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College Majors: engineering/mathematics

  1. Mar 24, 2013 #1
    Hello all,

    I am currently a sophomore in high school, but I am thinking about this now because I know that it will be a tough decision down the road. Basically, I love math, and would love to solve challenging integrals all day, but I know that this is a very naive desire. I have a few questions- if you could answer one or more, I would greatly appreciate it.

    1. Does an engineering major pair well with pure math for a double major?

    2. Are there different types of engineering majors?

    3. Obviously this is specific to schools, but generally how time consuming are pure math and engineering majors? Would I have any free time as a double major?

    4. If I decide to pursue a Ph.D in engineering, what will my employment options be?

    5. Engineering careers are obviously heavily dependent on mathematics, but how much math could I expect to do by hand? (i.e. would I ever solve a differential equation again, or is everything done by computers?)

    I am sure that I will have more questions soon. For now, I am going to bed, but I look forward to reading any replies in the morning. Thank you for your time.
  2. jcsd
  3. Mar 24, 2013 #2
    1. Not really

    2. Yes

    3. Really time consuming, and if your time management is on point you should have free time. Just don't expect to be partying every week.

    4. Mainly if you go for a phd you wish to enter some form of higher research or academia.

    5. Not a lot, now with software's like matlab a lot of complex equations are done on the computer.

    - engineering major
  4. Mar 24, 2013 #3
    1. Sure, I think electrical and chemical engineering are the most mathematical. Only do it if you like it though, because pure math is unlikely to be of use in the real world. Since you said you like doing integrals and differential equations, you are more likely to enjoy applied math than pure math anyways. I would suggest engineering major and applied math minor.

    2. Yes, plenty. Aerospace, mechanical, chemical, electrical, nuclear, civil, biomedical, the list goes on.

    3. If you double major, you will most likely take longer than four years to graduate. You would not have a life if you try to take a 5 classes of only physics, math, and engineering courses, with no other "fluff" courses like english or whatever. There is generally a lot of homework in math classes, and a lot of studying and projects to be done in your engineering classes. As I said, I recommend your choice of engineering major and a minor in mathematics.

    4. I am planning on doing this, but take my advice with a grain of salt. It's mostly Research positions in industry, or getting a postdoctoral fellowship for a few years and then becoming a professor. But there is a huge competition for becoming a professor right now and you are unlikely to get the job unless you are highly networked or you are just a child prodigy. You'll likely end up doing the same job with an engineering PhD that you could have done with just a masters.

    5. Probably not much math by hand, mostly you will be programming equations and algorithms into software like MATLAB which will solve the equations for you. You will still have to understand what is going on inside the program, though, so when you take the classes in college you will of course be doing it by hand. Most of the problems that arise in the real world are too computationally intensive to do by hand, so we let the computer do it.
  5. Mar 24, 2013 #4
    Ok, what other good Ph.D's would I be eligible for as a math/engineering guy? The way you put it, it seems like an engineering Ph.D isn't that great.

    Also, this is obviously a major generalization, but how are engineer salaries for the jobs you mentioned (not in academia)?
  6. Mar 24, 2013 #5
    Above all I recommend that you do what you enjoy. I don't have a PhD, so I can't really tell you whether or not they are ultimately beneficial or "pay for themselves" in the long run. I do plan on entering a PhD program, though, so I certainly do think there is value to it even if one is doing a PhD for its own sake. However if you aren't at all interested in an academic career, then it could be argued that a PhD is not the right choice for you. A master's can significantly increase your salary over a bachelor's in the private sector, though. http://www.topuniversities.com/student-info/careers-advice/masters-and-phd-salary-benefits
  7. Mar 24, 2013 #6
    1. Pure math takes you beyond what you'll need for engineering, so it wouldn't be that helpful to be honest. Applied math could be more useful. If you're doing it because you just love math, that's fine too.

    2. Yes. They generally have the same classes for the first two years so you have time to decide what you like.

    3. I didn't do a double major and it took most of my time to excel at an Engineering major. Typically Engineering majors don't have a lot of free units so if you want another major you will probably take more than 4 years.

    4. Depends. Some areas of signal processing and integrated circuit design are hiring Ph.D.s more and more. But as has been said, unless you work in academia, you can get the same jobs with an MS. Getting a Ph.D. is great (I have one) but it doesn't pay off financially.

    5. I do integrated circuit design. I do a lot of circuit analysis (mostly algebra) by hand. I use a computer to solve differential equations (which I do daily). Understanding things like differential equations and Fourier transforms and the like are critical to interpreting the output of the software, though.
  8. Mar 24, 2013 #7
    If you want to focus on pure math, you will never have to solve integrals, maybe the first year of college, and never again.

