Algebra 1 - MATH-UA.0343-001 (Fall 2018)

Course description

Lectures: Mondays, Wednesdays, 2:00-3:15PM, in CIWW (Courant Institute) 317.
Office hours: Mondays 3:30-4:30pm; Wednesdays 11:30-12:30am. Office WWH926.
If needed, possibility to set up appointments by email (thomasl@math.nyu.edu)
Recitation sessions: Fridays, 2:00-3:15PM in CIWW 512.
Course description: An introduction to abstract algebra. We will study the fundamental algebraic structures: groups, rings, fields.
Prerequisites: At least one "proof-based" class. The equivalent of discrete mathematics would be helpful. We will give examples and applications, but this is certainly an abstract course.
Textbook(s): We will use the open source textbook "Abstract algebra: Theory and applications." by Thomas W. Judson. You can read it online and download it as a PDF, for free, from the book webpage.
A classical reference that you may consult is Algebra by Michael Artin.
Good lecture notes ("Abstract Algebra", Alexander Paulin, Berkeley University)
Grading: Homework (25%), Midterm 1 (20%), Midterm 2 (20%), Final exam (35%).
Class outline
  • Groups: definitions, subgroups, cyclic groups, permutation groups, group (iso)morphisms.
  • Rings: definitions, examples, ideals, integral domains, principal rings.
  • Fields: definitions, fields of fractions.
Remark: you may want to check the webpage for other sections of the same class, taught by Liming Pang, here. Syllabus is a bit different from ours.
Sessions