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Starting Postgraduate Programme in Economics, Advice for Calculus - Real Analysis

  1. Jul 30, 2011 #1
    Hello,

    I am starting a postgraduate level Economics course in two months. I will have to go through some kind of a Math Camp before the course, lasting more or less 10 days. Here is my curriculum;

    1. REAL ANALYSIS

    Topics:
    • Sequences and Convergence
    • Function on Rn
    • Continuity
    • Differentiability
    • Riemann’s Integral

    2. METRIC SPACES & TOPOLOGY

    Topics:
    • Metrics and Metric Spaces
    • Open and Closed Sets
    • Compactness
    • Connectedness
    • Fix Point Theorems


    3. LINEAR ALGEBRA

    Topics:
    • Vector Spaces
    • Linear Applications and Matrix Representation
    • Matrix Calculus
    • Projections
    • Eigenvalues and Quadratic Forms

    4. OPTIMIZATION

    Topics:
    • Convex Sets
    • Convex and Concave Functions
    • Unconstrained Maximization
    • Contrained Maximization, Lagrange’s Method and Kuhn-Tucker Theorem
    • Dynamic Programming

    ----------------------------------------------------------------------

    Now, I want to prepare as best as I can for this curriculum since success at these coursese will affect bursary levels. I took a few courses at undergraduate level for calculus but just consider I am almost new to these topics and I want to start over from beginning with a good Mathematical mind, want to get these concepts before I begin the curriculum.

    What are your suggestions at this point? Should I start from calculus or real analysis? Any advice for some links or lecture notes online?
     
  2. jcsd
  3. Jul 30, 2011 #2

    micromass

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    Hi nosfnosf! :smile:

    Reviewing calculus is useless in my opinion. Just make sure that you're comfortable with the notions of integrals, continuity, derivatives. You just need to know what the concept means and you just need to calculate the basic examples. That'll be enough.

    If I were you, I would start reviewing some basic analysis and linear algebra. Here is a site with many free lecture notes:
    For analysis: http://hbpms.blogspot.com/2008/05/stage-3-introductory-analysis.html
    For linear algebra: http://hbpms.blogspot.com/2008/05/stage-2-linear-algebra.html
    Just check a few free lecture notes and see which one you like.

    If you prefer a book: the book "understanding analysis" by Abbott is written for people like you!!

    Anyway, analysis and linear algebra aren't the easiest topics if you've never seen much math before. That's why I want to encourage you to ask a lot of questions on the material.
     
  4. Jul 30, 2011 #3
    =OO

    !!!!!!!!!

    (lol)
     
  5. Jul 31, 2011 #4
    Thanks for the reply.

    So you think it will be enough for me to learn basics of these concepts? I was thinking learning these topics almost full. Will these links provide them to me considering I have two months to prepare and can study a few hours a day? I will try to get the book from libraries too.
     
  6. Jul 31, 2011 #5

    micromass

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    The more you know about the topic, the better prepared you will be. So learning the topics almost full would be the best choice. But knowing the basics should get you there too. It's a matter of how much time you're willing to put in :smile:
     
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