for work.

 

[twofish-quant]

Is physics at the stage where, like engineering once did, it needs to split? Has it gotten too big, with E&M, quantum, fluid mechanics, thermodynamics, computational, solid state, optical, laser, plasma, astro, classical, relativistic, etc, that saying "I'm a physics major" is more of an umbrella term than an actual major, like saying "I'm an engineering major" means you aren't majoring in "engineering" but a certain kind of engineering?

The problem with that is that:

1) it's a bad into to get overly specialized
2) every field of physics interacts with every other field. You aren't going to be a decent astrophysicist without some exposure to EM, QM, fluid mechanics, themodynamics, solid state, etc. etc.

FWIW, I'm all in favor of ditching virtually all GECs. I would love to be able to at least have the option of trading one more English or art history class to get a better understanding of how water works its mojo.

I'm not. The problem is this is really going to bite you went you start looking for work. If you want to apply your physics knowledge to something non-trivial, then you'll need to under how English and art history work. Just as example, right now I'm trying to figure out how to display multi-dimensional data, and having some very, very basic art history gives me some ideas on how to go about doing that.

Are you saying that heat transfer and fluid mechanics has too much turbulence or too many atoms or something to be modeled mathematically in a solvable way, so all solutions for a given problem are derived numerically?

Not even numerically. If you want to see how much friction there is when you pump water down a pipe, you get a pipe, pump water down it, and measure how much friction there is. We don't really have much of a clue how to calculate it. You can do complex CFD simulations, but in the end there are always a ton of fudge factors that you have to correlate back to experiment.

And if so, since it's still physics, why not at least talk about it?

Because there isn't much to talk about. If you want to see what happens, you look up the number in a table and that's about it. If you want to do a numerical simulation, you load that table into the computer and that's it.

This is in contrast with say calculating the orbitals of the hydrogen atom, in which you can start with some basic principles and come up with some solutions. Also there *are* problems in thermo which you can start with basic principles and then calculate solutions. With fluids and heat transfer, it's mostly "measure it" and put it into a table.

The other thing is that with most of the things that they teach in physics classes, you learn one rule, and you can apply it in a 100 different places. Most heat transfer and fluids problems end up being extremely specific and there isn't a general rule that you can apply to 100 different places.

 

[Andy Resnick]

Is physics at the stage where, like engineering once did, it needs to split? <snip>

That's sort of happening already- at my undergraduate institution, one can major in Physics, Applied Physics, Engineering Physics, Physics with a concentration in: Optics, Microelectronics, Nuclear Science, Computing, Biology and Medicine, Environmental Science, or Space Science. Physics majors can also minor in Astrobiology.

It does increase a risk to the student- early specialization in a field that is no longer relevant upon graduation, but it also increases opportunities for the students who can create a unique niche for themselves.

 

[Andy Resnick]

<snip>Most heat transfer and fluids problems end up being extremely specific and there isn't a general rule that you can apply to 100 different places.

This is clearly false, and possibly reflects an underlying ignorance of the relevant science.

 

[atyy]

I don't really understand the approach that 'GR is too mathy, we cannot teach it to undergraduates.' It seems to me absolutely unacceptable that an undergraduate go through his education and be called a physics major without having learned, at least at a basic level, GR. I see no reason why courses based on Hartle or Schutz shouldn't be required just as much as a course in QM at the undergraduate level. Obviously all physics subjects have many layers of understanding, but strangely many people seem to think that if you're not going to teach GR with a full introduction to differential geometry then it's not even worth teaching.

Nonsense.

You are right. But only because you are young:) Newton's laws of gravity used to be cutting edge. Now, they are high school physics. (I confess the find the non-Gauss's law proof that the gravitational field inside a shell is zero to be difficult.)

 

[atyy]

I've been trying to think of alternate approaches to the BS Physics degree; approaches that serve a larger number of students better than the current curriculum. The two I've come up with so far are:

1) get rid of the 3 or 4- credit hour course and replace them with more focused 1- or 2-credit hour courses. This could offer more options to the student, and keep the overall level of content high. Seriously, why spend 8+ credit hours on Physics I and II, only to cover those topics *again* at the 300/400 level? If it's a question of mathematical sophistication, then it's not an issue with the Physics- the Physics department could offer a "mathematical methods for Physicists" class that properly prepares the students.

