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

[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