San Francisco State University
Department of Mathematics
Course Syllabus
MATH 435
MODERN ALGEBRA II
Prerequisites
Math 335
Bulletin Description
Advanced topics in group theory: group actions, conjugacy classes, Sylow’s
Theorem. Modules and vector spaces, and the main theorem of finitely
generated modules over PIDs. Fields and field extensions, finite fields. And
a miscellaneous topic chosen from topics such Galois theory, Groebner bases
and computational algebraic geometry, algebraic coding theory, algebraic
number theory etc.
Course Objectives
The course introduces more advanced topics in modern algebra. It is
a course for those students who wish to have a solid base in abstract
algebra beyond introductory concepts in group theory. This course
will be also a good preparation for graduate students who will take Math 850.
The students are expected to do proofs routinely.
Evaluation of Students
There will be weekly homework assignments, two midterms and a
comprehensive final exam.
Course Outline
Groups (3-4 weeks): some review followed by group actions, conjugacy classes,
and the statement of Sylow’s theorem and its simple applications. Modules
and vector spaces (4 weeks): submodules, homomorphisms, quotient modules,
direct sums, free modules, and the statement of the main theorem of finitely
generated modules over PIDs. Fields and field extensions (4 weeks): algebraic
extensions, minimal polynomials, splitting fields, finite fields. Miscellaneous
topics (4 weeks): a well-established topic from topics including Galois theory,
Groebner bases, algebraic coding theory, algebraic number theory etc.
Textbooks and Software
Any slightly advanced algebra book such as Abstract Algebra by
Dummit and Foote would suffice. Depending on the miscellaneous
topic additional textbooks/material might be required. Free
software such as Macaulay 2, Singular, GAP as well as Mathematica
might be needed.
Submitted by: __Serkan Hosten _____
Date: _21 February 2005______