## Dilemma: Engineering vs. Math -- Help me Decide!

Hello everyone.

I'm in a weird position. First a little background: I'm 27 years old. I dropped out of high school when I was 16. I returned to school two years ago and have done very well at my local community college. And now (this is the crazy part!) I was just accepted to Northwestern University as an electrical engineering major. Northwestern was very generous with me, and they have agreed to pay for almost all of my expenses! I'm pretty poor, so this is like the biggest thing that has ever happened to me (I don't think I even really believe it yet).

My problem is that ever since I was about 23 years old I have been in absolute love with math (the purer the better). I have no real educational background (I dropped out of HS with a 1.65 gpa), so I pretty much taught myself algebra, trig, and precalc before I took calc during my first semester returning to school. Although electrical engineering seems sort of interesting, there's no way I could say I "love" EE. The reason I applied as an engineer is because I make almost no money, and I really want to make a wise career choice (especially since I'm approaching the big 30!).

But now that I've actually been accepted to a good school, I'm flirting with the idea of switching my major to applied math. Northwestern's applied math major is sort of a hybrid between a math education and a general engineering education. Is this a risky major? What kind of job oppurtunities would there be if I only had my B.S.? I would like to go to grad school, but I'm worried that the money might not be available. If I knew I could afford grad school, I think I would more easily forget about EE and just focus on applied math or even pure math. But that's my fear: that I won't be able to go to grad school.

Another option I've thought about is going for my B.S. in EE, which I think would give me some good job options. And then, if the financial aid is availabe, go to grad school for pure or applied math. Is such a move from EE to math difficult?

So, to summarize my rather long post, my two questions are:

1) Is applied math a risky major, career wise, if I only go as far as a B.S.?

and

2) If I went ahead and got my B.S. in Electrical Eningeering, would it be a difficult transition to go to grad school for a degree in pure or applied math?

Thanks for any help you can give! You might just make my mind a little less confused and my heart a little less undecided. :-)
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 I can't really help you, since I don't know much about applied math as a career at all. Congrats on getting into a good school. I know plenty of people who go back for their BS in mid-20's so you're in good company. But I will say that, at my school, a lot of people in "pure" majors like physics, math, etc., take a few upper level advanced courses in EE and CS to make sure they have a fallback career option. CMOS circuit design, microprocessor design, and programming seem to be popular classes, since it's actually possible to "self-study" whatever prereqs are needed.
 That's pretty adventurous at the age of 32 with only a BS certificate handy Being a teacher or a writer may be a profession to choose then...

## Dilemma: Engineering vs. Math -- Help me Decide!

I don't think I could be a teacher in high school or something like that. It's not that I look down on it, but I just think that I'd be really bad at it.

 But I will say that, at my school, a lot of people in "pure" majors like physics, math, etc., take a few upper level advanced courses in EE and CS to make sure they have a fallback career option.
So what about the other direction? Is getting a b.s. in EE then going to grad school for pure math a difficult thing to pull off?

I've also thought about sticking with EE and minoring in pure math. Is this a crazy thing to do? I'm guessing an EE/math double major would be downright delusional.

