Syllabus for Abstract Algebra -- Math 321
Fall 2006

 This syllabus is, of course, tentative! Monday Wednesday Friday 8/28 8/30 Welcome and Introduction 9/1 Ch.1: Symmetries of a Square Ch. 1: Symmetries of a Square Ch. 0: Facts about Integers 9/4 Labor Day 9/6 Ch.0: Integers, Equiv. Rel'ns 9/8 Ch. 2: Defining a Group Adopt groups Examples of Groups PS 1 (Individual) Due 9/11 Ch. 2: More Examples of Groups 9/13 Ch. 2: Properties of 9/15 Ch. 3: Subgroups Groups Rewrite of PS 1 due Ch. 3: Order of a Group Discussion of adopted groups Short paper on gp due Ch 0 &1 defs and thms due PS 2 (Group) due (verify it is a group) 9/18 Ch. 3: Subgroup Tests 9/20 Ch. 3: Centers, Centralizers 9/22 Ch.4: Intro to Cyclic Groups Classifying all groups of order 4 Ch.2 def'ns and thms due PS 3 (Individual) due Rewrite of PS 2 due 9/25 Ch. 4: Fund. Thm of Cyclic Gps 9/27 Ch. 4: What the FToCG does for us! 9/29 Ch. 5: Permutation Groups Ch. 5: Intro to Permutations Rewrite of PS 3 due Ch. 3 def'ns and thms due PS 4 (Group) due Deadline-1st adopted group mtg 10/2 Ch. 5: Even & Odd Permutations 10/4 Ch. 6: Define isomorphisms, 10/6 Ch. 6: Properties of Alternating groups Examples of isomorphisms Isomorphisms Ch. 4 def'ns and thms due Hand out Take-Home Ex 1 Turn in Take-Home Ex 1 10/9 Fall Break 10/11 Ch. 6: Automorphisms 10/13 Ch. 7: Define cosets Rewrite of PS 4 due Ch. 5 def'ns and thms due PS 5 (Individual or group) due 10/16 Ch. 7: LaGrange's Thm 10/18 Ch. 7: Consequences of 10/20 Ch. 7: Consequences of LaGrange's Theorem; LaGrange's Theorem; Discussion of your gp PS 6 (Group) due Short paper on group due Ch. 6 def'ns and thms due Deadline-2nd adopted group mtg (Interesting/confusing aspects) 10/23 Ch. 8: External Dir. Products 10/25 Ch. 9: Define Normal Subgp 10/27 Ch. 9: Test for Normality Rewrite of PS 5 due Ch.7 def'ns and thms due PS 7 (Individual) due Rewrite of PS 6 due 10/30 Ch. 9: Define Factor 11/1 Ch. 9: Work with Factor 11/3 Ch. 9: Factor groups Groups Groups Hand out Take-Home Ex2 Ch.8 def'ns & thms due Turn in Take Home Ex 2 11/6 Ch. 9: Work with factor gps 11/8 Ch. 10: Properties of 11/10 Ch. 10: Kernels & The first Ch.10: Intro to Homomorphisms Homomorphisms, isomorphism Thm Rewrite of PS 7 due Ch.9 def'ns & thms (pt 1) PS 8 (Group) due Deadline-3rd adopted group mtg 11/13 Ch. 10: Using the 1st 11/15 Ch. 11: Fundamental Thm 11/17 Ch. 11: Fundamental Isomorphism Theorem of Abelian Groups Thm of Abelian Groups Ch.9 defn's & thms (pt 2) 1st draft due (to peer) PS 9 (Individual) due Rewrite of PS 8 due 11/20 Ch. 12: Rings, and the 11/22 Thanksgiving Break 11/24 Thanksgiving Break rules of multiplication 2nd draft due (to me) 11/27 Ch. 12: Rings 11/29 Ch. 13: Integral Domains 12/1 Ch. 14: Ideals & Factor Rings Ch. 13: Integral Domains Ch. 14: Ideals & Factor Rings Ch.10&11 defs & thms due PS 10 (Group) due Rewrite of PS 9 due 12/4 Ch. 14: Ideals & Factor Rings 12/6 Ch. 15: Ring Homomorphisms 12/8 Ch. 15: Ring Homomorphisms Hand out Final PS 11 due Final Draft due Ch. 12,13,14 defs & thms due Rewrite of PS 10 due The Final will be due at 2:30pm on Friday 12/15.

Janice Sklensky
Wheaton College
Department of Mathematics and Computer Science
Science Center, Room 109
Norton, Massachusetts 02766-0930
TEL (508) 286-3973
FAX (508) 285-8278
jsklensk@wheatonma.edu

Back to: Abstract Algebra | My Homepage | Math and CS