Transitioning from mathematics to engineering (electrical/comp)

[themathguru]

Hello all,

I am new to this forum thing when it comes to mathematics and science but I have found much help on other issues thanks to this wonderful thing we call forums online nowadays. Anyway, my dilemma involves trying to make a change (course correction) in my current path to a career. I am currently about to enter my second year of graduate study in mathematics and have concentrated somewhat heavily in statistics in the past. However, on further inspection of what I want and enjoy in life I have found that I enjoy the notion of engineering, specifically electrical engineering. In researching the career path all avenues intrigue me. I would like to say that my program is not a statistics program and I have the availability of choosing to go a "different" way in my study of mathematics. I would really like to complete my master's program in mathematics but I don't know if that would be a good way to do it or possibly just try to get into the electrical engineering department at my current graduate institution. While I am fairly well versed in physics, I have the problem of absent coursework in the subject. I have studied it on my own off and on in my spare time during the undergraduate years and even now during graduate school, but I have practically no coursework to show that I have done so. (Bummer, I know.) I really want to make the switch without having to redo too much undergraduate equivalencies to have any programs even look at me when applying. I know the mathematics degree would probably help in a good way but I'm afraid my lack of "official" science background and experience will drag me down. I am highly motivated and dedicated to something that I start. I hate to leave things unfinished and want to excel in life but not by taking a "joy" ride through life but rather through working hard at something rewarding. I believe that I could change focus easily enough but I am just worried and would like any input as to how to maybe go about making the change and how to prepare myself for the change. As some of you will probably wonder, why didn't he take Physics courses to supplement the mathematics in undergrad? Well truth be told classes were a bit of a joke to me earlier in school and then I realized that I needed it to treat it as a "job" and at that point I had to take major classes to fulfill my requirements. I had an undergrad GPA of 3.9+ and a current graduate GPA of 3.7+. In summary I would appreciate guidance on:

1) Although I realize the transition will by difficult (possibly) but very rewarding, I would like to know any opinions on the matter.

2) As i would need to switch my math concentration, would looking into an analysis concentration in math help as a finish to my masters degree?

3) How would you recommend to fill the gap with basic proof of physics and electrical engineering knowledge that any graduate school would require for admittance into a program?

4) (If you want) What areas of Electrical engineering might intrigue me the most? Maybe give a quick sentence or two plug about a concentration that you enjoy and might help me decide further down the road what I want to do with the knowledge I gain.

5) How to gain practical experience when I have no engineering background (formally) to make myself more marketable and what not.

6) Anything else or little tidbits that might be of help.

I am just finally glad that after 20+ years I am finally figuring out what it is I want to do and be happy with it for the long haul. I thank you all in advance of your help and I hope to find many intriguing comments and questions for me to contemplate over the next few days/weeks. I appreciate it immensely. Be frank with me and I will find little offense if some of you think its too difficult.

Tell me as it is and don't hold anything back! Thanks!

 

[sus4]

A strong math background can be an excellent way to transition into an engineering graduate program. I have personally known people to go from a math undergraduate to an electrical engineering graduate phd program in the past. I would assume that it is not too difficult of a transition, as long as you have a good ability to learn physics.

You mentioned you have an emphasis in statistics. I'm not sure if that's because you prefer to focus on statistics and enjoy it more, or just saw it as being more practical in industry. Either way, the math required for most graduate electrical engineering is probably already covered in your studies. For most cases, PDE, 3 semesters of calculus and some background in probability is sufficient. This heavily depends on whether you decide to stick to the theoretical side of engineering (almost seems like an oxymoron) or the applied side. The difficulty in making the switch will be covering the engineering material required for these grad classes; there is a lot more to engineering than the math and it will probably add time to your expected graduation.

As far as math intensive subjects, you are looking at anything with a focus on electromagnetics. This includes the pure study of electromagnetics, certain areas of communications, semi conductors, imaging, etc. If you would like to spend a lot of time on prob and stat still, you could have a go for systems engineering (closest to pure math in my opinion), or rf engineering.

I honestly don't have a lot of experience with circuit design except for a few undergraduate classes, so I can't comment much on that. The computer engineering is very interesting work. I enjoy it a lot, but it isn't usually as math intensive as the other areas. The only way you would know for sure is to try out a few different areas and see for yourself.