 Quote by jmcgraw I've also thought about sticking with EE and minoring in pure math. Is this a crazy thing to do? I'm guessing an EE/math double major would be downright delusional.
Not at all. A lot of engineers are downright awful at math and it's such a desirable thing to have behind you as an engineer, especially if you do grad school engineering. I would consider the time/financial investment in a double major, though.
 Thanks for the feedback jbusc. I actually have noticed that my very engineering minded friends tend to think that the word "proof" is an obscenity. :) I, on the other hand, absolutely love rigorous math. I took a very "engineering-centric" differential equations class at my CC this semester, for example, and I kept finding myself extremely annoyed when we passed over most of the proofs and theory. Experiences like that are why I've been wondering if engineering is even for me. To think that I might never take analysis and abstract algebra courses makes me almost want to cry. But because of career considerations, I think I might stick with EE and try a minor in pure math. The double major might just be too intense, especially since I hear EE has one of the biggest workloads.
 One curious thing, is that once you get into advanced and grad-level EE there's a lot of abstract, pure math around. You get an early taste of it with fourier analysis, which is probably about the sophomore level or so, but unfortunately to get the full dose of it they make you go through a lot of circuit and digital systems courses first. I would suggest, after reviewing if it's financially and practically in the books, to consider trying for a master's degree in EE at a school where you can focus on communications theory which is very heavily pure mathematical and uses the abstract algebra and analysis that you like so much. Comm theory engineers get paid a lot too (probably because not so many can handle the math) If you're lucky, you might even find a job where they'll pay your tuition to get a part-time MS while working. Those jobs are rarer now that the economy has tanked, but they're still out there.
 Thanks for the comm theory suggestion! That definitely looks very interesting. And even better, from your description, it looks like something I could really get into. I didn't even know there was much application for the purer math subjects! (I guess I'm pretty naive) I will definitely look into communications theory. Thanks jbusc! :-)
 Three things: 1 - If you do not like EE, you will not do well. There is no way to force yourself to get through 4 years of engineering. It is insanely brutal at times, and if you have no love for the subjects, you will certainly give up. 2 - If you truly love mathematics, then do it. You will not be happy in life unless you pursue your dream. 3 - If you don't completely hate EE, there are a lot of fields that are VERY math heavy. As mentioned before, Communications theory is very mathematical. So is advanced Signal Processing, Control systems, and Electromagnetics, etc. An EE major with a math minor is very reasonable. Some people do a double major, but you won't be finished in 4 years. Best of luck in whatever you decide.
 Maxwell (Very electric name, btw ) The only exposure I've had to what EE might be like is my Electricity and Magnetism class. I've taken no actual engineering classes yet. I love Gauss' law, ampere's law, Faraday's law, magnetic fields (particle accelerator problems and stuff). But I hated circuits. I did well, but circuits are just so damn boring. :-) In other words, when we hit the more abstract/theory electrical stuff, I loved it. But when we had to solve circuits (which most students find easier) I felt like puking. I can't stand all the tedious algebra. I know I'll have to take circuits classes... But are they something that I could just force myself through as long as I am passoniate about the more imaginative topics? And what is more of EE like? The tedious circuit side, or the more abstract stuff?
 Become a mechanical engineer, problem solved
 Nahhh... Mechanical is even less abstract, as far as I know.

 Quote by jmcgraw Maxwell (Very electric name, btw ) The only exposure I've had to what EE might be like is my Electricity and Magnetism class. I've taken no actual engineering classes yet. I love Gauss' law, ampere's law, Faraday's law, magnetic fields (particle accelerator problems and stuff). But I hated circuits. I did well, but circuits are just so damn boring. :-) In other words, when we hit the more abstract/theory electrical stuff, I loved it. But when we had to solve circuits (which most students find easier) I felt like puking. I can't stand all the tedious algebra. I know I'll have to take circuits classes... But are they something that I could just force myself through as long as I am passoniate about the more imaginative topics? And what is more of EE like? The tedious circuit side, or the more abstract stuff?
There tends to be a mixture of abstract and practical classes in EE. Your E&M class, which I'm assuming was a Physics class, did not even come close to tapping the beauty of circuits. There is far, far more to electrical circuits than just resistors, capacitors and inductors. Even during your first linear circuits class, you'll still be dealing with different methods to solve RLC circuits. The tedium of the circuits you solved in Physics gets a little bit better - you learn better methods for analyzing circuits in a proper EE circuits class. However, the real awesomeness of circuits shines when you take an electronics class. Learning about transistors, digital circuits, etc was fascinating and extremely cool. I guess you could call it "applying" your circuit knowledge.

However, EE is a rather funny major. One class might superficially have nothing to do with the other. For example, you could reasonably teach a Signals course without mentioning circuits - but applying those ideas to electronics makes it so much more intuitive to an EE - and much cooler.

As an EE, you will have to take an applied E&M class, which will include circuits. You will see how you can actually apply Gauss's Law, etc.

EE is not all about solving circuits. A good EE program will bring electronics/circuits into every class, but a good deal of it is the analysis of abstract signals - that is, you perform operations and use various mathematical techniques to change or filter a signal. Abstractly, a circuit might not even need to be mentioned - but how do you think those mathematical operations are performed IN REAL LIFE? Not just on paper.

Even with Communications theory, you deal with performing some sort of operation on a signal - you modulate or demodulate it. You can explain what is being done to the signal mathematically, but the way you actually perform the operation is with electronics!

