Syllabus for Abstract Algebra -- Math 321
Fall 2008

 This syllabus is, of course, tentative! Monday Wednesday Friday 8/25 8/27 Welcome and Introduction 8/29 Ch.1: Symmetries of a Square Ch. 1: Symmetries of a Square Ch.0: Facts about Integrers 9/1 Labor Day 9/3 Ch.0: Preliminaries 9/5 Ch. 2: Defining a group, Adopt groups Examples of groups PS 1 (Group) Due 9/8 Ch. 2: Examples of Groups, 9/10 Ch. 2: Properties of 9/12 Ch. 3: Subgroups Groups Rewrite of PS 1 due Ch. 3: Order of a Group Discussion of adopted groups Short paper on gp due Ch0&1 defs and thms due PS 2 (Individual) due (verify it is a group) 9/15 Ch. 3: Subgroup Tests 9/17 Ch. 3: Centers, Centralizers 9/19 Ch.4: Intro to Cyclic Groups Classifying all groups of order 4 Ch.2 def'ns and thms due PS 3 (Group) due Rewrite of PS 2 due 9/22 Ch. 4: Fund. Thm of Cyclic Gps 9/24 Ch. 4: More on the FToCG 9/26 Ch. 5: Permutation Groups Ch. 3 def'ns and thms due What the FToCG does for us! Hand out Take-Home Ex 1 Turn in Take-Home Ex 1 9/29 Ch. 5: Even & Odd Permutations 10/1 Ch. 5: Working with Symmetric Groups 10/3 Ch. 6: Define Isomorphisms Alternating groups Ch. 6: Intro to isomorphisms Examples of isomorphisms Ch. 4 def'ns and thms due PS 4 (Group) due Rewrite of PS 3 due 10/6 Ch. 6: Properties of Isomorphisms 10/8 Ch. 6: Automorphisms 10/10 Ch. 7: Define cosets Rewrite of PS 4 due Ch. 5 def'ns and thms due PS 5 (Individual) due Deadline-1st adopted group mtg 10/13 Fall Break 10/15 Ch. 7: LaGrange's Theorem 10/17 Ch. 7: Consequences of LaGrange's Theorem; Discussion of your gp Short paper on group due Ch. 6 def'ns and thms due (Interesting/confusing aspects) 10/20 Ch. 7: Consequences of 10/22 Ch. 8: External Dir. Products 10/24 Ch. 9: Define Normal Subgp LaGrange's Theorem; Ch.7 def'ns and thms due PS 6 (Group) due Rewrite of PS 5 due 10/27 Ch. 9: Test for Normality 10/29 Ch. 9: Define Factor 10/31 Ch. 9: Work with Factor Groups Groups Ch.8 defs & thms due Hand out Take-Home Ex2 Turn in Take Home Ex 2 11/3 Ch. 9: Factor groups 11/5 Ch.10: Intro to Homomorphisms 11/7 Ch. 10: More properties of A few properties; kernels Homomorphisms Rewrite of PS 6 due Ch.9 def'ns & thms (pt 1) PS 7 (Group) due Deadline-2nd adopted group mtg 11/10 Ch. 10: Kernels & The first 11/12 Peer Review of Papers 11/14 Ch. 11: Examples using the isomorphism Thm Ch. 10: Using the 1st Fundamental Thm Ch. 11: Fund. Thm of Abelian Gps Isomorphism Theorem Ch.9 (pt 2), Ch.10 defn's & thms 1st draft of project due (to peer) PS 8 (Individual) due 2nd draft due (to me) 11/17 Ch. 11: Fundamental 11/19 Ch. 12: Rings, more on the 11/21 Ch.13: Integral Domains Thm of Abelian Groups rules of multiplication Ch. 12: Intro to Rings Ch. 11 defs & thms due Rewrite of PS 7 due PS 9 (Group) due Rewrite of PS 8 due 11/24 Ch. 14: Ideals 11/26 Thanksgiving Break 11/28 Thanksgiving Break Final Draft due 12/1 Ch.14: More on Ideals 12/3 Ch. 14: Ideals & Factor Rings 12/5 Ch. 14: More on Factor Rings Ch. 15: Maximal and Prime Ideals Ch.12, 13, 14 defs & thms due PS 10 (Individual or Group) due Paper exchange! Rewrite of PS 9 due Hand out Final The Final will be due at 4:00pm on Friday 12/12. This year's Norman W. Johnson lecture is Thursay October 2, at 5:30pm.

Janice Sklensky
Wheaton College
Department of Mathematics and Computer Science
Science Center, Room 101A
Norton, Massachusetts 02766-0930
TEL (508) 286-3973
FAX (508) 285-8278
jsklensk@wheatonma.edu

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