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I have two Bachelor's degrees. One is electrical engineering and the other one is mathematics. I am studying mathematics (partial differential equations) in the graduate school (Master course) now. But I want to study electrical engineering later (for Doctor's degree). So I have a question here.

Would you tell me a field(or major) in electrical engineering which is deeply concerned with mathematics?

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  • \$\begingroup\$ I had a Professor who said that he got his PhD from examining the field in the gap between a dish antenna and a cetral coaxial monopole. \$\endgroup\$ – Russell McMahon Sep 15 '12 at 6:33
  • \$\begingroup\$ Is your aim to do new math or apply existing math? \$\endgroup\$ – markrages Sep 15 '12 at 23:38
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    \$\begingroup\$ With a Bachelor's in each, I think the original poster is almost uniquely qualified to answer the question on his/her own! Seriously, the PhD should fit into the career path that's planned, not the other way around. You don't start a PhD program looking for a career-- you should have a well defined career in mind, and understand why you need a PhD to get there. There are much more pleasant, less expensive, and more productive ways to spend 5-7 years than pursuing a PhD that might or might not support your career goals, especially in engineering. \$\endgroup\$ – Scott Seidman Sep 16 '12 at 12:04
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Other math intensive fields of electrical engineering are signal processing (which includes the detection of signals in noise as well as spectral analysis and reconstruction of distorted signals) and communications (which includes coding theory and cryptography). Also theoretical circuit analysis is highly mathematical.

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  • \$\begingroup\$ Practical circuit analysis is also pretty math oriented. One of my regrets is that I didn't learn proper understanding of s-plane math and transformations and have never really done the grunt work to learn it afterwards. For feedback loop analysis it comes up again and again and it'd be infinitely easier to implement models for practical circuits if I had deeper of it. The textbooks tend to go into the deep end which may be difficult to convert to real world simulation problems. My B.Eng classes concentrated on doing the transformations manually which is pretty useless. \$\endgroup\$ – Barleyman Nov 18 '16 at 11:26
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There is field known as EMFT(Electromagnetics field theory), it starts with some equation and ends with another.Best part is that, you barely bother to think about its physical nature, its all in Calculus ;)

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One field I stay away from, mainly because of mathematics, is advanced motor control. Non-linear systems are generally a tough issue, and engines are among the most complicated and most common systems you'll find in the industry. Field-oriented control, rotating coordinate systems, nonlinear transformations.

It's a multidisciplinary field. Engine systems have to be powered, controlled, modelled. They're an electrical system, but also a mechanical one. There is a lot of signal processing involved in this, too. Engines are everywhere. Every single factory relies on them, every power plant, hydrostation, processing line. An engineer who knows his engines will find a job everywhere.

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Simulation of nano-electrical systems. Apply boundary conditions to quantum physics and Maxwell's equations.

PhD would be investigating yet-unknown boundary conditions in interesting systems.

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I’m currently writing a PhD at an electrical engineering department. I say mostly everything is kinda math heavy :)

Some example projects at my department: We develop finite element methods for computing losses in motors, we build geometrical optimization tools for these motors finding n-dimensional solutions, we work with advanced signal processing and control theory to make the devices work at all, we model semiconductors with large state-space equations, we build numerical software running on GPUs to study the aerodynamical interactions with the electromechanical system in HA wind turbines, we study oscillations in the power grid with large system models including power stations in the whole nordic grid, we build large models which try to predict the weather so optimal locations for wind turbines can be found with regards to grid stability, we build numerical models for how wave power buoys interact with waves during different loading conditions, etc etc etc.

If you wanna go for heavy math you probably can’t choose wrong at my department ;)

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