Math 335 (Abstract Algebra I) Syllabus, Fall 2011

The following is a tentative syllabus for the course.  In case of conflicts between this syllabus and in-class announcements, the announcement takes precedence.

The handout of course procedures, etc., given out on the first day of class.

Syllabus for Math 335
(Last modified 25 November 2011)
Date  Section
Topics
 Homework Due Presentation Problems

F 26 Aug

 1 Introduction    
         
M 29 Aug 2 Binary Operations Section 1 #4, 6*, 8, 10, 16, 18*, 20, 22, 24, 26*, 32*, 37*, 38  
W 31 Aug   Student Presentations   Section 1 #33, 34, 35, 36; Section 2 #26, 35, 36, 37
F 2 Sep 3 Isomorphisms in Binary Structures Section 2 #1, 2, 3, 4*, 5, 7, 8, 9, 10*, 17, 18*, 19, 20, 21, 22*, 24, 28*, 33*, 34*  
         
M 5 Sep 4 Groups Section 3 #1, 2, 3, 4*, 6*, 7, 15, 16*, 21, 23*, 27*, 28, 29*  
W 7 Sep   Student Presentations Quiz on Sections 1-3 HW Section 3 #31, 32; Section 4 #33, 34, 36, 41
F 9 Sep 5 Subgroups Section 4 #3, 4, 5, 6*, 8, 9*, 19, 20*, 23, 24*, 27*, 28*, 29*  
         
M 12 Sep 6 Cyclic Groups Section 5 #1, 2, 3, 4*, 5, 6, 7abcd*ef, 14, 15, 16, 17, 18*, 19, 20*, 27, 28*, 36*, 40*, 42*, 54*  
W 14 Sep 6 Cyclic Groups cont'd Quiz on Section 4, 5 HW, plus the proof of Theorem 6.6  
F 16 Sep 8 Permutation Groups Section 6 #5, 6, 7, 8, 9, 10*, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22*, 24, 26, 27*, 29, 32, 33, 34*, 35, 36*, 37, 44*, 45*, 48*, 49*  
         
M 19 Sep   Student Presentations   Section 5 #46, 57; Section 6 #51, 52, 55, 56
W 21 Sep 8 Permutation Groups cont'd Quiz on Section 6 HW  
F 23 Sep   Introduction to GAP    
         
M 26 Sep 1-6 Midterm #1    
W 28 Sep 9 Orbits, Cycles, and Alternating Groups Midterm #1 take-home portion  
F 30 Sep 10 Introduction to Cosets  

 
         
M 3 Oct   Student Presentations Section 8 #1, 5*, 6, 7*, 9, 10, 11, 12, 13, 16, 17, 18*, 23, 24, 25, 26, 27, 28, 35, 46*, 47* Group 1: Section 9 #27a, 30
Group 2: Section 9 #27b, 31
Group 3: Section 9 #27c, 32
W 5 Oct   Student Presentations Quiz on Section 8 HW Problems from 30 Sept Handout
         
M 10 Oct   GAP Project #1    
W 12 Oct 10 Cosets and Lagrange's Theorem Section 9 #1*, 2, 3, 4, 6, 7, 8, 9*, 10, 11*, 12, 13*, 14, 15, 17*, 20, 21, 22, 23, 26*, 29*, 33*  
F 14 Oct 11 Direct Products Rubik's Cube GAP Project Write-Up, #4, 6, 7 only  
         
M 17 Oct 11 Finitely Generated Abelian Groups Section 10 #1, 2, 3, 4, 6*, 7*, 9*, 10*, 11*, 19, 21, 22, 23, 24, 25*, 28*, 29*, 34*  
W 19 Oct   Student Presentations Quiz on Sections 9, 10 HW Section 10 #27, 35, 36, 39, 40
F 21 Oct 13 Homomorphisms Section 11 #1, 2*, 3, 4, 5, 6, 7, 8*, 10, 13, 14, 15, 16*, 19, 20, 21, 22, 23, 24, 25*, 29*, 32, 33, 36, 39, 40, 41, 42, 46, 50*, 51*  
         
M 24 Oct   Student Presentations Quiz on Section 11 HW Section 11 #52, 53, 54
W 26 Oct 14 Factor Groups Section 13 #1, 2, 3, 4*, 5, 6*, 7, 8, 9, 10, 11, 16, 17, 18, 19*, 20, 21, 22*, 23, 24, 25, 26, 27, 28, 29, 32, 33, 34, 35, 36, 37*, 38, 39*, 40, 41, 42, 47*, 48, 49, 51, 52*, 53*  
F 28 Oct   Student Presentations   Section 13 #44, 45, 50, 55
         
M 31 Oct 14 Factor Groups cont'd Quiz on Section 13 HW  
W 2 Nov 14 The Fundamental Homomorphism Theorem Section 14 #1, 2*, 3, 4, 5, 6, 7, 8, 9, 10*, 11, 12, 13, 14, 15, 21, 23abdghij, 24*, 25*, 34*  
F 4 Nov   Catch-up and Review SET Project; Section 14 #16, 17, 19, 23c, 27, 29, 38  
         
M 7 Nov 8-11, 13, 14 Midterm #2    
W 9 Nov   GAP Project #2 Midterm #2 Take-Home Portion  
F 11 Nov 15 Simple Groups    
     
    
M 14 Nov 16 Group Actions Section 15 #2, 4, 6, 8, 10*, 12*, 16*, 19, 20, 26, 30, 33*, 40*, 41*
  
W 16 Nov 16 Group Actions cont'd  Quiz on Section 15 HW
  
F 18 Nov
Student Presentations  GAP Project #2 Write-up
 Group I: Section 15 #34, 35
Group II: Section 15 #36, 37
Group III: Section 15 #38
         
M 28 Nov 34 The Three Isomorphism Theorems    
W 30 Nov 36 Revisiting Lagrange and p-groups  Section 16 #2*, 4, 5, 6*, 8, 10*
  
F 2 Dec 36 The Normalizer of a Subgroup  Section 34 #4*,6*, 8*; Quiz on Section 16 HW
 
         
M 5 Dec 36 The Sylow Theorems  Quiz: State and Prove Sylow Theorem #1
  Section 34 #9
W 7 Dec 36 The Sylow Theorems cont'd  Quiz: State and Prove Sylow Theorem #2 and 3
  
F 9 Dec 37 Applying the Sylow Theorems  Section 36 #2*, 4*, 6*, 12*, 14*
  Section 37 #5, 6