Can Engineers with PhDs Effectively Teach Math at the University Level?

[sutupidmath]

An engineer teaching Math!

I was just wondering how decent would it be for a person who has a PhD in Engineering to teach Math at a University? In other words does an engineering degree really prepares one to teach Math courses at a University level? Or, what courses would it be all right for him/her to teach, that wouldn't really make any difference whether he is a pure mathematician or an engineering?

Thnx for your replies!

 

[quadraphonics]

Depends on which math courses and what kind of engineer. Most people would probably agree that someone with a PhD in engineering is plenty qualified to teach, say, freshman calculus. Also, there are certain fiels of study in engineering that pretty much ARE math (Information theory is probably the best example, but there's also controls and coding), and so you have engineers teaching (and researching) math all the time. It's not uncommon for math-inclined engineers to end up as joint professors between an engineering department and the math department. One of the control systems professors where I went to school would teach the graduate real analysis course on alternating years, for example. Likewise, it's fairly common for certain math courses to be populated mostly by engineering students (probably owing to the fact that engineering departments tend to be much larger than math departments). It's also not uncommon for engineering students to earn an MS in math before getting a PhD in engineering, or to take a large number of math classes while doing their PhD. It's also pretty common for engineering PhD's to have a math professor on their thesis committee.

 

[NeoDevin]

No! Having been on the receiving end of this I would say that an engineering PhD is no indication of mathematical ability. I had a Chem E teach my PDE's course, and he didn't know half the material himself (seriously, he spent 10 minutes one class trying to figure out what an odd function was).

That's not to say all engineers would be unqualified, just that an engineering PhD cannot be taken as evidence for mathematical knowledge.

 

[ice109]

i would go as far as saying that one shouldn't learn math even from a physicist

 

[quantumdude]

Most engineers stop taking math at differential equations, which means they really don't know much about math at all. Before I would trust an engineer to teach a math course, I would want to know a thing or two about his preparation. For instance, I wouldn't let anyone teach even calculus unless he had a decent sequence in either advanced calculus or real analysis. I am of the opinion that if someone is to be prepared teach a subject, then he should have studied it well beyond the level of the course he intends to run.

 

[quadraphonics]

i would go as far as saying that one shouldn't learn math even from a physicist

I resent the implication that physicists know more about math than engineers :P

 

[rbj]

I don't have a PhD (was ABD from Northwestern in the 80's), but I taught calculus at another school. I think a PhD in EE, who has had some serious courses in Diff Eq, Applied Math, Vectors and Matrix Theory, Probability and Random Processes, Complex Variables and Functions, Numerical Methods and Approximation Theory, Real Analysis, Metric Spaces and Functional Analysis, and who has used such concepts in their research and publication as well as in the EE courses they have taught would be plenty qualified in the material to teach nearly any such courses (maybe leave out the Real Analysis and Functional Analysis) as far as their own competence in the math is concerned. If the EE prof doesn't know how to teach in the first place, then they might not be any good, but it wouldn't be because they didn't know their stuff.

 

[quadraphonics]

Most engineers stop taking math at differential equations,

I don't think that's accurate if we're talking about people with PhD's in engineering.

 

[rbj]

Most engineers stop taking math at differential equations, which means they really don't know much about math at all.

I don't think that's accurate if we're talking about people with PhD's in engineering.

yeah, it's not true at all. at least for EE. i took at least one semester (but most of the time, two) in each of the fields i listed above.

 

[sutupidmath]

Would it be offensive if i posted here the name of the proffesor in particular for which i am interested to know. He seems to have some publications. I am asking this, because i am wondering whether it is okay to take him in one of my math courses, or should i take someone else.
He has his name at my university's web page, but can i post it here?

 

[Feldoh]

i would go as far as saying that one shouldn't learn math even from a physicist

Why not? Some of the greatest mathematicians of all time were physicists. I mean let's be honest, without application mathematics itself is pretty pointless, sure it's great to do but it has no real importance unless it can be applied somewhere. Why should someone who works to apply math to real-life problems not be allowed to teach it?

 

[rbj]

That's not to say all engineers would be unqualified, just that an engineering PhD cannot be taken as evidence for mathematical knowledge.

how does one get a PhD in engineering without being pretty damn good at applied mathematics? are they giving the degrees away?