I have probably missed a few points or said something wrong, but I wrote this reply in a bit of a rush, so feel free to follow up and maybe I can clarify.

 

[jasonRF]

3) How would you recommend to fill the gap with basic proof of physics and electrical engineering knowledge that any graduate school would require for admittance into a program?

4) (If you want) What areas of Electrical engineering might intrigue me the most? Maybe give a quick sentence or two plug about a concentration that you enjoy and might help me decide further down the road what I want to do with the knowledge I gain.

5) How to gain practical experience when I have no engineering background (formally) to make myself more marketable and what not.

6) Anything else or little tidbits that might be of help.

I am just finally glad that after 20+ years I am finally figuring out what it is I want to do and be happy with it for the long haul. I thank you all in advance of your help and I hope to find many intriguing comments and questions for me to contemplate over the next few days/weeks. I appreciate it immensely. Be frank with me and I will find little offense if some of you think its too difficult.

Tell me as it is and don't hold anything back! Thanks!

3) every department is different - some have "core" grad courses you will need to take some number of, in which case you need the prerequisites. Some have qualifier exams that will cover portions of the undergrad material. Where I went to grad school, we had NO course requirements of any kind, and all of the exams were determined by your graduate committee. So a department may not need this "proof" at all. If they do then you will have to see what they are looking for - for departments with formal qualifier exams, passing the exam would count I would think. Others will simply make you take a few selected make-up undergrad courses to fill in the holes that they are most concerned with. I have seen grad students forced to TA a class in order to learn the material - this can either work great or be a total disaster.

Regardless, to be a reasonable electrical engineer you really do need to know some key undergrad stuff: something about electromagnetic waves (propagation, radiation, guided), signals and systems (a core subject that should be EASY for you), and have at least a passing knowledge of elementary analog and digital electronics.

4) These days I enjoy signal processing and electromagnetics the most. Signal processing essentially applies statistics, Fourier analysis, linear algebra, optimization and numerical methods, to design algorithms (that can run fast enough on actual hardware) that help make real-life systems work properly/better/optimally. Sometimes the best algorithm is the one that best exploits the relevant physics, while sometimes it results from mathematical insight or brute-force numerical optimization. I would think that the more mathematically intensive specialties within EE (signal processing, communications and information theory, controls, ...) would be an easier transition for you, and in these fields your math background will be greatly appreciated by some.

5) this can be an issue in principle - without undergrad engineering and only specialized graduate coursework and research, you may be attractive to a narrower set of potential employers. On the other hand, if for example you got a PhD in signal processing and someone is looking for a true "hard-core" mathematical signal processing expert you may look great to them.


jason

 

[thegreenlaser]

4) As far as I know, the math-intensive areas of engineering are in electromagnetics, signal processing and communications, and control systems (at a graduate level, at least). With your statistics background you might be able to do something interesting with stochastic processes. I'm not super-familiar with the area myself, but uncertainty, randomness, and noise are definitely of interest in a lot of areas of EE (e.g. making communication systems which try to automatically detect and filter out noise, or dealing with electromagnetic waves underground, where the medium is randomly-varying). As I understand it, a lot of pretty intense math dealing with random processes shows up in those kinds of problems.

 

[jasonRF]

4) As far as I know, the math-intensive areas of engineering are in electromagnetics, signal processing and communications, and control systems (at a graduate level, at least). With your statistics background you might be able to do something interesting with stochastic processes. I'm not super-familiar with the area myself, but uncertainty, randomness, and noise are definitely of interest in a lot of areas of EE (e.g. making communication systems which try to automatically detect and filter out noise, or dealing with electromagnetic waves underground, where the medium is randomly-varying). As I understand it, a lot of pretty intense math dealing with random processes shows up in those kinds of problems.

Yep - stochastic processes show up everywhere, if for no other reason because everything has noise in it, and good designs / algorithms take this into account. Most engineers do not need the rigorous stochastic processes background that I expect mathematicians learn - there are a few EE professors here and there that use measure theory but most of us get by just fine with the non-rigorous approach used by electrical engineers.