Re: problem 'getting into' the spirit of abstract algebra
- From: Jim Spriggs <jim.sprigs@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Fri, 1 Apr 2005 19:50:10 +0000 (UTC)
"porky_pig_jr@xxxxxxxxxxx" wrote:
>
> I have fairly decent undergrad level of math. Took calculus I/II/III,
> intro to diff equations, and intro to complex variables. No problems,
> got excellent grades, enjoyed all the courses, but - more importantly -
> was able to 'gulp' the entire topics, so to speak. However, with Linear
> Algrebra, it was entirely different story. I had to literally grind
> through the proofs and assignments (and that's me. can't blame either
> instructor or textbook).
>
> Now when I'm thinking of enrolling into master level program, I'm
> afraid I'll have more problems like this with abstract algebra. Like, I
> took a look at some graduate text on analysis, and point-set topology.
> I 'feel' what's going on, and I assume I won't have serious problems
> with those topics. However reading some intros to group theory, number
> theory, etc leaves me with the same feeling I had while learning Lin
> Alg. Have to go trhough the proofs very slowly, don't have the
> intuitive feeling of what's going on.
Dear Mr Pig, or may I call you Porky?
Three thoughts:
(1) Didn't you come across linear algebra in calculus and differential
equations? If you review those parts of analysis that use linear
algebra you might find it more amenable. I mean if you creep up behind
it you may be able to subdue it. For example, the role of linear
algebra in differential equations is made very clear in Hirsch and
Smale's "Differential Equations, Dynamical Systems and Linear Algebra".
But it seems to me that linear algebra crops up all over calculus.
Similarly, there is that branch of number theory that uses (complex
often) analysis, called analytical number theory.
(2) Do an MSc in analysis! Avoid algebra if you can! Ask the
admissions tutors (or whatever they are called where you are) if the
courses do much algebra. Actually, that kind of information is probably
available on Web sites now-a-days.
(3) Resign yourself to having to go though the proofs very slowly
whatever the topic. At Masters level it's bound to be harder than at
undergraduate level.
.
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