Topics They Don't Seem to Teach in Undergrad

[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.

 

[twofish-quant]

The mathematics of non-relativistic quantum mechanics is, in my opinion, more difficult than the mathematics of general relativity.

I agree. The basic ideas of general relativity you could probably cover in a freshman or early sophomore class while you are teaching vector calculus.

Typically, an undergrad physics major is introduced to quantum mechanics in a Modern Physics course, and then takes two more semesters of quantum mechanics.

Yup. And the reason for this is that the bills get paid by people that are interested in building better bombs and toasters. You need QM and thermo to build a bomb and a modern toaster, you don't need GR. So there has been a ton of effort making QM accessible to undergraduates.

 

[twofish-quant]

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.

That's why it's important to teach people how to critically evaluate information. One problem is that the classroom is probably the worst place to do this because you are in a highly authoritarian situation in which you are expected to uncritically accept the teachings of an authority figure or else get a bad grade.

 

[Andy Resnick]

<snip>
Students acquire more facility with the mathematics of quantum mechanics because they spend more time studying it.
<snip>

Well put!

 

[Andy Resnick]

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.

I don't understand what you mean.

 

[twofish-quant]

I don't understand what you mean.

One important part of my undergraduate education was when I was involved in an "education reform" movement in the late-1980's which ultimately involved going to a lot of committee meetings in which nothing got done. I ended up rather disgusted and frustrated by the process, and one of my important experiences was when I ended up talking with a dean who was also rather disgusted and frustrated by the process.

So the question that I've been thinking about over the last few decades is "if we are going to get nothing done by going to committee meetings, is there a way of bypassing the committee?" which leads to the question "why do we want approval from the committees anyway?"

And it basically boils down to money. Right now, I don't have to go through a committee to upload lectures on to YouTube, and I don't have to go through a committee to set up a calculus study group. The problem is that the money part doesn't work. People are willing to pay a university large sums of money to get calculus taught because they end up with a piece of paper that will let them make money. They won't pay me to teach the exact same or better course, because they won't get that piece of paper.

Now that's how far I've gotten. There are some more missing pieces, but I expect them to be filled in within the next decade.

 

[Andy Resnick]

So the question that I've been thinking about over the last few decades is "if we are going to get nothing done by going to committee meetings, is there a way of bypassing the committee?" which leads to the question "why do we want approval from the committees anyway?"

Committees have many functions, and there are many different kinds of committees. I was on a search committee for our current Dean, for example- that process should not be performed by an individual. I'm also on a committee for academic standards: we consider students who petition the university for things like waiving requirements, suspected cheating, selecting the valedictorian, etc- those should not be up to a single person.

What I have found is that the lower the stakes, the more argumentative the committee. I select my committee duties thusly.

 

[mdxyz]

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.

Or come to Britain where there are no humanities in a physics degree :D

Perhaps that is why thermo/stat mech was given as much time as QM/EM here, and GR is an undergrad elective? Actually saying that, GR is not very useful for the vast majority of people, while being mathematically beyond many even at top university. Absence of fluid mech is much stranger and still present here. Fluids are a significant proportion of stuff in the universe. Would think it belongs in year 2/3 core.

 

[D H]

Or come to Britain where there are no humanities in a physics degree :D

That appears to be a key difference between undergraduate education in the US versus Europe. Some physics programs in the US offer a bachelor's of arts degree. The general education requirements for a BA/AB in the US are rather high. Students may well be required to take more classes outside of math and physics than they take in math and physics. Other schools offer a bachelor's of science degree. Here general education requirements are significantly reduced compared to a bachelor's of arts, but are still much higher compared to European systems.

There are advantages and disadvantages to the various approaches. The US produces better rounded students (at least that is the goal) but at the expense of less training in their degree discipline.

 

[mdxyz]

I'm unsure of the definition of roundedness, or how it can be measured, so I'll just take your word for that. Some might argue it just wastes time and inflates the bill by justifying 4 years rather than 3, or is remedial study to make up for US's non-standardised high school system.

I have seen some shocking physics degree programmes from the US - covering about 1-1.5 years here. It doesn't surprise me there is no accreditation board, although I don't understand how these people can be eligible for PhD study. That said, all were at low ranked institutions, so I doubt it's the case at the top places.

As for European systems - I don't know about that. Every European country has a different system and I'm only familiar with one.