 

[rbj]

Would it be offensive if i posted here the name of the proffesor in particular for which i am interested to know. He seems to have some publications. I am asking this, because i am wondering whether it is okay to take him in one of my math courses, or should i take someone else.
He has his name at my university's web page, but can i post it here?

it wouldn't offend me, and I'm not going to sue you.

i can't speak for others.

 

[sutupidmath]

MOreover, the proffesor that i am talking about has gotten Ph.D. in engineering mechanics from University of Texas at Austin.

I am concerned because at my university there are only 3 pure math proffesors who have phd's at math. The others either have phd's in engineering mechanics, nuclear engineering, electrical and computer engineering.

Here is the link:

http://www.tlu.edu/academics/academic_departments/mathematics/mathematics_faculty

 

[quadraphonics]

A relevant quote I read somewhere (I think it was IEEE Spectrum):

A Bachelor's degree proves that you have the basic skill set required for your field.
A Master's degree proves that you are an expert in some particular field.
A PhD proves that you have the ability to become an expert in any particular field.

So, someone with a PhD in engineering should certainly have the ability to master the math material at the appropriate level. The question is: did they actually do this? The degree doesn't really tell you (even if it was a math degree, it's still no guarantee), you have to find out by asking people who've taken the classes before, or just see for yourself. Although, presumably, the department wouldn't let him teach the course if they didn't think he knew the material well enough. Also, bear in mind that people don't stop learning when they finish their PhD, particularly people who stay in academia. Just because someone got a PhD in engineering doesn't mean that he hasn't spent all the intervening years dorking out on math textbooks and classes.

And of course, having an appropriate mastery of the material is still no guarantee that they can actually teach worth a damn.

 

[quadraphonics]

yeah, it's not true at all. at least for EE. i took at least one semester (but most of the time, two) in each of the fields i listed above.

Likewise. And, again, that's just 'real' math courses. If you start counting EE courses that are nothing but math, it begins to look even more impressive. Although I suppose that EE is somewhat more mathematical than other types of engineering, except for control systems...

Also, what's ABD?

 

[D H]

All But Dissertation. A particularly nasty way to end one's college career with just a Masters degree to show for it.

 

[quadraphonics]

Aaaaaah. Where I went to school, you'd end up with a CPhil in addition to the Masters in that situation...

 

[Troels]

i would go as far as saying that one shouldn't learn math even from a physicist

I had a cource "Applied math for physicists" which was being taught by... a mathematician. I have since tried to find a suitable word to describe this arrangement and I have come to settle on the word... disasterous.

And by the way, I do study physics and nanoscience but technically I'm an engineering student. I can vouch for the mathematical skills of my kind.

 

[Dr. Courtney]

Odds are that roughly half of the teachers you will have in your college experience will be below average.

Complaining about perceived poor teaching does little good.

Being a good enough student to learn from the below average teachers is a requirement to succeed in college.

There are two kinds of students (which become two kinds of employees):

1. Those who are content with having a good excuse for failing to accomplish the goal. No one is really impressed with the quality of your excuse.

2. Those who find a way to accomplish goals even though significant obstacles must be overcome.

If you cannot learn to succeed in a class with a professor who is below average, how will you succeed in a job with a boss who is "below average"?

Michael Courtney

 

[D H]

I had a cource "Applied math for physicists" which was being taught by... a mathematician. I have since tried to find a suitable word to describe this arrangement and I have come to settle on the word... disasterous.

That sounds a lot like my optimal control theory class taught by a pure mathematician. Disaster. We didn't make it past the introductory material. It wasn't the class that held the instructor back. It was the instructor who balked at the less-than-perfect rigor presentation style of the introductory concepts in the text.

 

[sutupidmath]

Thanks a lot for your input guys!

 

[rbj]

All But Dissertation. A particularly nasty way to end one's college career with just a Masters degree to show for it.

It's dissappointing but i would say "particularly nasty" and "just a Masters degree" is a bit of hyperbole.

as with any work, i have frustrating experiences. but I'm 52 and not terribly unhappy with my life at the moment. i know more than one PhD where that person's marriage was sacrificed for the PhD. that seems even more particularly nasty to me than the academic failure indicated by ABD.

