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

[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