Which electrical engineering subdiscipline uses the most math?


by Only a Mirage
Tags: control theory, electrical engineer, electromagnetics, math, photonics
Only a Mirage
Only a Mirage is offline
#1
Nov13-12, 02:11 AM
P: 48
Between control theory, photonics/optoelectronics/semiconductor devices, electromagnetics (antennas or other application), which of these fields has the potential to expose me to the most mathematics in graduate school?
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Klungo
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#2
Nov13-12, 09:08 AM
P: 136
It sounds to me like you would prefer becoming a mathematician than an EE.
Most of which you mentioned are the most physics based EE courses so they will have a bit more (and different) maths than other specialties digital logic, processors, etc. [maa on undergrad EE] You could ask your professors for specifics.

But why more math? As an EE, you should choose what interests you most (which may very well be the one(s) with the most math).

[Note: I'm only a freshman CompEE major but the mathematics you will roughly use is given by MAA EE chapter (and to me by my EE orientation)]
clope023
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#3
Nov13-12, 09:18 AM
P: 593
electromagnetics and semi/super conductor physics.

some aspects of electronics (filters) are pretty mathy too.

DrummingAtom
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#4
Nov13-12, 10:19 AM
P: 660

Which electrical engineering subdiscipline uses the most math?


This thread might have some good advice for you:

http://www.physicsforums.com/showthread.php?t=332777

I know it's not on your list but I currently have a professor that is in communication theory that talked up DSP to us earlier this semester so I looked up some of his work. His papers and others I've seen within DSP/communications read like a pure math paper; definition, theorem, proof, repeat. By the way, I'm only a junior in EE right now.

I would like to hear what people have to say about control theory or other branches that use a lot of math.
Only a Mirage
Only a Mirage is offline
#5
Nov13-12, 05:01 PM
P: 48
Thanks a lot for the responses, guys. The subdisciplines I mentioned are the main ones I am considering.

Klungo, I really like math and physics, but I also want to directly contribute to new technology. I also think an engineering graduate degree might be more marketable than physics/math grad degrees for industry/government research jobs. Also, while I like both, if I had to pick between learning more math and learning more physics, I'd pick math.

Clope023, can you please give specific examples? The two courses I took in semiconductor electronics were not highly mathematical. They mostly consisted of "plug-and-chug" problems and applying physics "rules of thumb" (quantum mech. Was not a prerequisite). As for Electromagnetics, it involves vector calculus and linear PDEs, but does it progress beyond that math wise? For example, nonlinear control theory makes use of Lie groups and differential geometry, from what I understand which seems much more advanced. Also, I don't know a lot about superconductors which you mentioned.

DrummingAtom, thanks a lot for the thread link. It was reassuring to see DSP, control theory, and communications listed because that was what I thought. Control just sounds the most interesting out of those to me though.

Thanks again everyone, and I'd love to hear any more advice.
Only a Mirage
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#6
Nov13-12, 06:56 PM
P: 48
By the way guys, I forgot to mention that I am a senior in EE. I've also taken a decent amount of math so far (calc 1-4, elementary ODEs, discrete math, linear algebra, elementary PDEs, vector analysis - will be taking complex variables and maybe advanced diff. eq.s in the spring).

I'm currently working on applying for grad schools/fellowships right now. My academic advisor is sort of a "theoretical" control theory researcher. He has said that if I choose control theory, he would be more than willing to help me with choosing schools and has even said he would email professors at other schools to "vouch" for me. I'm just trying to make a decision soon with deadlines coming up.
clope023
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#7
Nov13-12, 11:32 PM
P: 593
Quote Quote by Only a Mirage View Post
By the way guys, I forgot to mention that I am a senior in EE. I've also taken a decent amount of math so far (calc 1-4, elementary ODEs, discrete math, linear algebra, elementary PDEs, vector analysis - will be taking complex variables and maybe advanced diff. eq.s in the spring).

I'm currently working on applying for grad schools/fellowships right now. My academic advisor is sort of a "theoretical" control theory researcher. He has said that if I choose control theory, he would be more than willing to help me with choosing schools and has even said he would email professors at other schools to "vouch" for me. I'm just trying to make a decision soon with deadlines coming up.
IMO, EE in undergrad is a math light degree; I've taken the same math courses you have but they were by no means required by my program. From what I understand the math in electrical engineering comes when you take the graduate level versions of your undergrad courses. Alot of EE's take E&M out of Jackson (the physics E&M grad book), and they look at real quantum mechanics not the light version of modern physics you see in solid states, etc. I've heard graduate/theoretical controls can get very intensive.
Only a Mirage
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#8
Nov13-12, 11:59 PM
P: 48
Quote Quote by clope023 View Post
IMO, EE in undergrad is a math light degree; I've taken the same math courses you have but they were by no means required by my program. From what I understand the math in electrical engineering comes when you take the graduate level versions of your undergrad courses. Alot of EE's take E&M out of Jackson (the physics E&M grad book), and they look at real quantum mechanics not the light version of modern physics you see in solid states, etc. I've heard graduate/theoretical controls can get very intensive.
Yeah, I've heard Jackson is pretty rough.

If I just went to graduate school for physics, I would learn a lot of physics (good!) and a lot of abstract math from the advanced courses like G.R., Q.E.D., etc. (also good!). But I want to do engineering for a few reasons. Within electrical engineering, I could do engineering physics (for example, MIT offers this as an area within EE: Area IV I believe). But the problem is that (I think) the physics used in electrical engineering physics is mainly Q.M. and electromagnetics. I like these topics, but I don't see the math progressing to the level of the math in G.R.

