Instructor: Ciaran Schembri

Course on canvas.dartmouth.edu.⇗

Textbook

Thomas W. Judson, Abstract Algebra: Theory and Applications ⇗

Course Catalogue Description

This course will provide an introduction to fundamental algebraic structures, including the basic algebraic structures of groups and rings. These objects are some of the most fundamental structures in pure math and have far reaching applications such as computer vision, cryptography and error correcting codes.

Syllabus

Date Description Book section
Th 6/20
  • Why abstract algebra?
  • Sets
  • Functions
 1.2
Tu 6/25
  • Equivalences
  • Group definition
 1.2, 3.1
Th 6/27
  • Group examples
  • Group properties
  • Intro to proofs
 3.1, 3.2, 1.1
Tu 7/2
  • Subgroups
  • Cyclic groups
 3.3, 4.1
Th 7/4 No Class
Fr 7/5 Homework 1 due
Th 7/11
  • Permutation Groups
  • Dihedral group
 5.1, 5.2
Th 7/11 Homework 2 due
Tu 7/16
  • Cosets
  • Lagrange's theorem
 6.1, 6.2
Th 7/18
  • Isomorphisms
 9.1
Th 7/18 Homework 3 due
Tu 7/23 No class
Th 7/25 Midterm
Tu 7/30
  • Normal subgroups
  • Factor/quotient groups
 Ch10
Th 8/1
  • Homomorphisms
  • The isomorphism theorems
 Ch 11
Th 8/1 Homework 4 due
Tu 8/6
  • Introduction to Rings
  • Integral domains & fields
 16.1, 16.2
Th 8/8
  • Ring homomorphisms
  • Ideals
  • Quotient rings
 16.3
Th 8/8 Homework 5 due
Tu 8/13
  • Maximal & prime ideals
 16.4
Th 8/15
  • Proof party
Th 8/15 Homework 6 due
Tu 8/20 No Class
Sat 8/24 Final Exam in Kemeny 006