**Instructor:** John Voight

**Course on canvas.dartmouth.edu.**⇗

## Syllabus

Course Summary: Date Details Mon Sep 12 Why Abstract Algebra? Wed Sep 14 1.1: Basic Axioms and Examples Thu Sep 15 0.1: Basics Fri Sep 16 1.2: Dihedral Groups Mon Sep 19 1.3: Symmetric groups Wed Sep 21 0.2: Properties of the Integers; 0.3: ZZ/nZZ Fri Sep 23 1.4: Matrix Groups; 1.5: The Quaternion Group; 1.6: Homomorphisms and Isomorphisms Mon Sep 26 1.7: Group Actions Wed Sep 28 2.1: (Subgroups) Definition and Examples; 2.2: Centralizers and Normalizers, Stabilizers and Kernels Thu Sep 29 2.4: Subgroups Generated by Subsets of a Group; 2.5: The Lattice of Subgroups of a Group Fri Sep 30 2.3: Cyclic Groups and Cyclic Subgroups Mon Oct 3 3.1: (Quotient Groups and Homomorphisms) Definitions and Examples Wed Oct 5 3.2: More on Cosets and Lagrange's Theorem Mon Oct 10 3.3: The Isomorphism Theorems, 3.4: Composition Series and the Hoelder Program Wed Oct 12 3.5: Transpositions and the Alternating Group Fri Oct 14 4.1: Group Actions; 4.2: Cayley's Theorem; 4.3: The Class Equation Mon Oct 17 4.5: The Sylow Theorems Wed Oct 19 5.1: Direct Products 12:15pm to 1:05pm Mon Oct 24 5.2: Fundamental Theorem of Finite Abelian Groups; Review Wed Oct 26 7.1: (Rings) Basic Definitions and Examples Fri Oct 28 7.2: Examples: Polynomial Rings, Matrix Rings, and Group Rings Mon Oct 31 7.3: Ring Homomorphisms and Quotient Rings Wed Nov 2 7.4: Properties of Ideals Fri Nov 4 8.1: Euclidean Domains Mon Nov 7 8.2: Principal Ideal Domains (PIDs) Wed Nov 9 8.3: Unique Factorization Domains (UFDs) Fri Nov 11 9.1: (Polynomial Rings) Definitions and Basic Properties; 9.2: Polynomial Rings over Fields I Mon Nov 14 Wrap-up