 

[rbj]

That sounds a lot like my optimal control theory class taught by a pure mathematician. Disaster. We didn't make it past the introductory material. It wasn't the class that held the instructor back. It was the instructor who balked at the less-than-perfect rigor presentation style of the introductory concepts in the text.

i remember a class in diff eq. in the math department, where we used an RC circuit as an example and the math prof literally got it wrong and refused to acknowledge the correct answer because we EEs don't deal with the Dirac impulse function as rigorously as the math guys would prefer. (speaking for me, at least, we EEs are perfectly fine with the Dirac delta being a "function" that is zero almost everywhere, yet integrates to 1. but the math guys are not perfectly fine with that.)

 

[bubbles]

I have a linear algebra class that is being taught by an Electrical Engineering PhD. He is knowledgeable about the subject, but simply cannot teach math. Sometimes I feel that some professors know too much to teach. Those professors should not be allowed to teach introductory undergraduate courses.

 

[Astronuc]

It might work for an engineer or physicist to teach an 'applied math' course in an area related to one's engineering discipline or physics. It may not work for an engineer or physicist to teach a 'pure' math course, unless that person has the proficiency/competence in that particular field. It would appear to be case specific.

 

[Troels]

It might work for an engineer or physicist to teach an 'applied math' course in an area related to one's engineering discipline or physics. It may not work for an engineer or physicist to teach a 'pure' math course, unless that person has the proficiency/competence in that particular field. It would appear to be case specific.

At least, I have never claimed that engineers should teach pure math, I totally agree that that ought to be left at the mathematicians - and the students that find that sort of thing interresting - at the math department. But then again, I regard "pure math" as a waste of time. This is after all a very specialized branch of math, that attract a limited crowd

I signed up for a "pure math" course in last term. I lasted three weeks... Boy that was boring, blackboard after blackboard of boolean relations and not a single word on what is was good for.

So for all practical and advanced applications, physicists and engineeres are more than qualified for teaching math.

 

[Troels]

(speaking for me, at least, we EEs are perfectly fine with the Dirac delta being a "function" that is zero almost everywhere, yet integrates to 1. but the math guys are not perfectly fine with that.)

As are we, physicists

 

[mgiddy911]

I'm perfectly fine with the dirac delta just being that funny little squigly that arises when I got something wrong in E&M

 

[zhentil]

Sometimes I think that physicists and engineering phds should teach the grad level math courses used in their disciplines. At least at my school, the engineering grad students who take math classes don't have the prerequisites (e.g. differential equations is not suitable preparation for measure theory), don't know how to prove things, and cannot stand the abstraction. And my school is top ten for engineering grad programs.

At some point, we need to realize that mathematicians and engineers are not going to agree on how a PDE course should be taught. An engineer has no use whatsoever for non-constructive existence theorems, and a mathematician has no use for solving the laplace in 18 different domains.

 

[zhentil]

At least, I have never claimed that engineers should teach pure math, I totally agree that that ought to be left at the mathematicians - and the students that find that sort of thing interresting - at the math department. But then again, I regard "pure math" as a waste of time. This is after all a very specialized branch of math, that attract a limited crowd

I signed up for a "pure math" course in last term. I lasted three weeks... Boy that was boring, blackboard after blackboard of boolean relations and not a single word on what is was good for.

So for all practical and advanced applications, physicists and engineeres are more than qualified for teaching math.

I'm sure a lot of physicists and engineers are glad that mathematicians "wasted their time" on pure math like complex analysis, differential geometry, and algebraic topology.

 

[Troels]

I'm sure a lot of physicists and engineers are glad that mathematicians "wasted their time" on pure math like complex analysis, differential geometry, and algebraic topology.

Then physicists need new math, they usually develop it themselves

 

[zhentil]

Then physicists need new math, they usually develop it themselves

I hope you're joking.

 

[mordechai9]

Someone with a Ph.D. in a mathematical subject like engineering is probably well suited to teach at least basic mathematics. For example, I definitely think someone with an undergraduate degree in engineering would be qualified to teach a secondary school course in mathematics.