2) Introduce a 'classical field theory' sequence (2 4-hour classes, for example) that covers continuum mechanics (including fluids), thermodynamics, and general relativity. Electromagnetism could also be included to some degree, but the sequence would replace courses covering thermo, modern, etc.

Again, I want to emphasize that the 'standard' curriculum is a lot more arbitrary than you think, and there isn't a set of rules about what subjects an accredited curriculum has to contain.

These guys seem to be trying something like that http://www.pma.caltech.edu/Courses/ph136/yr2006/text.html

 

[Nabeshin]

Newton's laws of gravity used to be cutting edge. Now, they are high school physics.

Indeed, and I think we've reached the point in GR's development where we can distill its essence down so that an undergraduate can understand and appreciate it.

With regards to string theory, it's obviously silly to have a course on this be required. Furthermore, since it's a very specialized area of research, it would seem difficult for many universities to find a professor to teach such a course (how many even have a string theorist working there?). That said, if possible I think it's wonderful to offer a Zwiebach course. As string theory is a sexy topic, tales of which likely got many of the physics students interested in the first place, it's great to get a flavor of what folks like Greene were so excited about.

 

[Andy Resnick]

These guys seem to be trying something like that http://www.pma.caltech.edu/Courses/ph136/yr2006/text.html

That looks like a good class! On a related note, a colleague showed me a copy of a new QM textbook by Townsend; it's for undergrads but immediately introduces the bra-ket notation- another good innovation. There's no reason to use textbooks that were written 50 years ago.

 

[twofish-quant]

This is clearly false, and possibly reflects an underlying ignorance of the relevant science.

My dissertation committee didn't think so...

You can write down the Navier-Stokes equations using conservation laws. Once you write them down, you find them unsolvable in the general case, and then what you then do is to develop approximations that cover a specific situation, and those situations are different enough from each other that you can't find a general rule the way that you can in QM.

You can describe the different domains in terms of dimensionless quantities like Reynold's or Prandtl's numbers and you can get somewhere by looking at scaling factors, but there is a lot of "this just works but we don't know why" in fluid/heat transfer.

 

[twofish-quant]

The way that I'd structure the undergraduate curriculum is to focus on core skills and core literacy. For example, if you have done a course in which you use PDE's and linear algebra for waves, then if you encounter a PDE in something else, you should be able to very quickly learn what it is that you need to know. If you've never seen a PDE, then you are going to be dead in the water if you see one.

 

[Angry Citizen]

The way that I'd structure the undergraduate curriculum is to focus on core skills and core literacy. For example, if you have done a course in which you use PDE's and linear algebra for waves, then if you encounter a PDE in something else, you should be able to very quickly learn what it is that you need to know. If you've never seen a PDE, then you are going to be dead in the water if you see one.

That's a pretty draconian approach to education. My aerospace engineering curriculum doesn't include partial differential equations (well, it does, but only because I'm wise enough to take it as an elective in lieu of a business course). Do you really want me to be 'dead in the water' with all the potential applications of PDE's, or do you want me to have some level of familiarity with them in case I need to quickly study them in-depth for a project of some kind?

 

[twofish-quant]

That looks like a good class!

One thing that I would question even more than the texts is the "format" of the class and the textbook. The way that classes and textbooks are structured have to do with technological limitations that no longer exist.

For example, the Caltech class would make a good starting point for a "textbook" with tens of thousands of pages of text with embedded video lectures, cross references to papers, etc. At that point rather than having a linear class that everyone goes through, you'd end up with a "choose your own adventure" textbooks.

Something that is sort of the format for what I'm thinking of is the "Great Books of the Western World" project that Brittanica tried to do in the 1950's. The first three chapters were basically indexes for the rest of the books. Today, we don't have to move dead trees to do that, and so you could come up with something much nicer.

