MATH 394
Galois Theory and Modules Fall 2013
Division III Quantitative/Formal Reasoning
This is not the current course catalog

In the 1830’s Evariste Galois developed a beautiful theory relating the structure of field extensions to the structure of a group. By understanding this relationship, one can often translate a problem about field extensions to a question about groups that is easier to answer. In this course, we will study Galois Theory and modules. A module is a generalization of vector spaces; in particular, a module can be thought of as a vector space with the weaker condition that the set of scalars are elements of a ring instead of a field. Possible topics covered will include field theory, galois theory, quotient modules, direct sums, free modules, and exact sequences.