542 - Modern Algebra
Prerequisites:
Math 541
Frequency:
Spring (II)
Student Body:
Math majors and graduate student in related areas
Credits:
3. (N-A) Recent Texts:
M. Artin, Algebra, Prentice-Hall 1991 /Bhattacharya, Jain and Nagpaul, Basic Abstract Algebra, Cambridge Univ. Press, 1994
Course Coordinator:
Don Passman Background and Goals:
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.
Alternatives:
n/a
Subsequent Courses:
n/a Course Content:
- 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