The other thing that I'd do is to separate evaluation and education. You'd come up with a test that covers "everything that you need to know" and if you pass the test, you get a Bachelors degree in physics. Then you can figure out for yourself how you go about learning the material you need to pass the test.

 

[twofish-quant]

Do you really want me to be 'dead in the water' with all the potential applications of PDE's, or do you want me to have some level of familiarity with them in case I need to quickly study them in-depth for a project of some kind?

It's not what I want. It's just the fact that to do any sort of physics research, you need a good grasp of PDE's. Without knowledge of PDE's, then you just can't do most research in physics, and you are "dead in the water."

PDE's are so vital for just about anything in physics, that I can't imagine someone getting an undergraduate physics degree without having a good familiarity with PDE's. Now PDE's may not be a core skill for other fields (aeronautical engineering), but I suppose that's what makes a physics major different from an aeronautical engineering one, not that either is better than the other.

One reason that I would put so much emphasis on PDE's is that they are vital for certain areas of finance and economics, which is why those areas hire physics majors.

 

[Mépris]

While we're at it, making the exams "open-book" would be a good move. Also, is the exam you're talking about going to assess *all* the knowledge that one was supposed to acquire throughout the course of the degree? If that's the case, I think having the exam spread over a few days would be a sensible thing to do.

I'm for those "pesky" GECs. The big reason as to why I'm so hell bent on attending college in the USA is because of their liberal approach to education. I like learning things.
I do like math but what happens if after two semesters, I realize that I don't like it anymore? In my country, what happens is I either complete the degree and try enroll in a master's program of my interest *or*, I start another degree from scratch the next year. For somebody studying any given college in America, they still have another 4 semesters of schooling left and there really is nothing stopping them from going to say, Economics or Comparative Literature. The other cool part is studying towards the math major for a year probably took care of a lot of the science class requirements.

I point this out because it seems to me that some students seem to take this for granted. I probably wouldn't be as fussed as I am if I had that kind of opportunity elsewhere.

two-fish, how is Art History useful to you? I don't seem to be able to draw any links. :S

 

[mal4mac]

I think it sets an awful precedent to teach theories for which there exists no experimental evidence. Indeed, even its theoretical basis is questionable. As a research topic it is fair game; but as an undergraduate class? You might as well be teaching Intelligent Design.

Surely students should get at least a glimpse of the research frontier? In many cases theories came along before strong experimental evidence is available. String theory is not akin to intelligent design - many of the best physicists are researching string theory in the most prestigious institutions, no serious scientist is researching intelligent design!

Students should of course encounter the criticism about there being no experimental evidence, and the difficulty of getting any! And they should also be told why physicists consider it worth pursuing, even though the experiments are not keeping up with the theories... they may end up an Angry Citizen and declare it wasn't worth studying! But, if so, good result! I can't see how such a course could not be interesting and instructional - given the 'wild frontier' aspects of it, though, it maybe should be kept optional - but the option should, surely, be there...

 

[Fusiontron]

How do you guys feel about the undergraduate curriculum at the University of Maryland? http://umdphysics.umd.edu/images/pdfs/ugrad/physprofreqs.pdf

 

[twofish-quant]

Surely students should get at least a glimpse of the research frontier?

Sure, but there are a hundred other research frontiers that a student can get a glimpse of.

I can't see how such a course could not be interesting and instructional - given the 'wild frontier' aspects of it, though, it maybe should be kept optional - but the option should, surely, be there...

Again the problem is the knapsack problem. Anything you put in, you have to take something else out.

 

[Andy Resnick]

You can write down the Navier-Stokes equations using conservation laws.

That's exactly my point- 3 equations (mass, momentum balance and energy balance) is all there is. Boundary conditions can be classified into broad categories as well. There are several FEA codes that then crank away to generate specific results for specific cases.

Yes, there are unsolved problems. This is also true for all of science.

