Engineer Grad Never Taken Proof-Based Math Course

harvard09 · 03-30-2008, 08:47 PM

I'm tutoring an electrical engineering grad student in an applied math course. He's struggling and can't do very elementary proofs (i.e. prove that the function is convex, prove that the function is a cone, etc.). He says that he has never taken a proof-based math course as an undergrad. Is this typical of an undergraduate engineering student?

Shackleford · 03-30-2008, 09:46 PM

It is typical.

harvard09 · 03-30-2008, 10:17 PM

I see. That means many engineers don't have a good understanding of the mathematics that they are applying.

bah · 03-30-2008, 10:27 PM

I'm afraid I'll never have a good understanding of the math I am learning...

I think it is rather typical. Proof based math? That's only in theory/proof based math classes (ie MATH 224: "Theoretical Linear Algebra and Calculus" using the textbook "Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach" by John Hubbard). Engineering math sequence here is all applications.

furyshade · 03-30-2008, 10:37 PM

is there anyway as a freshman EE student next year to take classes like that? in my senior year of HS i am taking number theory which i like a lot and want to continue that line of math.

roroAutomAtic · 03-30-2008, 10:50 PM

"I see. That means many engineers don't have a good understanding of the mathematics that they are applying."

LOL. Yes, not only because we don't have to, but the competitive nature of the program and the silly profs obsessions with making life unnecessarily difficult means that even though some of us would rather know this, it is in our best interest to concentrate on getting a good grade than actually "learning" the material.

Sad but true. Blame the system.

Shackleford · 03-30-2008, 11:34 PM

Well, it's more than adequate to know how to use the math than to know how to prove the math. It's like trying to ask a carpenter to prove how a house stands up. He can, but only to a degree, beyond which is unnecessary. Other people figured out how to make it stand up which ultimately led to the simplicity in building for the carpenter. Yes, I know it's a horrific analogy, but I'm very tired and did most of my cal homework earlier through the tiredness.

harvard09 · 03-31-2008, 12:06 AM

What if after the carpenter finishes building the house, a part of it falls down. The carpenter doesn't know why. Or what if we want to extend the house so that it is not a typical house? The carpenter doesn't know how. It's true that the carpenter's skills are more than adequate, but to truly stand out and impress people, he/she needs to know the fundamentals of house building.

This leads me to believe that a lot of engineering schools are churning out engineers that can adequately use math tools for their applications, but can not adequately do mathematical research in their field. This is why the grad student I'm tutoring will probably have a very hard time with his PhD even though he was an excellent student.

md5fungi · 03-31-2008, 08:32 AM

At my school only Computer Engineers have to take proof-based math, i.e. Discrete Math. Abstract Math is another option for Engineers at my school who want to pursue a math minor. I suppose Random Processes involves some of that as well, but not to a very high extent.

Shackleford · 03-31-2008, 09:13 AM

harvard09, I meant the carpenter probably couldn't down to a very rigorous mathematical/physical level like, say, a structural engineer or even architect could.

aibarr · 03-31-2008, 09:37 AM

Harvard09, to engineers, math is a tool. For my graduate work, I needed to know how to do tensor calc, tops. A lot of matrix manipulation. The stuff I needed to know how to do, I knew how to do well. Engineers don't need to know math to the degree that math majors know how to do math because there is an exorbitant amount of *other* stuff that engineers have to learn that *math* majors don't. Saying that engineering majors need to be well-versed in mathematical proofs in order to understand what we're doing as engineers is kind of like saying that in order for mathematicians to understand the implications of the math that they're doing, then they need to be well-versed in what engineers do... and if you were, you wouldn't be quite so incensed that we don't know math backwards and forwards!

For your carpenter analogy counterexample, when a house falls down (or when your math falls down) you don't even ask the carpenter what happened. You call in a structural engineering forensicist. Likewise, in the rare case that an engineer encounters math that they (or Mathematica) can't handle, they'll call in a mathematician, who can help out with highly abstract math, which engineers run into probably a few times in a lifetime. That's why we specialize in different things. It's unreasonable to expect an engineer to be highly versed in how to do proofs, since that's not what they're being trained to do. It's not my job to do mathematical research in my engineering field. It's my job to do *engineering* research in my engineering field. There's a lot more to engineering than just math. Rest assured that while we may not know *everything* in math, we know a heck of a lot about engineering.

(To your original statement, I'd have to dredge out my vector calc book, but I'm reasonably sure I could prove that a particular function describes a cone. It wouldn't be pretty, kind of like how my programming's always horribly inefficient... which is another reason why I'm an engineer and not a programmer, and probably ties into the reasons why I'm not a mathematician either... but it'd get the job done. My engineering's at least really pretty.)

jessiehl · 03-31-2008, 10:22 AM

At most schools, yes, what you are describing is typical.

At some very high-ranked schools, it's not. But even engineers at those schools are not likely to have the theoretical math skills of a math major.

The ones who want to do heavily math-based research in their fields will take the classes that prepare them for this as electives.

A possible exception to the "typical" thing is computer science (which is part of the school of engineering in many schools, including Harvard). Most computer science majors have to take a discrete math class, and that class usually involves proofs.

furyshade · 03-31-2008, 04:51 PM

is it possible for an EE major to do a double major in math or is that just an unrealistic goal given the work load?

aibarr · 03-31-2008, 05:08 PM

Furyshade, it might be a bit much, but it'd possibly be doable. ABET requirements for EE make it one of the most time-consuming majors, so that might make it really difficult to add another major to... Still, there's really nothing to stop you from just taking some extra math courses that seem interesting to you, though, instead of doing a whole double major in it. You can tout on your resume that you have a particular interest in math and that you took whichever courses you ended up taking, but the pain-to-benefit ratio of getting a whole second major in something that probably won't make you *tremendously* more interesting than other job or grad school candidates might be lower than you'd expect it to be. Take a look at the requirements, ask around, and see if it's something you ultimately would be interested in doing... you might decide it's worth it to you!

RacinReaver · 03-31-2008, 07:24 PM

You might be better served just getting a minor in math instead of a double major. There's probably a whole bunch of required classes that won't interest you, and if you decide to do a minor you won't have to bother with them. That's the main reason I got a minor in physics instead of a double major. I didn't have to take the higher-level boring physics classes, and I could focus instead of taking quantum mechanics, extra thermodynamics, and solid state physics classes instead.