 

[D H]

The real reason we do things the way we do is that we Americans are a pretty conservative lot. The concept of a four year college is now writ in stone. As for a lack of a standard curriculum, that is partly because of the huge spread in how much freedom departments have in levying requirements; schools that grant BA degrees have a lot less freedom than do those that grant BS degrees. Another factor appears to be a laissez-faire attitude by the American Physics Society. I don't see a recommended curriculum at the APS site. Other professional societies are much more vocal than is the APS regarding undergraduate education.

 

[twofish-quant]

I'm also on a committee for academic standards: we consider students who petition the university for things like waiving requirements, suspected cheating, selecting the valedictorian, etc- those should not be up to a single person.

There are lots of different multi-person decision mechanisms that are possible that don't involve committees. For example, there are relatively few committees in most businesses. One person makes the decision, but in the process of making the decision, they have to consult with other people. The point of having one person make the decision is so that if it turns out that it's a bad decision, you have one person responsible for it.

You can have one person have the authority to make a decision subject to approval by some other person. In a lot of situations, there is a deliberate effort not to create a committee so that the other person reviews the decision independently.

Then you have markets, which is a very complex system for making decisions that don't involve committees.

 

[twofish-quant]

There are advantages and disadvantages to the various approaches. The US produces better rounded students (at least that is the goal) but at the expense of less training in their degree discipline.

To be fair, one of the purposes of US colleges is to teach things that would have been taught in secondary school in other countries.

 

[twofish-quant]

The real reason we do things the way we do is that we Americans are a pretty conservative lot.

I think it's also a function of the fact that US education is extremely decentralized. For example, if you wanted to push classes from college to secondary school, then in a lot of countries you'd have the national Ministry of Education issue new standards and that's it.

In the US, the Department of Education doesn't have this sort of power, and most people don't want the USDOE to have this sort of power, so if you want to do something major it involves negotiating with a thousand different stakeholders with different goals.

Also, if you look at the history of how stuff happens. It's usually that one school tries it, it works, and then everyone copies them.

Another factor appears to be a laissez-faire attitude by the American Physics Society. I don't see a recommended curriculum at the APS site. Other professional societies are much more vocal than is the APS regarding undergraduate education.

I think that part of it is that there is less professional coherence in physics. For example, for aeronautical engineers, we can reasonably assume that the purpose of a degree of aeronautical engineering is to train aeronautical engineers and so we can get a group of professional aeronautical engineers together to figure out what training is necessary

For the undergraduate physics degree, it's difficult to get agreement on what the point of the degree is.

 

[Andy Resnick]

There are lots of different multi-person decision mechanisms that are possible that don't involve committees. For example, there are relatively few committees in most businesses. One person makes the decision, but in the process of making the decision, they have to consult with other people. The point of having one person make the decision is so that if it turns out that it's a bad decision, you have one person responsible for it.

You can have one person have the authority to make a decision subject to approval by some other person. In a lot of situations, there is a deliberate effort not to create a committee so that the other person reviews the decision independently.

Then you have markets, which is a very complex system for making decisions that don't involve committees.

Yes, but academic institutions- all academic institutions public and private- involve the idea of 'shared governance'. This is a fundamental quality control issue- without shared governance, administrators decide what students learn (see, for example, intelligent design).

 

[twofish-quant]

Yes, but academic institutions- all academic institutions public and private- involve the idea of 'shared governance'. This is a fundamental quality control issue- without shared governance, administrators decide what students learn (see, for example, intelligent design).

1) Shared governance effectively gives people veto power for any sort of change, which means that nothing gets done.

2) Given the number of people that believe in creationism and intelligent design, I don't think it's that effective a quality control mechanism. One issue is that by the time the student gets to college he or she is already influenced very heavily by their surroundings and the type of education they've already gotten, and that's something that is out of the control (and should be out of the control) of most academics.

One reason that things would be easier with smart thinking students is that if you view students as something other than empty vessels ready to have knowledge poured into them, it becomes a lot less important what ideas they are exposed to.

And you really can't control what ideas someone is exposed to. Even if you don't teach intelligent design in the classroom, the student is going to learn it in church, from their parents, and from a million different places on YouTube.

You can teach the student the basic philosophy and culture of science so that when someone does see an video on intelligent design on YouTube, the person can think from themselves and reject the ideas as being unscientific, but that involves having the student accept the basic philosophy and culture of science, which is impossible to do if your institutions are authoritarian. Actions speak louder than lectures.

There's a weird bizarre contradiction here "Think for yourself, we are ordering you to!"

The other problem with shared governance is that it's not really that shared. Adjuncts and students aren't part of the shared governance, and that produces a nasty class structure that undermines the cultural message that I think we are trying to present.