But, my advisor (controls guy) has given me examples about how a lot of the math in advanced physics also shows up in control theory. For example, differential geometry (used in G.R.) is used in nonlinear control.

So I kind of view my choice as one between EE + more math(controls) or EE + more physics(but not more math). So I think I should choose controls in lieu of photonics or electromagnetics if learning math is more important to me than learning physics.

Edit: Also, my advisor claims that if I "want to do theoretical controls, I can go as far with math as I want"
rbj
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#9
Nov14-12, 12:29 AM
P: 2,265
Quote Quote by Only a Mirage View Post
Between control theory, photonics/optoelectronics/semiconductor devices, electromagnetics (antennas or other application), which of these fields has the potential to expose me to the most mathematics in graduate school?
maybe it's signal processing and "none of the above".
Woopydalan
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#10
Nov14-12, 12:30 AM
P: 746
Don't you think it would be wise to pick whatever area of research you enjoy the most, rather than picking out the one with the most math? The difference in the amount of math probably isn't substantial.

If you really love doing hard math, then just do math.
Only a Mirage
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#11
Nov14-12, 01:00 AM
P: 48
Quote Quote by rbj View Post
maybe it's signal processing and "none of the above".
I'm not saying signal processing isn't mathematical. It's just that I like the applications of other areas more. For example, I like the idea of robotics and aerospace applications of controls.

Edit: the areas I listed in the OP were the ones I was considering; they were not intended as a comprehensive list of EE disciplines
Only a Mirage
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#12
Nov14-12, 01:03 AM
P: 48
Quote Quote by Woopydalan View Post
Don't you think it would be wise to pick whatever area of research you enjoy the most, rather than picking out the one with the most math? The difference in the amount of math probably isn't substantial.

If you really love doing hard math, then just do math.
I like math, but I don't want just do pure math because I'd like to see more immediate real world applications of research I do. I share the sentiment I've heard before, "I like math, but I also like having toys."

I like technology, electricity, and "physicsy" kinds of things. But I also like math and wouldn't mind learning as much math as possible while pursuing my other interests
clope023
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#13
Nov14-12, 09:57 AM
P: 593
Quote Quote by Woopydalan View Post
Don't you think it would be wise to pick whatever area of research you enjoy the most, rather than picking out the one with the most math? The difference in the amount of math probably isn't substantial.

If you really love doing hard math, then just do math.
Maybe he wants to do engineering work that is mathematical, I feel the same.
Only a Mirage
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#14
Nov14-12, 10:27 AM
P: 48
Quote Quote by clope023 View Post
Maybe he wants to do engineering work that is mathematical, I feel the same.
Hit the nail on the head
homeomorphic
homeomorphic is offline
#15
Nov15-12, 12:04 AM
P: 1,022
If you really love doing hard math, then just do math.
I made that mistake. Now, I am facing an existential crisis because math is too removed from reality and applications. Don't face the existential crisis. Even applied math isn't safe from this. Do something mathematical that's not math.

My dad does control theory and says the top people in the field are just like mathematicians.
Only a Mirage
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#16
Nov15-12, 01:45 AM
P: 48
Quote Quote by homeomorphic View Post
I made that mistake. Now, I am facing an existential crisis because math is too removed from reality and applications. Don't face the existential crisis. Even applied math isn't safe from this. Do something mathematical that's not math.

My dad does control theory and says the top people in the field are just like mathematicians.
Sorry to hear that. That's kind of something I worried about that kept me from choosing a math degree. Are you having trouble finding work because of your degree choice? Or are you just wishing your work was more "applied"?

Awesome to hear about your dad, that's reassuring.
DrummingAtom
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#17
Nov15-12, 02:40 AM
P: 660
Quote Quote by Only a Mirage View Post
For example, nonlinear control theory makes use of Lie groups and differential geometry, from what I understand which seems much more advanced. .
Whoa.. I didn't know that EE can get into that kind of math. I was going to go the E&M route and hopefully one day conquer a book like Jackson but maybe I'll peak into controls a bit.

By the way, does anyone know of branches in EE that get into the theoretical stuff from linear algebra? Like vector spaces, inner products, orthogonality, etc.
Only a Mirage
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#18
Nov15-12, 03:12 AM
P: 48
Quote Quote by DrummingAtom View Post
Whoa.. I didn't know that EE can get into that kind of math. I was going to go the E&M route and hopefully one day conquer a book like Jackson but maybe I'll peak into controls a bit.
Neither did I until I started talking to my advisor! If you google search "geometric control theory", "nonlinear control", etc. you'll see what I mean.

Quote Quote by DrummingAtom View Post
By the way, does anyone know of branches in EE that get into the theoretical stuff from linear algebra? Like vector spaces, inner products, orthogonality, etc.
I like the linear algebra stuff too. I bet there are other examples of linear algebra in EE, but I do know "modern" control theory makes extensive use of linear algebra. From what I've learned in my first controls class, classical control theory is mainly using Laplace transforms, etc.

However, modern control theory is formulated in the time domain. The "state" of dynamical systems are represented as a vector in a vector space. Instead of the transfer function model of classical control theory, dynamical systems are represented in "state space" using matrix equations.

Systems are analyzed using linear algebra techniques- for instance, the location of eigenvalues of a certain system matrix in the complex plane determine the stability of the system. Another example of linear algebra computations used is using change of basis transformations to represent a system with a different set of dynamical variables as the basis vectors.

Some intro university classes focus on classical control theory, but mine has been using both approaches.


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