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

1. Jun 12, 2006

### jmcgraw

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. :-)

2. Jun 12, 2006

### jbusc

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.

3. Jun 12, 2006

### MemoryOfUs

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...

4. Jun 12, 2006

### jmcgraw

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.

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.

5. Jun 13, 2006

### jbusc

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.

6. Jun 13, 2006

### jmcgraw

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.

7. Jun 13, 2006

### jbusc

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.

8. Jun 13, 2006

### jmcgraw

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! :-)

9. Jun 13, 2006

### Maxwell

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.

10. Jun 13, 2006

### 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?

11. Jun 14, 2006

### Cyrus

Become a mechanical engineer, problem solved

12. Jun 14, 2006

### jmcgraw

Nahhh... Mechanical is even less abstract, as far as I know.

13. Jun 14, 2006

### Maxwell

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.

Last edited: Jun 14, 2006
14. Jun 14, 2006

### jmcgraw

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!

15. Jun 16, 2006

### ircdan

I would not study math unless
1. You know you want to teach at a higher level than highschool; ie, you plan on getting a phd and going into academia. Jobs outside of academia are few and far between.
2. You REALLY like math, it's very hard.

Now the problem here is, at this point, it's hard for you to really decide if math is what you want. The reason being I'm sure is that well, you just have not been exposed to enough of it yet and so you are unsure whether your decision is the right one.
I guess what I'm trying to say is, if you choose to study math, think hard about it, make sure it's right decision.

One option is to go into engineering and get a minor in math, if you don't like engineering, you can always switch to math and you'll have a better of idea of whether math is what you really want to do after taking some more advanced courses. 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.

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), but after taking several math courses, I realized that math is what I must do. It's never too late, just realize you must work very hard in whatever you decide to do.

BTW if you decide to go the engineering route with a minor in math. 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'm not saying you don't, but I've had plenty of friends who have switched to other majors after being exposed to more difficult proof based courses.

Last edited: Jun 16, 2006
16. Jun 16, 2006

### jmcgraw

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.

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.

Is it really free? That's awesome if it is. But how would they make their money? :-)

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! :zzz:

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.

17. Jun 16, 2006

### ircdan

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.

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.

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:)

Last edited: Jun 16, 2006
18. Jun 16, 2006

### jbusc

as long as the financials work out that sounds like it's a good idea.

Most major universities guarantee funding for their PhD students - meaning tuition, fees, and health insurance are paid for. Plus, you get a small stipend which is really barely enough to live on.

The money comes from several places. The most coveted is a fellowship, which essentially grants you freedom to work on anything you want.

The next most wanted is a Research assistantship, where you work for a professor doing research that someone is paying for (usually externally, like a nonprofit research foundation, corporation, or the government) where you have less freedom but you're still working on what interests you.

Finally there is the teaching assistantship, which is not as glamourous as it sounds. Even those who like teaching prefer other funding, because it is a distraction from research, and TA's do more grunt work like grading and proctoring than actual teaching anyway. When no funding is avaliable, PhD students get TA ships.

Masters degree students rarely get funding or financial of any kind. This is not so important as getting a graduate degree in engineering is worth taking loans out for (money-wise) and no one really gets master's degrees in math anyway. Masters students do sometimes get grading jobs and such that pay a little, but don't usually cover tuition.

I think, anyone who would be really interested in _serious_ math has/had to teach themselves anyway. The US public school system is awful in terms of educating really good engineers & mathematicians.

Last edited: Jun 16, 2006
19. Jun 16, 2006

### maverick280857

Isn't that a generalization

Anyway, as far as I know (I am almost getting into an EE program now), Electrical Engineering is quite mathematical. A double major is not an option in our part of the world, but I think EE allows you to keep your options open and go into pure mathematics later on. You can keep studying mathematics, taking courses that appeal to your intuition on the way and eventually when you have graduated with an EE degree, decide what you want to do (EE or hardcore pure math minus EE). In fact, a mathematician advised me to do EE instead of physics which I wanted to do. A lot of EE people I know are hardcore mathematicians!

20. Jun 16, 2006

### jbusc

Sure. I think it's accurate though though. I didn't say all engineers or even most engineers. What's a lot? I think 20% of engineers is a lot, for example, but I just threw that number out there.

I meant the more "pure", theoretical math as well, not the mainstream math most engineers use.