Re: problem 'getting into' the spirit of abstract algebra

<porky_pig_jr@xxxxxxxxxxx>
> 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.
>
> A question to those who teach math: Are you familiar with the cases
> like mine? Is there any way I can deal with this problem, or you think
> I should give up on the idea of enrolling into the grad program?
I'm not a teacher but I've heard similar plaints quite a few times
on sci.math and elsewhere on the net. Maybe the problem is not
so much with the algebra (which I guarantee is not a big deal) as
with the style of exposition. In particular, if it is in the axiomatic
diagramless style of Hilbert-Bourbaki, and this your first encounter
with that style, it will take some getting used to.
Algebra is about calculation. You'll end up with a few important
algorithms for calculating stuff (diagonalization, solvable groups,
invariant factors, etc.) plus a few proofs of impossibility (trisecting
an arbitrary angle with conics, solving an arbitrary quintic by
radicals). If you are in awe of undergraduate algebra, rest assured
that the material does not deserve it.
It might pay (it did for me) to have a look at summary
treatments of (ee.g.) group theory and multilinear algebra
that were written for physicists. They make the stuff look
less intimidating, not to say less barren.
LH


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