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Preparing for General Topology

  1. Jul 25, 2012 #1
    Hey everybody,

    I just wanted to ask a general question about Topology. I am planning on taking a General Topology course in Spring 2013 and first of all I don't know what it is. I am finishing up Differential Equations 1 right now with an A. By the spring I will have taken linear algebra 2 and complex variables. I have already finished Calculus 1-3 and linear algebra 1, all with high A's. Unfortunately I have not and probably will not take a geometry class by this spring. The catalog simply says that linear algebra 1 is sufficient but I have my doubts.

    What is topology? What do I need to study and know before I take the course?
     
  2. jcsd
  3. Jul 25, 2012 #2
    Without a background in analysis, the motivation for a lot of the concepts will be lost, but you shouldn't find it overly difficult provided you're proficient in proof writing.

    Topology generalizes a number of concepts in analysis like convergence and continuity of sequences and functions. You've already encountered these concepts in calculus, but only in the context of the reals, which possess a number of unnecessarily restrictive qualities (like the notion of "distance", which topology dispenses with).
     
  4. Jul 25, 2012 #3
    Like Number Nine says, with out analysis, some of the stuff might seem odd since it is generalisations of real stuff. However, in my Complex class, we did lots of stuff with open sets and what not, so if you do this as well, you might get most of the motivations.

    Topology is a very interesting class. It will be the most abstract class you have taken, and this will make it tough. But it is well worth it. I didn't take it as an undergrad, but I have spent this summer working through a book. You'll have fun if you like abstract math.
     
  5. Jul 25, 2012 #4
    Would changing my complex variables class this fall for a real analysis class better prepare me for topology?
     
  6. Jul 25, 2012 #5

    micromass

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    Complex variables can actually be a very good precursor to topology. Many things in complex variables lead naturally to concepts in topology.

    Can you tell us what the complex variables class covers?? What book does it use?
     
  7. Jul 27, 2012 #6
    FUND.OF COMPLEX ANAL.F/MATH,SCI.+ENGR.
    Author SAFF
    Edition 3RD 03
    ISBN 9780139078743

    MATH 4391 - Complex Variables
    3 Class Hours 0 Laboratory Hours 3 Credit Hours
    Prerequisite: A grade of “C” or better in MATH 2203 (Calculus 3).

    The study of complex variables is a central subject in mathematics, important for students in mathematics, engineering and physical sciences (due to so many applications to fluid mechanics, heat conduction, and electromagnetic theory). Complex variables are a very powerful tool for solving problems that are either difficult or virtually impossible to solve in any other way. Topics covered in MATH 4391 provide an introduction to the subject, including basics from complex function theory: numbers, analytic functions, Cauchy-Riemann conditions, elementary functions, complex integration, Cauchy’s theorem and integral formula, power series, residues and applications.
     
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