Math 370
## Math 370

** ALGEBRA **

This is the first half of a year long course in algebra, with emphasis
on the ways in which algebra and geometry interact and complement each
other. We will cover groups, subgroups, homomorphisms, equivalence
relations and cosets, quotient groups, products of groups, generators
and relations, calculations in the symmetric group, the isomorphism
theorems, fields and vector spaces, basis and dimension, linear
transformations and matrices, change of basis, direct sums,
eigenvectors, characteristic and minimal polynomials, diagonalization,
the Cayley-Hamilton theorem, Jordan canonical form, the fundamental
theorem of algebra, matrix exponentials, solving linear ODE,
representations of finite groups: invariant subspaces, complete
reducibility.

A basic goal of the course is to use the abstract theory to develop
an intuition in concrete examples and learn to understand
and produce sound mathematical arguments.