Necessity of formal math education for Electrical Engineer?

[RubinLicht]

So, I am majoring in Electrical engineering, and probably doing a decent amount of Physics and Computer science courses until I can no longer squeeze it into my schedule. In the far future, I definitely plan to work in industry, and hopefully in R&D type engineering work. Will I ever in my career wish that I had learn calculus from Apostol, and learned how to do proofs, instead of learning calculus from Gilbert Strang?

My current situation: going to college in two months, I took all of calculus and linear algebra in a community college in high school, two years ago. I want to review, I am debating between gilbert strang and Apostol. If I do apostol, I will also read Velleman's How to Prove it, since it seems like I have trouble following even the most basic of proofs in the book about axioms for a real number system. (I know what it means, I do not know how to create the proof from nothing)

EDIT: I think it is good to consider Electrical Engineering and Comp sci research (professor) open as a possibility. Take this into account.

 

[FactChecker]

For engineering, applications of math and mathematical calculations are much more important than formal mathematical proofs. You should still try to get an intuitive understanding of the math, but the formal proof is often different.

 

[Dr.D]

Formal proofs are relatively rare in engineering mathematics, but informal proofs or demonstrations are quite common. Just yesterday, I was working through a linkage problem (I am an ME), and I applied Grashof's theorem to prove that there were no cranks in a particular four-bar linkage that I was looking at.

I'm not a fan of Apostol, so I would suggest not going that way if engineering is your future.

 

[Crass_Oscillator]

I think it's a waste of time to pursue fancy, formal math from an engineering standpoint (electrical engineering grad student here, seeking an industrial or academic R&D position), but pure control theorists in math and EE departments like fancy stuff.

However, there are few jobs where you'll get paid to use or perform formal mathematical analysis of control systems; far more jobs look look dirty, intuitive applied math/engineering/physics.

I think a lot of the formal stuff is academic pathology, but I can't say for sure.

 

[Dr.D]

I think a lot of the formal stuff is academic pathology, but I can't say for sure.

Most of the time, this is entirely correct. The interesting occasions arise, however, when it is not true. As an ME, I have solved lots of problems using things like Green's Theorem where none of the other engineers could get close. I took a ton of math classes, and I don't think any of them ever proved to be wasted. Most of my education was pre-computer era (there were computers, but only for research), but I find now that I can implement many of those techniques in the computer where I was just unwilling to do the dog work to carry out all the hand calcs.

 

[Crass_Oscillator]

Most of the time, this is entirely correct. The interesting occasions arise, however, when it is not true. As an ME, I have solved lots of problems using things like Green's Theorem where none of the other engineers could get close. I took a ton of math classes, and I don't think any of them ever proved to be wasted. Most of my education was pre-computer era (there were computers, but only for research), but I find now that I can implement many of those techniques in the computer where I was just unwilling to do the dog work to carry out all the hand calcs.

I agree, but it is important to distinguish between different types of advanced mathematics. I too took many advanced mathematics courses which went into great detail regarding how to prove such things as the fundamental theorem of calculus.

It is important to note that some mathematics arises from a need to solve a general mathematical problem, and some arises to solve what I like to refer to as abstraction induced problems, which are artificial in nature. Green's theorem arose from the need to solve practical problems and was established likely without the out of control rigor and frivolous abstraction of the (pure) math department today. Green proved his theorem in 1828 and titled his paper "An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism".

You can read the essay for yourself: aside from stiff 19th prose, it is manifestly readable. Abstraction induced problems occur when people want to exalt objects such as real numbers with an ontological status they don't deserve*, or when they want to divorce the mathematics from its original application oriented purpose.

Green's Essay:
https://books.google.com/books?id=GwYXAAAAYAAJ&pg=PA10#v=onepage&q&f=false
https://books.google.com/books?id=GwYXAAAAYAAJ&pg=PA10#v=onepage&q&f=false
*i.e. rather than viewing the square root of two as an algorithm (common sense!), they try to endow it with properties similar to numbers by creating a new number system, which winds up just creating convoluted philosophical problems.

Of course all of this is boring philosophy to me: I prefer to just solve problems

 

[jasonRF]

My current situation: going to college in two months, I took all of calculus and linear algebra in a community college in high school, two years ago. I want to review, I am debating between gilbert strang and Apostol. If I do apostol, I will also read Velleman's How to Prove it, since it seems like I have trouble following even the most basic of proofs in the book about axioms for a real number system. (I know what it means, I do not know how to create the proof from nothing)

If you will be transferring the credit and taking classes in a couple of months that assume you know that material, then the first thing you should do is make sure you really know the math in those classes very well. You should be able to solve the types of calculus problems you were able to solve two years ago. You should know your linear algebra - not just how to solve systems of equations but understand what linear independence means, what eigenvalues and eigenvectors are and how to compute them for small matrices (2x2, 3x3), how to diagonalize an operator, etc. Only after you are comfortable you know all of that should you think about moving on to a more theoretical treatment from a source such as Apostol.

