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Which advanced math courses are favored by top graduate programs?

  1. Jul 28, 2009 #1
    Hey all.

    I'm actually a math and chemistry major at the Univ. of Illinois Chicago. I have a competitive GPA, research experience, and an overal good academic history. What I'm trying to do is plan my advanced math courses to not only be functionable within my area of interests (engineering, applied mathematics, physical chemistry), but are respected and appreciated by graduate admission review boards.

    Here are my options.

    Analysis II
    Topology I & II
    Linear Algebra II
    Abstract Algebra II
    Partial Differential Equations
    Complex Analysis
    Probability Theory
    Statistical Theory
    Mathematical Models
    Numerical Analysis
    Advanced Calculus
    Differential Geometry

    Any suggestions not listed?

    So within the fields of applied mathematics, engineering, and chemistry which would give me the best edge?
  2. jcsd
  3. Jul 28, 2009 #2
    If you are going for the applied route rather than looking into pure mathematics, Numerical Analysis, PDEs, and Advanced Calculus (assuming you mean vector calculus) are good choices (Numerical Analysis and Advanced Calculus are usually required courses for applied math modules). Complex Analysis and Functional Analysis are also good courses to have.

    As for the pure math courses you mentioned - Topology, Analysis, Complex Analysis, Abstract Algebra, and Differential Geometry - they are definitely useful for pure math degrees - in fact all of them (except possibly Differential Geometry) should be taken if you are looking into grad school for pure math. Ring Theory, Field Theory, and Measure Theory are also good courses in pure math. But if you are deciding to go for applied math, most of these courses won't be as useful as taking upper year applied math courses.
  4. Jul 29, 2009 #3
    Since my question is related to the OP's line of inquiry, I hope I'm not hijacking this thread. Is Advanced Calculus usually a course on multivariable calculus/vector calculus? I have taken a rigorous calculus course this past year and I plan to take a rigorous real analysis course this upcoming year. Our school doesn't really offer an honors multivariable calculus course, nor does it have an advanced calculus course. Although I have been reviewing more introductory analysis topics and studying topology on the side, should I work through an advanced calculus text? I have a good grasp of the computational aspects of multivariable calculus, but I will be going through calculus on manifolds by spivak in my real analysis course next year, I think. Thanks.
  5. Jul 29, 2009 #4
    For admission to graduate school in mathematics. Of the ones listed, the essentials would be Analysis II, Abstract Algebra II. plus subject matter GRE.
  6. Jul 29, 2009 #5
    Thank you for the advice. I agree with you on the applied path, as pure mathematics is something I really don't see in my future (although appreciated of course). Are you familiar with any applied courses that are respected in the physical sciences besides the basic Calculus sequence and Differential Equations? I hear a second course in Linear Algebra, sometimes Complex Analaysis... each opinion varies.

    And does anyone know if a course in Statistical Methods or Statistical Theory would be more rigorous?

    Does anyone know the type of mathematical training a school such as MIT would want for lets say graduate chemistry (physical), engineering, or geo studies?
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