    May be you could get a copy of Spivak's calculus, read the first few chapters and do the exercises. That will give you a better idea on what to expect if you follow the path of pure math.
  9. Mar 25, 2013 #8
    1. If you go into electrical engineering it probably would. Most people think of circuits when they think of electrical, but if you focus on other areas like signal processing or control theory or electromagnetics there's a lot of very challenging mathematics involved. Also, I would echo what people said above and say that you should do applied math rather than pure. Pure math is probably not what you think it is, and applied math is not for people who aren't smart enough to do pure math. Applied math can be extremely difficult, and it will definitely be more useful when paired with engineering.

    2. Yes. Some will use more math than others. Electrical seems to be one of the more math-heavy types of engineering (depending on what areas you focus on).

    3. I decided to drop my electrical engineering/physics double major to electrical engineering with a physics minor because it wasn't worth the work load to me. I would VERY seriously consider just doing a minor rather than a double major. The double major really won't get you that much more, and even just doing one of those two degrees is a lot of work.

    4. Don't know enough to answer this.

    5. Don't be discouraged by the idea that a computer will do everything. That doesn't mean you'll never have to use your math/physics knowledge. The computer does all the tedious stuff that would take forever to do by hand so you can work on the more interesting aspects of the problem. I would hope that in the course of your engineering/math degree you'll find problems that are a lot more interesting and challenging than just solving an integral or a differential equation. I certainly have, and I'm only in 3rd year.
  10. Mar 26, 2013 #9
    Double major is a real time suck in engineering. Too may classes. I believe science degrees have alot more free electives, In the flow sheet at UKY, you literally have 1 elective. Also, after taking two real analysis classes and a vector analysis class, I can say that it won't help you in your engineering courses at all. I took these courses because I wanted to, I love math. Advanced math is about understanding, in engineering/physics and other sciences, knowing how and not WHY is all that matters(for the most part). Cheers.
  11. Mar 26, 2013 #10
    How do you like pure math? Another poster made it sound like I wouldn't like it.

    Since you said that science majors have more free time, what do you think about pure/applied math and chemistry?
  12. Mar 26, 2013 #11
    I love math pure math, and of course it is not truly a waste of time for an engineering/science major. I feel as if the extra pure math I have under my belt will be really beneficial in graduate studies. As far as pure/applied math and chem, don't see why not. However, if I were you and I wanted to compliment a science major with pure math, I would certainly major in physics. At my university, a Physics BS degree REQUIRES pretty much the same math as an engineering degree (calc 1-4, LA, and some PHY-XXX math courses), but my friends in physics usually take a load of math as electives. In the real analysis course, about a third of the students were physics majors. If you love math like I do, you have to remember this: if you are not a math major, you are not a math major! At some point, I had to decide to become an engineer, and accept that I will never be able to prove certain things(general stokes theorem/theory of PDE and the like). Engineering/Science students use math as a tool. Don't make the mistake I did, and slack in your science or engineering courses to write derivations and proofs in your free time, unless you decide to major in math or course.
  13. Mar 26, 2013 #12
    New question: since by the time I get to college I will have already finished calc 3 and DE or complex analysis, will that get me off the hook for a lot of the required courses for a math major? How much easier would the math part of a double major be if I already had those courses out of the way?

    Also, if I'm doing a math/engineering or math/science double major, how how plausible is it that I would have time to take pre-med courses and have med-school in the back pocket?
  14. Mar 26, 2013 #13
    Wow! You will be pretty much done with your engineering math requirements. (Calc 1-3, linear algebra, ODE, PDE usually required, also vector analysis if it isn't part of calc 3)

    As a math/science double major you will probably have most of the pre-reqs for med school built in. I think they are usually 8 credits of biology, 8 credits of Gen. Chem, 8 credits of Organic Chemistry, 8 credits of physics, Calc1-2, maybe inorganic chemistry. You wiill have the physics, math, and general chemistry already as a science or engineering major, and you could use the chem/bio as electives. However you may not have so much wiggle room as a double major.
  15. Mar 26, 2013 #14
    There is no way you will be able to get a double major with Engineering and a science AND get your pre-med requirements out of the way. There just isn't time.

    Also, you'll be at a disadvantage getting into med school because your GPA probably won't be as good since you're doing Engineering and you won't have time for tons of internships.

    What a friend of mine did was do an MS in Electrical Engineering, then he took the pre-med courses at the local college while working. Now he's a doctor.

    My ex-roommate in undergrad who is also a doctor did a BS in biology and pretty much studied or did internships 18 hours a day, 6 days a week. The only people who work longer hours in college than Engineers are serious pre-med students.

