Math majors and graduate student in related areas
Math 541 and 542 together constitute an introduction to modern algebra at the undergraduate level. Math 542 covers linear algebra at a level deeper than Math 340, and a little field theory. It is essential for students preparing for graduate studies in mathematics and in some related fields.
- Modules: submodules, homomorphisms, quotients, simple modules, cyclic modules, free modules, linear transformations
- Matrices: determinants, elementary matrices, Smith normal form over a PID, characteristic roots
- Finitely generated modules over a PID
- Classification of Finite abelian groups
- Normal forms for matrices: rational canonical form, Jordan canonical form
- Field extensions, roots of polynomials