Once you start getting into higher-level or college-level coursework, the situation changes a bit. For a lot of courses, such as undergraduate calculus and differential equations, proofs have little to no role in the course material (which I think is bull****, but that's the reality). So an engineer, who has substantial training in non-proof based mathematics, would probably be quite capable in this position. However, an engineer in a proof-based course I would expect to be much less qualified compared to a similarly educated mathematician. "Pure" engineers just don't have the necessary experience in proofs and rigor that you get after taking upper-level courses in math. However, a "mathematical" engineer, or someone who has for example double majored in math and engineering, I think could still be quite qualified. Similarly, I think a math professor could do a great job teaching engineering if they came from that background. Basically, that's the background I'm trying to create for myself right now.

One remark closely related to this discussion: there's a big problem with undergraduate mathematics education in the USA. People aren't taught to reconcile their enjoyment of both pure and applied mathematics. In my experience, my math courses at UT Austin have done a horrible job of synthesizing mathematics and applications together. Usually, the math classes have erred on the side of overly applications. There's very little proof of what you're being told, and very little exploration of the root ideas. Hence, after a few years, the concepts become quite muddy and you start to question that the ideas even work. You can only use the "chain rule" so long before you wonder, "where the *** did that come from?" Anyways, this could probably be the topic of another post...

 

[zhentil]

Oh, man. The absolute least a calc teacher could do is teach you the "non-rigorous" proof of the chain rule. Use the definition of the derivative, and multiply on bottom and top by g(x+h)-g(x), if you're differentiating f(g(x)).

 

[Troels]

I hope you're joking.

I don't.

The novel mathematical formulation of Quantum mechanics for instance, was almost entirely developed by physicists.

 

[ice109]

I don't.

The novel mathematical formulation of Quantum mechanics for instance, was almost entirely developed by physicists.

maybe but it was of course made more rigorous by a mathematical physicist.

 

[Eidos]

Someone's signature on this very forum is: "Theoretical physics is locally isomorphic to mathematics"

Who cares what name badge we wear? Understanding the material and being able to teach it are what are important in this discussion. George Green, a famous mathematician whom which I'm sure most of us are familiar with, was a baker and mostly self taught.

http://en.wikipedia.org/wiki/George_green

So the name badge you wear "Physicist", "Mathematician" or "Engineer" are not necessarily proof that you cannot teach a field outside of what is normally associated with your profession. Likewise, as someone has already pointed out, having a Phd, publishing papers regularly and being renowned in your field does not mean that you can communicate your ideas effectively as a teacher.

Teaching itself is an art form and I believe should be made to appeal to the intended audience's intuition. But that is a whole other discussion.

 

[George Jones]

I don't.

The novel mathematical formulation of Quantum mechanics for instance, was almost entirely developed by physicists.

And allows stuff like https://www.physicsforums.com/showthread.php?t=122063".

Don't get me wrong, I think Dirac was a genius, a term I use for very few people.

maybe but it was of course made more rigorous by a mathematical physicist.

I would call Johnny von Neuman a pure mathematician who sometimes worked (very productively!) on physics.

He could also be called a chemical engineer, since he got a degree in chemical engineering.

 

[Troels]

And allows stuff like https://www.physicsforums.com/showthread.php?t=122063".

*offtopic*

No it doesn't. QM-operators do not operate on states to the left, so the step:

\left\langle a|AB|a\right\rangle = a\left\langle a|B|a\right\rangle

is faulty when A and B don't commute... at least i my undergraduate QM-school.

EDIT: Ah it works out! It is corrected by the assumption that A is self-ajoint (hermitian) so:

\left\langle a|AB|a\right\rangle = A^\dagger\left\langle a|B|a\right\rangle = A\left\langle a|B|a\right\rangle =a\left\langle a|B|a\right\rangle

 

[reilly]

Engineers with PhD degrees in 1. EE, or 2. Control Engineering, and or 3. Aeronautical Engineering typically have very sophisticated math backgrounds -- functional analysis, nonlinear DE's numerical solutions of PDEs, mechanics of fluids, chaos and turbulence and on and on. Of course, such a background does not guarantee teaching ability. You have to go case-by-case.
Regards,
Reilly Atkinson