So EE is a very mixed bag - there is plenty of applied and abstract material. You'll see plenty of math and physics blended together and applied to real situations. That's the beauty of it.

Good luck.
 Thanks, Maxwell. I think I will find EE interesting enough to get through the program. I definitely don't hate it, and it's nice to know that circuits don't stay boring. I also think there's a good chance that I'll love it once I take a couple of good classes. Thanks again!

 Jobs outside of academia are few and far between.
Yes, this is what worries me most. For that reason, I don't think I will abandon EE. But I'm starting to think more seriously about a double major: pure math and EE. I'll finish a year late, but that's o.k. with me.

 The reason being I'm sure is that well, you just have not been exposed to enough of it yet.
That's probably true. But I have been exposed to a lot more than my engineering friends have. I've studied real analysis on my own, mathematical logic, and a book on proof writing that focused on set theory. I loved it all so much more than the applied math I've studied at school. I love the purity of it. With applied math you always have a cord tying you down to something real and tangible. When I do pure math I almost feel like I've left earth and entered Plato's world of the forms. It's almost like a drug.

 Also don't worry about grad school, it's free, and they support you. If you have a wife and kids, it will be harder, but it's still possible.
Is it really free? That's awesome if it is. But how would they make their money? :-)

 Take a course like Advanced Calculus, or a proof based linear algebra course along the way, or maybe a course on group theory. After a taking a course like this, you'll have a better idea about what math is about.
I lust after proof based classes! I took linear algebra that was sort of proof based (at my community college). I loved the proofs so much. On the other hand, it wasn't totally proof based: I absolutely hated doing row-reductions by hand, which was required!

 As a sidenote, I also started college late(at 24) and I also dropped out of highschool with almost straight F's. I started as a Computer Science major with an extremely weak math background(I'm talking like 9th grade level math here heh)
That's awesome, dude! You sound a lot like me!! I was absolutely horrible in math when I was young. The highest I got to in high school was like "Math 1A," and I flunked! I didn't start to like math until I took a Euclidean geometry course at my CC and was introduced to proofs for the first time. That's when I first fell in love with math.

After that, I was so desperate to learn math that I started by teaching myself arithmetic from beginner's texts (I couldn't even add fractions or do long division at the time). I taught myself everything between arithmetic and pre-calculus... And then I placement tested into Calculus and got an easy A. Since then I took all 3 calc courses, lin algebra, diff, 3 semesters of physics, and got accepted to Northwestern. It's been a trip.

 Quote by jmcgraw Yes, this is what worries me most. For that reason, I don't think I will abandon EE.
Hmm yea. Personally I don't think I would have studied math, no matter how much I liked it, if I wasn't sure I'd enjoy teaching.

 Is it really free? That's awesome if it is. But how would they make their money? :-)
Yea it's free. Some also provide health insurance, either free or at a reduced cost. They also pay you a stipend to live off. I've been looking at graduate programs for a few weeks now(I graduate next year) and it really does vary. Some schools pay $12,000 a year, others pay$18,000 - \$21,000 a year, and some even more with fellowships. Typically you teach a recitation for a course, an introductory undergraduate course like college algebra or calculus, or perhaps just do grading, it depends on the school. Some schools require no teaching the first year(Notre Dame), others do. But from all the schools I've looked at, all pay for tuition and provide a stipend to live off. If you have a family, most campuses have apartments for people with families, at reduced rates too. Some have apartments strictly for graduate students, again at reduced rates, and close to campus.

 And then I placement tested into Calculus and got an easy A. Since then I took all 3 calc courses, lin algebra, diff, 3 semesters of physics, and got accepted to Northwestern. It's been a trip.
Northwestern is a good school for math.

A double major is a good idea. I was also a double major for a while, math/computer science, but I found myself looking for computer science courses that involved math, and I knew that I wanted to go to graduate school for math, so I figured I might as well just do math so I could focus on that. Just remember EE is very hard also. I have lots of friends who study EE and they are constantly studying, but then again so am I during semesters because math is also difficult. I guess what I'm saying is, it's gonna be tough to do both, so keep that in mind, but I think after your first semester you'll have a better idea of what you really want to do. It took me like a year of serious thought to decide. Perhaps get a part-time job tutoring math at your school to see if you enjoy helping others. Tutoring is different from teaching , but it's the same in the sense that you are helping others learn. Goodluck:)