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Which electrical engineering subdiscipline uses the most math?

  1. Nov 13, 2012 #1
    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?
  2. jcsd
  3. Nov 13, 2012 #2
    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)]
    Last edited: Nov 13, 2012
  4. Nov 13, 2012 #3
    electromagnetics and semi/super conductor physics.

    some aspects of electronics (filters) are pretty mathy too.
  5. Nov 13, 2012 #4
    This thread might have some good advice for you:


    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.
  6. Nov 13, 2012 #5
    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.
  7. Nov 13, 2012 #6
    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.
  8. Nov 13, 2012 #7
    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.
  9. Nov 13, 2012 #8
    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"
  10. Nov 14, 2012 #9


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    maybe it's signal processing and "none of the above".
  11. Nov 14, 2012 #10
    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.
  12. Nov 14, 2012 #11
    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
    Last edited: Nov 14, 2012
  13. Nov 14, 2012 #12
    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
  14. Nov 14, 2012 #13
    Maybe he wants to do engineering work that is mathematical, I feel the same.
  15. Nov 14, 2012 #14
    Hit the nail on the head
  16. Nov 15, 2012 #15
    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.
  17. Nov 15, 2012 #16
    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.
  18. Nov 15, 2012 #17
    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. :cool:

    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.
  19. Nov 15, 2012 #18
    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.

    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.
  20. Nov 15, 2012 #19
    Just thought of another example (can't believe I forgot, as I had a research grant for this one :D)!

    Computer vision is very linear algebra-heavy. I did a research project last spring in which I needed to take a picture with a camera, match it with a picture in a database taken by a different camera, and determine the relative rotation and translation between the two cameras-just from the pictures. My first three months of research were spent reading about linear algebra and projective geometry. Matrices are used for everything, and in my algorithm I used thinks like singular value decomposition, linear least squares, etc.

    (Unfortunately my code doesn't work yet :( )

    The math was different from what I was used to, but interesting. Related to computer vision is image processing, which from what I hear is also linear algebra heavy.
  21. Nov 15, 2012 #20


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    Most of the mathy stuff is in graduate school; undergrad is more modest.

    Anyway, besides controls, here are some more ideas:

    communications and information theory - see the following for a mathy take on digital communications (lecture notes are what you want)


    also signal processing, statistical signal processing, etc. Most EEs in those fields are required to take a fair amount of math while in grad school - where I was those folks had to take a year each of analysis and algebra (at the highest undergrad level). Some took grad math courses as well, but that was much less common. Some in these fields are required to take measure-theoretic probability, depending upon the advisor. So this can be mathematical. If that is what you want chose your graduate school and advisor carefully.

    the applied physics branches of ee tend to use different sorts of math. In electromagnetics you are usually solving PDEs or integral equations, either analytically or numerically. Approximation techniques are often key to gaining understanding in these types of calculuations. The analytical part uses lots of complex analysis, Green's functions, integral transform techniques, asymptotic expansions of integrals, manipulations of special functions, etc. The numerical part relies on numerical linear algebra to a large degree.

    best of luck,

  22. Nov 15, 2012 #21
    As an undergrad, the Heaviest math will probably be in Analog and Digital Signal Processing/Communications. Control Systems uses signal processing but less math intensive more often than not.

    As a grad student, many more areas become much more mathematically involved - the biggest differences include that every subject now includes nonlinear, time-varying, and stochastic versions of what was done in undergrad.

    Signal Processing and DSP - Stochastic processes are added into the mix. Complex Analysis is suddenly needed.
    Control Systems - Nonlinear Systems become very mathematically intense - time-varying, systems, stochastic systems, all of which must be controlled. Very involving - research involves neural networks.
    Communications - this becomes information theory! Holy Crap!
  23. Nov 16, 2012 #22
    Just wishing my work was more applied. Haven't started looking for a job yet. I am not too worried about that, but I probably won't be using much of what I learned in grad school.

    Communications and control do. To my mind, the theoretical stuff in linear algebra shouldn't be separated from the "practical" stuff. If you are just doing matrix calculations without understanding the meaning of the concepts behind them, that's not being practical, it's just having poor taste. It may take you years to learn advanced topology, but the basics of linear algebra you can learn in one semester, so there's no excuse.

    Quantum mechanics uses a lot of linear algebra, so if you get into the physics side of electronics, it will be there.
  24. Nov 17, 2012 #23
    Thank you everyone for all of the feedback, commentary and advice. I have decided to pursue control theory. It was really hard to make a decision, but it's getting to the point where I need to just pick one and I think it sounds the most interesting to me
  25. Nov 18, 2012 #24
    That's what I do. You'll enjoy it. And as a present, here are some underactuated control lectures from MIT

    Last edited by a moderator: Sep 25, 2014
  26. Nov 18, 2012 #25
    Coincidentally, I'm actually reading about underactuated control in the context of legged robot locomotion right now. I'm trying to write a draft for the NDSEG fellowship essay today, and I don't really know much about control other than what I've learned in my first control theory course. I'm proposing that I do research in robotics, so I'm trying to figure out what sort of research would be relevant, and also within the scope of my abilities as a first-year grad student. I'm really interested in learning differential geometry to apply to nonlinear control problems, but that is a little beyond what mathematics I've learned thus far.

    Thanks for the videos, I think they should help me. I'm glad you're happy with your choice of field.
    Last edited by a moderator: Sep 25, 2014
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