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For an idea of what this course is like, we covered:

basic vector/matrix stuff

linear transformations

epsilon-delta definitions of limits and continuity in the multivariable context

basic topology (open, closed, compact sets, bolzano weierstrass theorem)

the derivative as a linear map

derivatives of matrix functions

continuity and differentiability

linear independence, span, bases, subspaces and vector spaces

images and kernels of linear maps

rank-nullity theorem

abstract vector spaces (space of polynomials, matrices, etc)

eigenvectors and eigenvalues

newton's method

in the first semester. In semester two I believe we discuss manifolds, integration, the generalized stokes theorem and differential forms.

So, my question is, what will I be ready for come next year? I'm thinking about taking an honors algebra course (another two semester long sequence) along with a semester each of differential equations and complex analysis. Would you say that this is an overload, just right, or could I take on more?

Also, should I try to take an intro. topology course before I tackle analysis? I've heard the topology in the course can hurt you if you're not experienced.

Thanks