Looking for project ideas to match my interests I have a Bachelor of Science in Electrical Engineering, concentrating in VLSI, and I am currently in the process of switching fields to go into Physics. I love physics, and mathematics. I like pretty problems that need subtle insight to solve, which is why I'm moving from engineering to physics. Even though the prettiness of a problem may be subjective, I like the "feeling" I get when I'm doing physics, which was totally absent when I was working in VLSI.

That said, before I make the transition complete, I would like to learn about other areas of electrical engineering that may be closer in spirit to physics and applied mathematics. I have a vague idea that signal processing and imaging are areas that may be quite different from VLSI. Are there any others? Which area should I dive into to get a feel for a different kind of electrical engineering? (I have matlab on my computer and I would like to make use of it). 

I especially like to use mathematics on real world problems, and the reason I didn't enjoy VLSI too much is because it is full of boolean algebra, which is somewhat boring and non-visual. It would be helpful if, along with your topic suggestion, you could tell me what areas of mathematics it would involve. Thanks in advance.

PS - I don't have enough points to add "projects" and "careers" tag, so it would be nice if someone could do that for me.
I am a former physician, having done half graduation in mechanical engineering, then a master degree in product design. Nowadays, I work for a biomedical/bioelectric-equipment company, doing mostly software design (algorithms and workflow), using Numpy (matlab like) for prototyping.

THAT fulfills my need (incredibly similar to yours) to solve new problems, work with pretty-picture generation via numbercrunching, programming, and putting the head to perform hard intellectual work very often. I can tell no two months from the three years I am working here have been like one another, and the product portfolio keeps increasing.

In my spare-time, I have interest in geospatial stuff, most probably because I like to ride bikes on relatively remote places with maps and GPS, and the very description of geographical stuff allows for a lot of pretty-picturing. Recently, the avalanche of bike-riding GPS data on sites such as Strava, and the current problems CAUSED by traffic-engineering in big cities makes me think these statistical analysis from people displacement's big data can form a body of knowledge for an "anti-traffic-engineering" oriented for actual people instead of private automobiles.

I can "feel" there's a huge future demand, arriving pretty soon, for software tools that transform datasets into useful information. That can happen with medical imaging, geo-statistical imaging, traffic-engineering micro-modelling, and a lot of fields where data collection, transformation, analysis and interpretation is of huge importance, but still needs further development.

I'm not sure I am actually answering your question, but I feel your question is open to some daydreaming, so I hope this helps, and would be glad to answer any comment you may have!