## Which electrical engineering subdiscipline uses the most math?

 Quote by DrummingAtom 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 by DrummingAtom 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.

 Quote by DrummingAtom 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.
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.

 Quote by DrummingAtom 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.
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)

http://ocw.mit.edu/courses/electrica...s-i-fall-2006/

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,

jason
 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!

 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"?
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.

 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.
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.
 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

 Quote by Only a Mirage 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
That's what I do. You'll enjoy it. And as a present, here are some underactuated control lectures from MIT

 Quote by X89codered89X That's what I do. You'll enjoy it. And as a present, here are some underactuated control lectures from MIT http://www.youtube.com/watch?v=Z8oMbOj9IWM
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.

 Quote by Only a Mirage 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.
I am a first year grad student as well! I'm hoping to do research in neural networks because I think control systems is the field that will turn into strong AI eventually (brains = nonlinear adaptive filters.).

I have limited abilities at this point as well, but they will grow over the next few years.

I actually had one lecture on differential geometry for control in one of my classes. It was pretty amazing, and definitely very very useful. Not too terribly complex for a first lecture if you have a professor that can explain it well. Anyways, good luck.

 Quote by X89codered89X I am a first year grad student as well! I'm hoping to do research in neural networks because I think control systems is the field that will turn into strong AI eventually (brains = nonlinear adaptive filters.). I have limited abilities at this point as well, but they will grow over the next few years. I actually had one lecture on differential geometry for control in one of my classes. It was pretty amazing, and definitely very very useful. Not too terribly complex for a first lecture if you have a professor that can explain it well. Anyways, good luck.
Woops, I meant that I'm going to be a first-year (still a senior in undergrad now).

That actually sounds really cool. I haven't heard much about neural networks yet.

Good luck to you too.

 Tags control theory, electrical engineer, electromagnetics, math, photonics