    Typically in Engineering when you need a particular advanced math subject you learn it as part of your Engineering courses. For example, I learned (somewhat) advanced quantum mechanics in my semiconductor physics courses in grad school (Bloch functions, reciprocal space, and the like). I only learned the very basics in undergrad. Likewise I learned about Hilbert space and Hilbert transforms in an advanced signal processing course.

    Mathematics courses are usually so abstract they almost aren't applicable to engineering. Also, nomenclature and notation matters for a lot. I can barely read signal processing papers from Computer Science or Mathematics departments because they use different notation and definitions compared to Electrical Engineering.
  16. Mar 27, 2013 #15
    How would an applied math/chemistry major be? I like chemistry and I get good grades in it, but I have to much work harder for it than I do for math. Would majoring in it be a bad idea since doesn't come very naturally to me? Would I be eligible for any Ph.D's other than math/chem (or possibly an M.D.)?

    Also, I hate to ask, but are there high paying salaries for science/engineering careers? I'm not all about money, but I want to live comfortably.

    Is it possible to get into a good med school without doing internships all the time?

    Another question (I've got plenty): obviously this will be a little hard to say, but based on my interests, do you think I would like being a doctor of medicine (specifically neurology)?
  17. Mar 27, 2013 #16
    I pretty much have a science/engineering dream job (I do research developing next-generation scientific imaging systems). I live comfortably, but I make a lot less than friends of mine who are physicians and bankers.

    I have no specific knowledge of this, sorry. But I can say in general med school is extremely competitive.

    I have a lot of friends who are physicians and generally they are terribly overworked but feel good about what they do for a living. They also do well financially but they don't make anywhere near as much as people assume. Cost of living is high (I live in San Francisco) and they have to work a lot of hours.

    There is one friend of mine who is a physician whose job I envy a bit. She is an emergency room doctor. Her work is always changing and exciting, and she gets paid by the hour and is rolling in the cash. The downside is she works weird hours (and a lot of them).

    I think being a physician is very different from being an engineer. Physicians need to have a lot of different bits of knowledge memorized at all times. Engineers need a much smaller set of facts but they have to understand them deeply. I think some people are better suited for one or the other. You probably don't know yet which is best for you but you'll figure it out in college.
  18. Mar 28, 2013 #17
    This needs to be posted here:


    All math is applied math... eventually.
  19. Mar 28, 2013 #18


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    I know others have already answered much of this, but I thought I would add my 2 cents.

    First, over the next few years try to figure out what interests you. You clearly enjoy math, so you will likely end up in a field that at least uses math. But there are many options! Pure math, applied math, physics, economics / finance, engineering, statistics, etc. As other have said, pure math is different than any math that you have likely done. My wife majored in math. Once she started the core courses for the major (abstract algebra, real analysis, etc.) she hated it because it was all abstract with no applications. So she took as much physics as she could and went to grad school in physics. Other folks LOVE the pure abstract math; it is hard to know until you do it (perhaps you already have ?). Anyway, yet another set of answers:

    1) It can, but depending on the school it may be almost impossible or at least very difficult. I know only one math - electrical engineering double major. However, I know many electrical engineering PhDs that had to take the equivalent of an undergrad math major while in grad school. I do know many math / computer science and math / physics double majors. At least where I went to school, physics and computer science had fewer major requirements than engineering so double majors were more do-able.

    2) many, as others have answered

    3) usually not enough free time. Some make it work. It can also depend upon the university. Where I was, engineering and math were in different "colleges" with completely different requirements. It was almost impossible to take all of the "engineering distribution" requirements for engineering (engineering majors had to take 15-20% more credits overall than math majors), and satisfy all of the extra language and extra humanities requirements for math.

    4. That is at least a decade away for you. No one knows.

    5. It can depend a lot, but a lot of jobs do use computers to "do" the math. Part of this is due to the fact that no one can actually analytically solve the equations we need to solve (fluid flow over an actual aircraft, electric potential inside transistors with real-life geometries, exactly predict the behavior of a real antenna with an actual feed-structure, etc.). But lots of insight can be had from understanding analytical solutions of simpler problems. For more advanced work, there can be lots of analytical work. For example, aspects of communication/information theory use lots of mathematics, some of it quite abstract. Also, I find myself doing lots of pencil and paper work, usually when I try to figure out how to model a new approach to solving a problem in order to estimate how much improvement we expect to gain. Brute force numerical analysis is often too slow, so doing as much analytically as possible usually pays for itself in the long run. And it sometimes leads to more insight.

    Anyway, try not to worry too much about job prospects, etc. Try to figure out what you like, instead. Given your background, you may want to check out the textbook forums; I am pretty sure there have been recomendations for books suitable for high-schoolers in order for them to get a view as to what pure math is like.

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