Math 71
Abstract Algebra

Last updated November 10, 2016 10:33:19 EST

## Syllabus

The following is a tentative syllabus for the course. This page will be updated irregularly.
On the other hand, the weekly syllabus contained in the Homework Assignments page will always be accurate.

Lectures Sections in Text Brief Description
9/12 1.1, 1.2 Introduction, sets and equivalence relations
9/14 2.1, 2.2 Properties of $\mathbb Z$: induction, division and Euclidean algorithm
9/16 3.1, 3.2 $\mathbb Z_n$: Integers modulo $n$, Symmetric groups, Dihedral groups $D_3$, $D_4$, matrix groups, Quaternion group
9/19 3.2, 3.3 Simple properties of groups, subgroups and characterization
9/21 4.1, 4.2 Cyclic groups, multiplicative group of $\mathbb C$
9/23 5.1, 5.2 Symmetric groups, cycle notation, general dihedral groups
9/26 6.1, 6.2, 6.3 Cosets; Lagrange's theorem, applications
9/28 9.1, 9.2 Isomorphism; direct products
9/30 10.1, 10.2 Normal subgroups; factor groups; the alterating group
10/3 11.1, 11.2 First Isomorphism theorem
10/5 Midterm Exam I
10/6 (x-hour) 11.2 The other isomorphism theorems
10/7 14.1 Groups acting on sets; Cayley's theorem
10/10 14.2 The class equation and applications
10/12 15.1, 15.2 The Sylow Theorems
10/14 13.1 Fundamental theorem of finite abelian groups; recognizing direct products
10/17 13.2 Solvable groups; Simple Groups and the Hölder prgram
10/19 16.1, 16.2 Rings; integral domains
10/21 16.2, 16.3 Integral domains, homomorphisms, ideals
10/24 16.3, 16.4 Maximal and prime ideals
10/26 Midterm Exam II
10/27 (x-hour) 17.1 Rings, Polynomial Rings, Finite Fields
10/28 17.2 The Division Algorithm
10/31 17.3 Irreducibility, Rational root test, Gauss's lemma
11/2 17.3 Gauss's lemma, Eisenstein's criterion
11/4 18.1 Integral domains and fields of Fractions
11/7 18.2 PIDs are Unique Factorization domains
11/9 18.2 $D$ UFD implies $D[x]$ UFD
11/11 18.2 Detecting multiple roots, irreducibility in $\mathbb Q[x,y]$
11/14   Cyclotomic polynomials
11/18 Final Exam 8-11am

T. R. Shemanske
Last updated November 10, 2016 10:33:19 EST