Schedule

Tentative syllabus (Just rough time-frame)

Week of Section Topic
Jan 10 0
1
Introduction, Sets and Relations
Jan 17 2
3
Binary Operations
Isomorphic Binary Structures
Jan 24 4
5
Groups
Subgroups
Jan 31 5
6
Subgroups
Cyclic Groups
Feb 7 8
9
Groups of Permutations
Orbits,Cycles, and the Alternating Groups
Feb 14 10 Cosets and the Theorem of Lagrange
Feb 21 11 Direct Products and Finitely Generated Abelian Groups
Mar 2 13 Homomorphisms
Mar 7 Spring Break
Mar 15 Midterm, Time: 8:00-9:15am, Location: Lander Auditorium, Hutchison 140
Mar 15 14
15
Factor Groups
Factor-Group Computations and Simple Groups
Mar 28 16
17
Group action on a set
Applications of G-Sets to Counting
Apr 4 18
19
Rings and Fields
Integral Domains
Apr 11 20
21
Fermat's and Euler's Theorems
The Field of Quotients of an Integral Domain
Apr 18 22
23
Rings of Polynomials
Factorization of Polynomials over a Field
Apr 25 26
27
Homomorphisms and Factor Rings
Prime and Maximal Ideals
May 2 Final, 12:30-3:30pm, Dewey 2162