Syllabus for Abstract Algebra -- Math 321
Fall 2004

 This syllabus is, of course, tentative! Monday Wednesday Friday 8/30 9/1 Welcome and Introduction 9/3 Ch. 0: Preliminaries Ch. 0: Preliminaries Ch. 1: Motions on the Square 9/6 Labor Day 9/8 Ch. 2: Cayley Table, D4, Dn 9/10 Ch. 2: Defining a group Lottery to adopt groups PS 1 (Individual) Due Quiz 1 9/13 Ch. 2: General Properties 9/15 Ch. 3: Order, Subgroups 9/17 Subgroup tests of groups Informal discussion of your gp Short paper on gp due PS 2 (Group) due (verify it is a group) 9/20 Ch. 3: Cyclic subgps, center 9/22 Ch. 3: More on subgroups 9/24 Ch. 4: Generators, centralizer, subgroup Ch. 4: Intro to cyclic groups Fund. Thm of Cyclic Gps lattice PS 3 (Individual) due Quiz 2 9/27 Ch. 4: Proof of FTCG 9/29 Ch. 5: Permutation Groups 10/1 Ch. 5: Decomposing PS 4 (Group) due permutations 10/4 Ch. 5: Alternating Groups 10/6 Ch. 6: Define isomorphism, 10/8 Ch. 6: Properties of examples isomorphisms Receive Take-Home Ex 1 Turn in Take-Home Ex 1 10/11 Fall Break 10/13 Ch. 6: Automorphisms 10/15 Ch. 7: Define cosets, Properties of cosets PS 5 (Individual) due 10/18 Ch. 7: Properties of cosets 10/20 Ch. 7: LaGrange's Theorem 10/22 Ch. 7: Consequences of LaGrange's Theorem Informal discussion of your gp Short paper on gp due PS 6 (Group) due (Interesting/confusing aspects) 10/25 Ch. 7: Consequences of 10/27 Ch. 7: Orbit-Stabilizer Thm 10/29 Ch. 8: External Dir. Products LaGrange's Theorem; Ch. 8: External Dir. Products Factor Groups (Definitions) orbits, stabilizers PS 7 (Individual) due Quiz 3 11/1 Ch. 8: External Dir. Products 11/3 Ch. 9: Test for Normality 11/5 Ch. 9: Work with normal Ch. 9: Define Normal Subgp subgroups Receive Take-Home Ex2 Turn in Take Home Ex 2 11/8 Ch. 9: Define Factor Groups 11/10 Ch. 9: Factor Groups 11/12 Ch. 9: More on factor groups PS 8 (Group) due 11/15 Peer Review of 1st 11/17 Ch. 27: Symmetry and 11/19 Ch. 27: Define symmetry draft of paper on Isometries groups your adopted group PS 9 (Individual) due Quiz 4 11/22 Ch. 27: Which groups are 11/24 Thanksgiving Break 11/26 Thanksgiving Break symmetry groups? 2nd draft due (to me) 11/29 Ch. 27: Rotation group of 12/1 Ch. 28: The 7 frieze groups 12/3 Ch. 28: The crystallographic cube; finite rotation groups groups in R3 PS 10 (Group) due 12/6 Informal discussion of your 12/8 Ch. 28: conclusion 12/10 Ch. 29: Symmetry & Counting groups Ch. 29: Symmetry & Counting Hand out Final Final draft due PS 11 due Quiz 5 12/13 Ch. 29: Symmetry & Counting 12/15 12/17 The Final will be due at 2:30pm on Friday 12/17.

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

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