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Applied and Pure Mathematics?

  1. Sep 19, 2011 #1
    Hi, I am applying in college this year, and I consider to major in mathematics. My desire is to understand the actual beauty of math, as well as its application. Therefore, I consider between Pure math and applied mathematics. Is it good to pursue in both branches? and How long it would take me to earn double doctorate degrees in pure and applied mathematics. Is it increase my opportunity of getting job after graduating? (note: I really love math)
  2. jcsd
  3. Sep 19, 2011 #2


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    Getting two PhDs, each being within pure or applied math, would be a waste of your time. My advice is to choose one or the other after you've taken some upper-division courses. Having a PhD in each will not help your chances of getting a job, as I cannot think of a position that would request for the applicant have such a ridiculous qualification.
  4. Sep 19, 2011 #3
    is it fun to study both ?
  5. Sep 19, 2011 #4


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    I'm not able to answer that for you because I have no idea what you will find interesting. So far in my education, I've found the theory more interesting than the applications, but this doesn't mean that it will be the same for you. You will have to see for yourself.
  6. Sep 20, 2011 #5


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    Hey xholicwriter and welcome to the forums.

    My advice to you is to take some courses in every kind of math (discrete, applied, statistics, pure) and use that as a basis for decision making.

    Beauty is something that is really subjective. Some people find a simple DE beautiful, others don't. Some people find obscure proofs beautiful, others don't.

    If you are doing mathematics to find some ultimate truth, you probably won't find it. That being said however, there is a lot of elements of truth that can be found in mathematics, and you might find that in itself is beautiful.
  7. Sep 21, 2011 #6
    Thanks Chiro,
    However, will I be able to apply in either pure and applied math phd programs, if I take the combination of pure and applied classes in my undergrad?
  8. Sep 21, 2011 #7
    Typically speaking you would use your undergrad to choose what courses suit you best (taking a variety of first and second year courses in analysis, discrete mathematics, applied/stats) then you would do either an honours year or a masters program, depending on your university choices.
    By the end of that, you will (most probably) have made your mind up about which one you want to choose :)
  9. Sep 21, 2011 #8


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    The short answer is "it depends".

    If there is some kind of funded research that is in a "specific" field, then chances are you need all the prerequisites for that field. If it's in say some applied field, you might be at a disadvantage if you haven't done applied courses in DE's, PDE's, or statistics. It's not that a pure math major isn't capable, it's just that its more preferential to have someone who's at least covered the basics.

    Also the context of pure and applied is different. Some pure mathematicians might say that the math in applied work is easy (or at least easier) in comparison to the stuff they study. But in applied math, that's only part of the thinking. When you are doing applied math, you are trying to answer a question and this requires a different kind of thinking. It's not as important to be able to prove theorem after theorem, but instead to be able to make good conclusions given some data in a particular context.

    Having said that though graduate programs are somewhat flexible. If you have a good undergraduate degree with relevant courses, you should be able to get in if you are competitive enough.

    Having said that if you want to get into pure math for graduate school, you should ultimately be doing a lot of upper division pure math (analysis, topology, differential geometry, and so on) because it can be very competitive for pure math. Also if this is the case, you will probably want to do all the honors courses (honors calculus, honors linear algebra, honors analysis etc), and it might be better going to a uni that has a tough and high level pure math stream.
  10. Sep 21, 2011 #9
    Hey chiro,

    I'm currently an EE major but have taken an interest in programming from a intro class I'm taking this semester. Now, I'm seriously considering changing over to Applied Math with a specialization in CS. I've read in some other posts that you're an Applied Math major, if you don't mind me asking, what year are you? I'm curious as to what your plans are with an applied math degree.

    I suppose my goals for doing this degree would be to get into a mathy software area, whether it's scientific, numerical, or even finance. Are there any courses that would help get an internship? Or maybe even leads on jobs?


    P.S. - If you don't feel comfortable answering those questions on the public forum, you can PM me. I would like to pick your brain about this stuff. Thanks again.
  11. Sep 22, 2011 #10
    This is the very question i have been trying to answer for two years.
    Pure mathematics and eternal truth or Applied mathematics/Physics and answers to the questions of reality?
    Hmmmm decisions...decisions.
  12. Sep 22, 2011 #11
    @chiro: Thank you for all the information you gave me. I actually want to use math to do something (like physics), but I also desire to challenge myself in pure mathematics. Therefore, I plan to do double major in physics and mathematics. I want to pursue master degree in physics and math, and phd in pure mathematics. What classes should I take for my undergrad? Is it a good combination between pure math and physics? How long will it take me to achieve my goals (note: time does not matter to me) What kind of job will I be qualified with a master in physics, and a phd in pure math?
    @Functor97: It's a hard decision to me
  13. Sep 24, 2011 #12


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    If you want to do something applied (applied math/statistics/engineering/physics) then your coursework should have a report component and you should be using packages to do numerical calculation (linear algebra, statistical simulation, DE's, PDE's, etc).

    Engineering degrees have tonnes of reports, and any applied math or statistic program worth its salt should also have it as well since this is what you do: half the work you do is to tell people who are busy your analysis in a way that they can understand.

    As far it goes for pure math, at the very least you should do some kind of upper level analysis courses (real, complex, functional) and some topology at the very least.

    There is so much out there though in terms of developments in pure math. It's just overwhelming when you see what is out there: I don't know if anyone could master pure math in even two lifetimes!

    In terms of time, it would probably take you 4-5 years for a double major in terms of coursework. Masters courses are about 1 to 1.5 years in length. This is the Australian system though, and at my uni we don't have to do general education subjects (I do four maths subjects every semester). In the states it might be different.

    A PhD in pure math should be 3-5 years after you have taken your Masters coursework. It may even be more.

    If you are keen to learn physics and pure math, by all means try it out. You might end up being bored by pure math or by physics, you never know!
  14. Sep 24, 2011 #13
    I don't think it would affect your application for pure or applied math Phd in any way because a lot of schools offer very broad math degrees.

    I've been doing research and there are also school's like Harvard that make you take a test which is very broad and touches upon most major branches of mathematics before getting past your first year (might be wrong about how long before you need to pass the test) as a Phd student.
  15. Sep 24, 2011 #14
    Thank you everyone,
    What can I do with a pure math degree? can I still be qualified for industrial works
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