 

[Andy Resnick]

While we're at it, making the exams "open-book" would be a good move. Also, is the exam you're talking about going to assess *all* the knowledge that one was supposed to acquire throughout the course of the degree? <snip>

My exams are open-book, and are cumulative as well. However, making the exams take-home or occurring over multiple days is going too far for undergrads, IMO- students are nervous enough about a 1-hour exam/2-hour final.

 

[Andy Resnick]

Surely students should get at least a glimpse of the research frontier? <snip>

To some degree, yes- it can be helpful to 'liven up' class discussions by adding some context as to why a particular topic is being taught. I try to include topics "ripped from today's headlines" in recitation- we have discussed the LHC neutrino measurement, the Fukushima reactor accident, computer animation in movies, astrophysical measurements of the fine-structure constant, etc.

In addition to demonstrating that science is 'organic', it also demonstrates why being scientifically literate is important- especially when we discuss intelligent design (in the context of scientific laws and theories), scientific ethics (HeLa cells, Tuskegee syphillis experiment, etc.), and legal issues (surveillance cameras, 'black boxes' in automobiles, etc.)

 

[D H]

However, making the exams take-home or occurring over multiple days is going too far for undergrads, IMO- students are nervous enough about a 1-hour exam/2-hour final.

That is a torture technique specially reserved for grad students. "You have two weeks to turn in this exam."

Exam, my rear! Those 20+ page write-ups required a full two sleep-deprived weeks to complete. My "favorites" were where the exam question asked the student to write their own exam problem, and then solve it.

 

[twofish-quant]

That's exactly my point- 3 equations (mass, momentum balance and energy balance) is all there is.

No there isn't. :-) :-)

Once you write down the N-S equations, the fun has just started unless you are dealing with extremely simple and usually physically unrealistic situations.

There are several FEA codes that then crank away to generate specific results for specific cases.

I spent a few years of my life working in convective codes. There's a lot of "secret sauce" in those codes.

What happens is that once you get any turbulence, then you can't model the flows down to the microscopic scale. What you do is to smooth over the microscopic scales and then semi-empirically model quantities like viscosity. What you end up with are lots of fudge factors that you tweak to make your results match experiment. Where you have a ton of experimental data, you can fix the fudge factors. Where you don't, you can't.

You end up with codes that work, but there is a lot of hand-waving and "this just works and we exactly aren't sure why" in them.

Yes, there are unsolved problems. This is also true for all of science.

The whole field of fluid dynamics for non-trivial problems is an unsolved problem. What you can't do with fluid mechanics is what you can do with QM and statistical mechanics is start out with microphysical principles (say Schoredinger's equation or the canonical ensemble) and then come up with numbers that match experiment (say the energy levels of hydrogen or the heat capacity of an ideal gas).

Getting back to pedagogy.

A lot depends on what you want to teach in an undergraduate physics program, and there are likely a lot of different approaches that work. My undergraduate program was very heavily "problem solving based." The idea is that you take a set of principles and then you learn enough to mathematically figure out the consequences of those principles.

To do that, Newtonian physics, EM, QM, and solid-state thermo make a good set of courses to build the degree around since they all start with some basic mathematical principles, and you pass the course when you can show that you can apply those principles to specific problems.

Fluid dynamics doesn't fit into this because you just can't start with Navier-Stokes and derive even simple stuff like the friction of water going through a pipe. GR also doesn't fit into this because the number of different problems that you can use GR principles to solve is rather small.

There are likely to be a lot of different methods for teaching physics that work, and I hardly think that the way that I was taught was the best way, but it's something that I'm familiar with, and for the most part I think it was successful so when I try to figure out how to set up a physics program, it's likely to revolve a lot around how I was taught.

Also one thing that was drilled into me as an undergraduate was that the classroom was only part of the education. One reason that I think certain courses should be required subjects and certain courses don't need to be, is if you can reasonably expect a student to be able to learn something on their own outside class, then it's not necessary to make it a required class. Introductory probability and statistics as taught in most social science departments would fall into that category.

 

[twofish-quant]

My exams are open-book, and are cumulative as well. However, making the exams take-home or occurring over multiple days is going too far for undergrads, IMO- students are nervous enough about a 1-hour exam/2-hour final.

