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Math needed to be a physicist/mathematician/computer scientist?

  1. Jun 16, 2011 #1
    My current circumstances do not permit me to get an undergraduate major in either of those three, though in grad school I'll probably take up one of those three. I would like a list of mathematical topics I should be well acquainted with to do any of those three in graduate school. I'm planning to do it in Europe though, and I heard they cover advanced mathematics in undergrad there. Here's what I think I should know:

    Calculus
    Multivariable Calculus
    Linear Algebra
    Ordinary differential equations
    Probability and Statistics
    Abstract Algebra
    Discrete Math
    Topology
    Real and Complex Analysis
    Partial Differential Equations
    Differential Geometry
    Calculus of Variations
     
    Last edited: Jun 16, 2011
  2. jcsd
  3. Jun 16, 2011 #2

    chiro

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    Science Advisor

    Hi zonk and welcome to the forums.

    I can't speak for physics, but I can speak for mathematics and computer science.

    It really depends on what you want to do. With statistics, you need the full calculus sequence as well as introductory A-level year of statistics and then you take specialist courses in probability, experimental design, linear models, and statistical inference. On top of that you will probably want a course in analysis, and then maybe some courses that are either highly specific to a subject area (like say biostatistics, financial math), or you do some more coursework and a thesis/project of some sort.

    Most computer science courses (at least in my country) require you do some calculus, discrete math, an intro stats (not like the A-level stuff I mentioned above), and then computer science specific courses. The courses encapsulate all the required math, so if its cryptography: all the number theory and so on is taught within the course. It's the same for stuff like automata, machine learning and so on.

    I love math, both applied, pure and statistics so I take as much as I can, but I'm lucky that I can take all math courses and I don't have the so called gen-ed requirements here (thank god).

    With regards to "math" degrees, no matter what your sub-major (stats, applied, pure, math+comp sci) you will need to take all Calculus (I,II,II,IV), Linear Algebra, some discrete subject, some applied math subject, some stats, analysis, group theory, and then specific courses for sub-major (at least in my uni and other unis in my country), so you will get a taste of whats out there on which you can use to choose where you will go with it.

    Also if I were you, I would choose somewhere that has a recognized degree in math and covers more or less the basics that I said above. If its a reasonably large uni, it probably will be alright, but if in doubt, get some feedback from a good source.

    If your pursue this field of study, I wish you all the best, and hope you enjoy your coursework and learning as much as I have.
     
  4. Jun 16, 2011 #3
    In several departments in the states you probably don't HAVE to take a discrete subject, some applied math subject, stat, etc.

    @OP, if you want to go to math grad school, start with analysis.
     
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