Math 71
Algebra (groups and rings)

Last updated July 18, 2017 09:28:24 EDT

## Syllabus

The main focus of the course will be Chapters 1-5, 7-9 of Dummit and Foote's's text Abstract Algebra. This is a tentative syllabus; the weekly syllabus contained on the Homework Assignments page will always be accurate.

Lectures Sections in Text Brief Description
9/15 0.1 - 0.3 Equivalence relations, partitions, $\mathbb Z/n \mathbb Z$
9/17 0.1 - 0.3 Equivalence relations, partitions, $\mathbb Z/n \mathbb Z$
9/19 1.1 Definition of groups; examples; begin dihedral group
9/22 1.2 - 1.3 Dihedral and Symmetric groups
9/24 1.4 - 1.5, start 1.6 Matrix Groups, Quaternions, Isomorphism
9/26 1.6, 2.1 Homomorphisms and subgroups
9/29 2.3 Cyclic groups
10/1 2.3, 2.4 Subgroups generated by a set; cosets
10/3 3.1 Cosets and homomorphisms; quotient groups
10/6 3.1 Lagrange's theorem. More on cosets
10/8 3.2 First isomorphism theorem
10/9 First midterm In-class part; take-home part due in class Friday
10/10 3.3 Other isomorphism theorems
10/13 3.5, 1.7, 4.1, 4.2 the alternating group; Group Actions and Cayley's theorem
10/15 4.2 Group actions continued
10/17 4.3 Groups acting by conjugation; the class equation
10/20 3.4, 4.5 Holder program; Sylow theorems
10/22 5.2, 5.4 Fundamental theorem of finite abelian groups; recognizing direct products; applications of the Sylow theorems
10/24 7.1, 7.2 Rings (basic definitions and examples); Polynomial rings
10/27 7.3 Homomorphisms; quotient rings
10/29 7.4 Quotient rings and properties of ideals
10/30 Second midterm In-class part; take-home part due in class Friday
10/31 8.1, 9.1 Euclidean domains; Polynomial rings
11/3 8.2, 9.2 PIDs
11/5 8.3 gcds; irreducibles; primes
11/7 8.3 Unique Factorization Domains
11/10 9.3 Gauss's lemma and consequences
11/12 9.4 Irreduciblity criteria
11/14 9.4 Extension Fields
11/17   Wrap it up

T. R. Shemanske
Last updated July 18, 2017 09:28:24 EDT