21-610: Algebra I, Fall 2017
Lectures MWF 12:30 - 1:20 in Wean 7201
We will study groups, rings, and fields. Like people, these structures shall be judged by their actions; as such, we must also study group actions, modules, and vector spaces.
This course assumes some familiarity with (finite) group theory and (finite-dimensional) linear algebra. That said, in this course we will routinely examine infinite structures as well.
Abstract Algebra, 3rd Edition by Dummit and Foote.
Free groups and paradoxicality
Prime factorization via ideals
Finitely generated modules over a PID
Polynomials and factorization
Tuesday noon - 1:30 or by appointment in 7121 Wean Hall.
Your grade will be determined as follows:
20% homework (see below for details),
20% each of two midterms,
40% final exam.
Homework will typically be assigned on Wednesday and due the subsequent Wednesday. Collaboration is encouraged on the assignments, but each student is expected to write up his or her own solutions. Occasionally there will be a starred problem as discussed below. Use of external resources (on non-starred problems) is also permitted, but in the interest of academic honesty please be sure to cite your sources.
Each assignment may contain a single starred problem for which no collaboration nor external resource is allowed. You may consult only the text and your notes.
HW1 (due Sept 6)
HW2 (due Sept 13)
HW3 (due Sept 20)
HW4 (due Sept 27)
HW5 (due Oct 4)
HW6 (due Oct 18)
HW7 (due Oct 25)
HW8 (due Nov 1)
HW9 (due Nov 8)
Clinton T. Conley