Also a lot depends on the students. I've found in teaching intro algebra that my main role is "math anxiety therapist" rather than purveyor of knowledge. In those courses, I try to avoid exams altogether if the school will let me, and use other ways to check that they learned the material. (I.e. picking a question at random from the homework and have the student explain how to solve the problem.)

There are also culture-dependent issues. American students like to talk but freeze in exams. East Asian students are the opposite. East Asian students tend to have zero test anxiety (because the entire educational system is test based) but are usually scared to death of expressing their opinions, which makes sense if you look at their background. If you were in Beijing and some random person asked you to put into writing what you really thought of the President of China, I don't think you'd do it.

 

[physics girl phd]

I think this is verging more into something that should be on the "teaching/education" part of this forum rather than the "academic advice" part... so I think that's why I've stayed out.

I also personally think (along with twofish's comments above) that core requirements do a pretty good job of picking some well-established basics -- but I do agree with Andy that there's often too much repetition (EX: do I really need classical mechanics AGAIN in graduate school?... which I think is why my old graduate program is now having students select 5-6 core courses from a list of selected coursework).

But I'll quote myself from a different recent thread, regarding how a student should look at the core curriculum:

A big problem is an assumption that *most* students initially make -- thinking that meeting the minimum [core] requirements for a major will prepare them for their future (be it direct employment or graduate school then employment). In fact, as MsSilvy mentions, getting A's in those minimum requirements still won't guarantee this. Preferably, if the courses are required or "core" course, the student will look into possible options of WHO teaches the course, and then seek to take a course from someone who is challenging (i.e. has high standards) but is thought to teach well (in other words, not take courses from someone who is "easy")... in order to get the best possible basis. But then, while those minimum requirements are still being met, the student needs to tailor his/her experience and take courses from complementary fields (or graduate courses in one's own field) and gain experience through internships or through research positions.

Students at ALL levels need to be thinking about this (from probably about 3rd to 5th grade in primary/elementary school... when tracking first starts) through the graduate/PhD level.

Would a "good" program require their students to take some upper-level courses from other complementary fields? Probably. Require research? Probably. But there are probably restrictions from the university about how majors and credit hours are defined that could cause this to spend HOURS in committee with no result.* Radical restructuring (along the lines of Oregon State's "Paradigms") is rare (and even they are still essentially teaching the same core curriculum... just in a fairly new and radical way).

*Ask me why I'm no longer on the undergraduate committee for our department? As a lecturer it wouldn't count worth @#$% towards tenure/promotion/pay... and I didn't see anything getting done except the slightest changes to catalog wording (I guess I wanted revolution)... and then we had kids, and the committee meets right when the school buses start arriving at home.

The thread also has gone off on a tangent about fluids... particularly the Navier-Stokes. I just want to briefly add that I used them (in some form) in the modeling of electron movement in a metal surface that was being exposed to an optical field. I know I've also often used fluid references in circuit analysis (which isn't novel). So fluids is a useful topic (that wasn't one I ever took a course on). But fortunately, as twofish again notes, at some point in a student's education:

.
...you can reasonably expect a student to be able to learn something on their own...

Sorry if I took this last quote a bit out of context twofish... I just liked your wording and wanted to use it.

 

[Dembadon]

*General relativity.
As others have noted, the math is a bit on the advanced side even for the typical senior physics major. Some colleges let seniors, with permission, take introductory graduate level courses.

...

No kidding!

Here's a snip from my university's course catalog:

MATH 443/643 DIFFERENTIAL GEOMETRY AND RELATIVITY I

Manifolds, the tangent bundle, differential forms, exterior differentiation, Lie differentiation, Koszul connections, curvature, torsion, Cartan's structural equations, integration of differential forms.


Prereq(s): MATH 311.

The prerequisite it mentions (MATH 311) is the second course in a two-course series called "Introduction to Analysis", which is a prerequisite for Real Analysis (Math 411). Surely physics majors should not be expected to take two semesters of analysis before they can take general relativity.