TEXTBOOK: Advanced Modern Algebra, by Joseph J. Rotman
GOALS: The goals of this sequence of algebra courses are
to impact an appreciation of algebra from both applied and pure math view
points, and to help students build up the mathematical competence in this
essential and important tool of mathematics.
COURSE DESCRIPTION: In the first semester, the following
topics will be covered. Groups and the structure of groups (through the
discussions on subgroups, normal subgroups, quotient groups, products,
centralizers and normalizers, normal sequences, among others), elementary
ring theory, factorization, PIDs and UFDs, polynomials and power series,
elementary properties of modules and vector spaces.In the Second semester, some of the
topics covered will be the theory of modules, (free, injective and
projective modules), field theory and Galois theory. If time permits, we
will also discuss other topics including finite fields, modules over finite
commutative rings and/or lattice theory.
HOMEWORK and EXAMS: Homework will be assigned and
collected every other week. Your homework average will contribute 25% of
your grade. There will be three midterm exams (together comprising 50% of
your grade) and a final worth 25% of your grade.