Topics They Don't Seem to Teach in Undergrad

[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.

 

[twofish-quant]

Surely physics majors should not be expected to take two semesters of analysis before they can take general relativity.

I'm pretty certain that the important parts of differential geometry can be taught in a freshman calculus class, and that it is possible to rewrite the vector calculus textbook to introduce differential forms. The latest differential geometry textbooks are a lot more accessible than the ones that I read in the late-1980's.

Something that is interesting to do is to read old textbooks and old papers to realize how much more advanced we are at teaching. If you read the original papers by Newton and Lebinitz, it took them a century to figure out how to do calculus, and their notation and concepts are archaic.

 

[twofish-quant]

Would a "good" program require their students to take some upper-level courses from other complementary fields?

There's a basic political problem. Every time you talk about course requirements, it goes to hours in the curriculum, and then every time you start talking about what courses are required or not, then you are talking about political battles from hell.

Personally, what I think would work better is to just have some sort of test, and what you did to learn the material to pass the test is irrelevant. The problem with this system (which does exist in some places) is that then you have political battles over the test, and then you have to figure out how to do funding.

One thing to remember is the the course curriculum in most universities is a sacred document that determines allocations of money and power. Part of what I've been trying to figure out is how to have discussions about what knowledge is essential without getting pulled into turf wars from hell.

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.

In fact there is a result, if you weren't in the committee room, you might be doing something dangerously useful.

Been there, done that. It's trench warfare. Part of the reason that I'm interested in technology is that it's likely that there are ways of bypass the trenches. Rather than spend hours in committee meetings, you create some youtube videos and upload those.

 

[Andy Resnick]

<snip>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.* <snip>

The more I dig into this question (Our Governor/Board of Regents have been discussing these 'foundational' issues lately), the less I understand. Ultimately it relates to Accreditation agencies, and since there many agencies, there is no 'one' definition, AFAICT- which is probably why there's so much committee discussion...

I liked the footnote, BTW.

 

[Andy Resnick]

<snip>
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.

I completely agree with this. Well... mostly I agree- the issue of "learn something on their own" gets cloudy pretty quickly when you take into account the easy availability of incorrect (or even partially-correct) information.

We are all agreeing that an undergraduate curriculum needs electives.

 

[Dembadon]

I'm pretty certain that the important parts of differential geometry can be taught in a freshman calculus class, and that it is possible to rewrite the vector calculus textbook to introduce differential forms. The latest differential geometry textbooks are a lot more accessible than the ones that I read in the late-1980's.

...

I asked one of my math professors about this and he said that physics majors are usually required to take a "mathematical methods for physics" course that teaches the additional topics. I looked in my course catalog and there is such a course offered by the physics department. Otherwise he said pretty much the same thing you have, that a readjustment of the standard structure in the calculus sequence would be needed, which he said probably isn't going to happen.

 

[George Jones]

Surely physics majors should not be expected to take two semesters of analysis before they can take general relativity.

While some physics majors might find a math department course on the mathematical structure of general relativity interesting, I think physics majors with an interest in general relativity are more likely to take the physics department course

PHYS 453/653 SPECIAL AND GENERAL THEORY OF RELATIVITY

Historical background, Lorentz transformations, Minkowski space-time, equivalence principle, covariant differentiation, curvature tensor, gravitational field equations, tests of general relativity, quantum gravity.

Prereq(s): PHYS 351; PHYS 473

Time to put a myth to bed.

*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.

*General relativity. As others have noted, the math is a bit on the advanced side even for the typical senior physics major.

The mathematics of non-relativistic quantum mechanics is, in my opinion, more difficult than the mathematics of general relativity. Students acquire more facility with the mathematics of quantum mechanics because they spend more time studying it.

At the level of mathematics taught by physicists, the mathematics of non-relativisitic quantum mechanics is somewhat more difficult than the mathematics of general relativity. Typically, an undergrad physics major is introduced to quantum mechanics in a Modern Physics course, and then takes two more semesters of quantum mechanics. In a one=semester general relativity course, the techniques and mathematics of general relativity are presented at light speed, and this perpetuates the myth that the mathematics is difficult. If the techniques and mathematics of general relativity were spread out over 2+ semesters, I don't think that things would seem nearly so difficult.

At the level of honest mathematics, functional analysis, the mathematics of non-relativisitic quantum mechanics is substantially more difficult than the differential geometry used in general relativity. For example, if operators A and B satisfy the canonical commutation relation \left[ A , B \right] = i \hbar, then at least one of A and B must be unbounded. Say it is A. Then, by the Hellinger-Toeplitz theorem, if A is self-adjoint, the domain of physical observable A cannot be all of Hilbert space! Also, the spectral decomposition for A will be given by the the spectral theorem for unbounded self-adjoint operators. It would be crazy, if not impossible, to teach quantum mechanics this way!

 

[Kindayr]

At the level of honest mathematics, functional analysis, the mathematics of non-relativisitic quantum mechanics is substantially more difficult than the differential geometry used in general relativity. For example, if operators A and B satisfy the canonical commutation relation \left[ A , B \right] = i \hbar, then at least one of A and B must be unbounded. Say it is A. Then, by the Hellinger-Toeplitz theorem, if A is self-adjoint, the domain of physical observable A cannot be all of Hilbert space! Also, the spectral decomposition for A will be given by the the spectral theorem for unbounded self-adjoint operators. It would be crazy, if not impossible, to teach quantum mechanics this way!

Not to a junior-senior level mathematician! (Depending how much linear algebra and functional analysis they have been introduced to).

In all honesty, the curriculum of physics isn't the only one being stranded or in need of reworking. I think the mathematics curriculum in its current state is in some trouble as well.

 

[George Jones]

Not to a junior-senior level mathematician! (Depending how much linear algebra and functional analysis they have been introduced to).

I think you are underestimating the difficulties involved. For example, the self-adjointness of the Hamiltonian for helium was not established until twenty years after von Neumann put the foundations of non-relativistic quantum mechanics on a firm mathematical footing

 

[Kindayr]

I think you are underestimating the difficulties involved. For example, the self-adjointness of the Hamiltonian for helium was not established until twenty years after von Neumann put the foundations of non-relativistic quantum mechanics on a firm mathematical footing

I am underestimating it. I should have probably made it more clear at my semi-attempt at humour :(

 

[twofish-quant]

The more I dig into this question (Our Governor/Board of Regents have been discussing these 'foundational' issues lately), the less I understand. Ultimately it relates to Accreditation agencies, and since there many agencies, there is no 'one' definition, AFAICT- which is probably why there's so much committee discussion...

Once you get boards of regents and accreditation committees involved, then you are working at an even higher level of trench warfare.

Something that has occurred to me is why is this committee meeting necessary?" and it boils down to money. The one thing that the committee can do is to hand you a piece of paper that will allow you to make money, and you can use that money to pay the salaries of the teachers.

So the way out of the committee room is to figure out alternative funding sources. If you could do something with youtube and facebook and create economic value from that and then get that money back to the content providers, then you can bypass the committee.