Math 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: Arun Ram, Steven Bauman
• 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

Content coverage:

• 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