So, I am majoring in Electrical engineering, and probably doing a decent amount of Physics and Computer science courses until I can no longer squeeze it into my schedule. In the far future, I definitely plan to work in industry, and hopefully in R&D type engineering work. Will I ever in my career wish that I had learn calculus from Apostol, and learned how to do proofs, instead of learning calculus from Gilbert Strang?.

I doubt it. Apostol in principle teaches both the computation and the proofs, but starting with just the computation is fine, and perhaps preferred for most of us.

Many R&D jobs require graduate school - a PhD would give you the most opportunities. In areas like communications/information, controls, and signal processing it is not unusual for grad students to take proof-based math classes in real analysis, algebra, geometry, etc., (usually undergrad level, but sometimes grad level) from the math department. By proof-based I mean that almost every homework problem was a proof. And in analysis class they learned how to do things like construct a function that is continuous everywhere but differentiable nowhere.

But here is the thing: most of them learn the proof-based math after they know the immediately practical computational versions. Also, I certainly know PhDs in those fields that did not take any hard-core proof-based math classes until graduate school. If you are really interested and have time in your schedule you can take a proof-based math class (or two) as an undergrad to see how you like it. But I suspect if you are taking a bunch of extra physics and cs classes, that you will need the appropriate math-methods kinds of courses and won't have a lot of room in your schedule for a lot of theoretical math. By the way, some computer science courses can be pretty theoretical and involve legitimate mathematical proofs.

Good luck!

jason

 

[FactChecker]

As @jasonRF says, R&D often prefers PhD degrees and some associated theoretical math. But you should not "jump the gun" and worry about that yet. There will be plenty of time to find out what that will require. If you try to guess now, you may spend a lot of time and effort on theoretical math subjects that will not help you.

 

[Crass_Oscillator]

As @jasonRF says, R&D often prefers PhD degrees and some associated theoretical math. But you should not "jump the gun" and worry about that yet. There will be plenty of time to find out what that will require. If you try to guess now, you may spend a lot of time and effort on theoretical math subjects that will not help you.

Which fields want associated theory from the math department? I know there are examples but I cannot think of any (I know numerous PhD controls people in industrial R&D and they do not use or perform proofy-math, although they were trained in it).

The only field I can think of off the top of my head that really seems to demand it is mathematical statistics, and that's still a very small number of industrial R&D positions.

Part of this depends upon how you define the phrase "uses theoretical math" however.

 

[FactChecker]

Which fields want associated theory from the math department? I know there are examples but I cannot think of any (I know numerous PhD controls people in industrial R&D and they do not use or perform proofy-math, although they were trained in it).

The only field I can think of off the top of my head that really seems to demand it is mathematical statistics, and that's still a very small number of industrial R&D positions.

Part of this depends upon how you define the phrase "uses theoretical math" however.

I don't know if I would say they were "from the math department", but research publications in optimal control are full of H^p spaces, NP-complete, convergence criteria, and other theoretical math considerations. I assume that other fields have similar theoretical issues.

 

[jasonRF]

Which fields want associated theory from the math department? I know there are examples but I cannot think of any (I know numerous PhD controls people in industrial R&D and they do not use or perform proofy-math, although they were trained in it).

The only field I can think of off the top of my head that really seems to demand it is mathematical statistics, and that's still a very small number of industrial R&D positions.

Part of this depends upon how you define the phrase "uses theoretical math" however.

Sure - much of the work that really uses high powered math seems to be from academia. I am not trainined in theoretical math, but certainly work with folks that have been, and do on (somewhat rare) occasions see theoretical math as part of someones work at my company. Here I am thinking people working in statistical signal processing and communications/information theory. Sometimes (perhaps most of the time?) the theorertical math is just window dressing and is not really necessary, but sometimes it really is required.

Note that part of the benefit of the mathematical training, even for folks working outside of academia that are not doing theoretical math anymore, is gaining the ability to actually understand and critically evaluate the published literature in order to incorporate new ideas into practical systems. The training also seems to yield strong mathematical modelling skills and facility with thenon-rigorous "advanced" math of the engineer.

At one point in my carreer I was re-organized into a group that did a lot of the more theoretical work at my company. Partially just for fun, but partially to help re-invent myself for this new environment, I systematically worked through a baby intro real analysis book and a reasonably theoretical undergrad linear algebra book (Axler). Did it turn me into a superstar for the group? Of course not. But it really did help me with the skills listed in the previous paragraph.

jason