The course content will be tailored for the students taking it.
However, the standard syllabus includes:
Rings: Polynomial rings, fields of fractions, and
other examples. Euclidean domains, principal ideal domains, and
unique factorization domains.
Fields: Field extensions and Galois Theory.
Solvability of equations by radicals. Ruler and compass
constructions.
Modules: Finitely generated modules over a principal
ideal domain. Applications to finitely generated groups over
principal ideal domains.
Other topics: These may include:
Representation theory of finite groups.
Algebraic geometry.
Error-correcting codes.
Prerequisites:
The needed background for this course is Math 417, Intro to
Abstract Algebra. Math 427 is also fine, though there is some overlap
between that course and this one.
Weekly homework assignments: (20%) These will typically be
due in class on Wednesday. Late homework will not be accepted; however, your
lowest two homework grades will be dropped, so you are effectively
allowed two infinitely late assignments. Collaboration on homework is
permitted, nay encouraged. However, you must write up your solutions
individually and understand them completely.
Two takehome midterms: (12.5% each) These are glorified HW
assignments that you are to work on individually. They will replace
the usual HW for two weeks of the term.
In class midterm: (20%) This one-hour exam will be held in
our usual classroom, on Friday, March 5.
Final exam: (35%) This will be Friday, May 7 from 1:30-4:30.