Fall 2006
(Last modified: Friday, October 6, 2006, 9:15 AM )
| 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