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Which class for undergrad math

  1. Oct 31, 2009 #1
    hey, I am trying to pick 2 out of these 4 classes. I want to be a well rounded under grad math major. I am in my second year and have done 2 semesters of analysis, 1 abstract algebra, 1 number theory, 2 stats, 1 complex analysis.

    these are the choices I have narrowed my options down to. I am leaning towards topo and field theory. of course there is no reason not to take the other two later, but these courses aren't offered every semester...

    Field theory
    Algebraic and transcendental elements, Galois theory, constructions with straight-edge and compass, solutions of equations of low degrees, insolubility of the quintic equation, Sylow theorems, fundamental theorem of finite Abelian groups.

    Axiomatic Set theory
    Development of a system of axiomatic set theory, choice principles, induction principles, ordinal arithmetic including discussion of cancellation laws, divisibility, canonical expansions, cardinal arithmetic including connections with the axiom of choice, Hartog's theorem, Konig's theorem, properties of regular, singular and inaccessible cardinals.

    Elementary Logic
    Elementary development of propositional and predicate logic, including semantics and deductive systems and with a discussion of completeness, incompleteness and the decision problem.

    Introduction to topology
    Metric spaces, topological spaces, connectedness, compactness (including Heine-Borel and Bolzano-Weierstrass theorems), Cantor sets, continuous maps and homeomorphisms, fundamental group (homotopy, covering spaces, the fundamental theorem of algebra, Brouwer fixed point theorem), surfaces (e.g., Euler characteristic, the index of a vector field, hairy sphere theorem), elements of combinatorial topology (graphs and trees, planarity, coloring problems).
     
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  3. Oct 31, 2009 #2

    HallsofIvy

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    Unless you are particularly interested in Symbolic Logic and "Foundations of Mathematics", I would recommend Field Theory and Topology.
     
  4. Oct 31, 2009 #3
    Topology and field theory. Although; I'm pretty surprised you don't have another course like 'Abstract Algebra 2' that covers everything in the field theory section along with some ring theory (ideals, euclidean domains, principal ideal domains etc.). If your school does, in fact, offer a class like that I would sugesst you take that instead. If not, definitely field theory and topology (since I assume that if you were really into set theory the other two would be no-brainers, so you must not be that into set theory).
     
    Last edited: Oct 31, 2009
  5. Nov 1, 2009 #4

    lurflurf

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    If Algebra 2 had everything in field theory why would both classes exist?
     
  6. Nov 1, 2009 #5
    Field theory and topology are obviously the more useful ones.
     
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