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
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