Undecided between Masters Degree in BME, EE or Applied Math

[undecidedshag]

Background story:

In high school, I fell in love with mathematics especially AP calculus (mostly because many other subjects in the sciences were not well taught in my school). I would often spend hours trying to learn the math in detail (often going more in detail then necessary on my own using many references online. I did things such as try to understand why the Fundamental Theorem of Calculus is true, prove the derivatives of functions, relate the chain rule with implicit differentiation etc.) I treated Calculus like a cult. When I went to college I wasn't entirely sure of what I wanted to do, so due to time pressure and pressure from my family, I decided to pursue an Electrical Engineering major at my current school. The first two years were great, I love learning the rest of the Calculus sequence, physics was pretty interesting, learning electrical and magnetism was insanely enlightening (even though I wish I had learned it in more detail, my school didn't go into much detail), my college didn't do a good job as undergrad in many of my classes including electrical engineering classes where I constantly felt like a pack mule doing labor work all the time. I tried to learn the theory behind EE, but it felt kinda convoluted at points especially with circuit analysis and microelectronic circuits. While the class was interesting in itself I felt like a lot of the logic they used in their book was very convoluted and may aspects of the theory were stretched to make things work. In college I did do some exploring a little bit and took math classes such as introduction to higher math, complex variables (a little bit lower version of a complex analysis class), probability theory, partial differiential equations, and etc. I love learning mathematics in detail and love creating my own equations from time to time (it seems like fun to write my own functions, and i absolutely love it). I did also enjoy coding a lot but most of the coding I love to learn was writing and creating my own code from scratch. I do not enjoy black boxes as much even though, I try to get pass that by thinking of black boxes as functions, with inputs and outputs and I do love the idea of manipulating functions a lot.

Reason I’m considering Electrical Engineering Masters:

I heard DSP uses a lot of mathematics and is one of the fields in Electrical Engineering where you get to implement and design algorithms all day. After researching about signal processing I fell in love with what it is about (the idea of information science is insanely cool), and decided that I would like to pursue this even more in detail. But I am insanely crazy about understanding the math component of signal processing, and feel cheated on because my university program sucked the living hell out of all my time in learning what I need to know.

Reasons I’m Including Biomedical Engineering:

I also do want to pursue studies and eventually work in biomedical engineering. I had a sister who was severely injured in my youth and would like to one day help out patients doing neural signal processing, http://www.ece.neu.edu/people/erdogmus-deniz

One of the main reasons I'm considering biomed engineering is because programs like this exist:

http://www.engineering.pitt.edu/Dep...g/_Content/Programs/Graduate/Graduate-Tracks/ Bioimaging and Signals

Reason I’m considering Applied Mathematics:

I’ve always insanely love math had a passion for it and know that I can work hard at it. I am always interested in understanding the theory or backhand of the math behind of an operation because it provides insight. I am interested in proofs, not because I want to design my own, but because they provide great insight into why something works. I prefer to deal with white box systems, instead of black box systems. However, I do shy away from getting stuck into the details of why something works. There are many logical proofs of systems that I do not enjoy, even tho they are logical, they don’t provide insight to me. For example induction to prove some formulas, does not provide insight to me at times. Ya it works, and its logically true but it doesn’t give me a good intuition on why it's true. Also going towards an applied math degree is a big commitment on my part right now due to the amount of catchup I have to do to get to where I want.

Some key quick facts:

1. My mind likes to make up general equations and write proofs of why things work instead of doing specific problems
2. Every time I see a specific problem I would like to model it and make it more general, when I analyze i problem I like to see it from a generic point of view (that's how I learn)
3. I can understand a proofs especially ones more correlated to algebra. I have a problem understanding discrete math, and it does not come naturally to me (thinking about sets, set notation etc.) However if I work hard at it after spending hours I tend to get a hang of it.
4. I spend hours manipulating equations I rather find a different way of expressing an expression. I love seeing algebra tricks
5. I enjoy learning biology, understanding physiology and etc.
6. I actually do enjoy electrical engineering but I do not like learning hardware cookie cutting stuff, I love learning things in a more theoretical point of view. I can make myself use equipment but I am not so thrilled about talking about hardware like many of my EE colleagues. Hardware doesn't stick to my mind that well, I'm not sure why.
   

 

[micromass]

To be honest, you sound like a mathematician. I think it would be perfect for you. I understand there's a lot to catch up, but it might be worth it.