Math 546/701I: Algebraic Structures I.

Section 001

Fall 2009

University of South Carolina

      Instructor  
      Matthew Boylan  
  Office     LeConte 400G  
  Phone     777-8874  
  E-mail     boylan@math.sc.edu  
  Office hours     Mon. 2:30 - 3:30  
  Tues. 1 - 2  
  Thurs. 10 - 11  
  And by appointment  

  • University of South Carolina Mathematics Department .

    • Course information :

  • Prerequisite : Math 241.

  • Text : Abstract Algebra, by Beachy and Blair, 3rd ed., Waveland Press (2006).

  • Course objectives : Students will master concepts and solve problems on permutation and abstract groups, subgroups, quotient groups, homomorphisms, isomorphisms, direct products, and rings. This course is the first of a two-semester sequence.

  • Class schedule :

          Section 001  
      Lecture     MWF     10:10 - 11:00     LeConte 303B  

  • Homework : Problem sets will be assigned each week and will be due the following Monday. They may be turned in during class on Mondays or to my mailbox any time before 3 pm on the due date. Some of the assigned problems will be graded. You will be graded on both the correctness of your solutions and on the quality of your exposition (i.e., how well you write the solution). You are encouraged to discuss problems with other students in the class. However, you must write solutions to the problems yourself (in your own words).

  • Exam schedule : (3 one-hour exams and a cumulative final exam)

      Exam 1:     Friday     September 18     10:10 - 11:00     LeConte 303B  
      Exam 2:     Wednesday     October 21     10:10 - 11:00     LeConte 303B  
      Exam 3:     Friday     November 20     10:10 - 11:00     LeConte 303B  
      Final Exam:     Tuesday     December 8     9:00 - 12:00     LeConte 303B  

    Missed exams will not be made up. Exceptions may be made for documented illness/family emergency.

  • Calculators (and computer software such as Maple) may be used on homework unless otherwise noted. They may not be used on exams.

  • Grading :

          Points/650     % of grade  
      Three hour exams:     100 pts. x 3     15% x 3  
      Final exam:     200 pts.     30%  
      Homework:     150 pts.     25%  
      Total:     650 pts.     100%  

    Graduate credit: Students enrolled in 701I are expected to do a term project, due at the end of the semester.

    Extra credit will not be offered.

    Letter grades will be assigned according to the following approximate scale unless otherwise noted:

      A     B     C     D     F  
      90 - 100     80 - 90     70 - 80     60 - 70     0 - 60  

    Note: The deadline to drop without a WF is Thursday, October 1.

  • Other policies : Cell phones and other electronic devices are to be turned off or put on silent or vibrate mode during class meetings. Homework and exam grades may be discussed only up to 7 days after being returned.

  • Other help resources : Math Lab (free drop-in tutoring at various locations on campus, including LeConte 105), Private tutors , On-line materials for courses   (546 websites from past semesters), Math library .

  • Syllabus (which contains all of the above information): (pdf)

    • Lectures and Homework :

    Lectures Homework
      Dates     Sections     Topics     Problems     HW due date  
      August  
      Week 1     21     F         Introduction to basic structures.          
      Week 2     24     M     2.1     Functions.     2, 7, 8 b, d, f, 15; Homework 1; Solutions.     9/2.  
      26     W     2.2     Equivalence relations.     3, 5, 8, 10.     9/2.  
      28     F     2.3     Permutations.     1, 2, 5, 9, 10, 11, 13, 15; 16 is a challenge problem. Homework 2; Solutions.     9/9.  
      Week 3     31     M                  
      September  
      2     W     3.1     Definition of a group.     1, 2 b, c, d, 3, 6, 7, 9, 10, 11, 13; Do one of 23, 24; for a challenge problem, do both; Homework 3; Solutions.     9/16.  
      4     F                  
      Week 4     7     M         No class.     Labor Day.      
      9     W                  
      11     F     3.2     Subgroups.     1 b, d, 4, 5 b, c, 6, 8, 11, 13, 14, 15, 17, 24 a; 5 d, 24 b, c, and 26 are challenge problems. Homework 4. Solutions.     9/28.  
      Week 5     14     M                  
      16     W                  
      18     F     Exam 1 guide.     Exam 1.     Covers: Information and homework from Sections 2.1, 2.2, 2.3, 3.1; Class notes: 8/21 - 9/11; Homework: 1 - 3. Solutions.      
      Week 6     21     M                  
      23     W                  
      25     F     3.3     Constructing examples.     1, 3 - 8, 11, 14. Homework 5; Solutions.    10/7.  
      Week 7     28     M                  
      30     W                  
      October  
      2     F     3.4     Isomorphisms.     Homework 6; Solutions.    10/14.  
      Week 8     5     M                  
      7     W                  
      9     F         No class.     Fall Break: 10/8 - 10/11.      
      Week 9     12     M     3.5     Cyclic groups.     1, 2, 3, 5, 7, 10, 11, 16; extra problems: 13, 14, 15, 18, 20. Homework 7; Solutions.     
      14     W                  
      16     F                  
      Week 10     19     M     3.6     Permutation groups.     1, 4, 6, 7, 8, 10, 12, 13, 14; extra problems: 19, 21, 25, 26. Homework 8; Solutions.     10/30.  
      21     W     Exam 2 guide.    Exam 2.     Covers: Information and homework from Sections 3.2, 3.3, 3.4, 3.5; Class notes: 9/14 - 10/16; Homework: 4 - 7. Solutions.      
      23     F                  
      Week 11     26     M                  
      28     W     3.7     Homomorphisms.     1 b, 2, 8, 12, 15; extra problem: 18; Solutions.     11/9.  
      30     F     3.8     Cosets, normal subgroups, and factor groups.     1 b, 4, 5, 6, 7; extra problems: 2, 9, 12; Homework 9; Solutions.     11/9.  
      November  
      Week 12     2     M                  
      4     W                  
      6     F     3.8         3.8 11, 13, 14, 16, 18, 20, 22, 25; extra problems: 19, 21, 23, 28. Homework 10; Solutions.     11/16.  
      Week 13     9     M                  
      11     W     7.2.     Conjugacy.     6, 8, 9, 12 b, 15; extra problems 10, 12 a, 17; Homework 11. Solutions.     
      13     F                  
      Week 14     16     M                  
      18     W                  
      20     F     Exam 3 guide.     Exam 3.     Covers: Information and homework from Sections 3.6, 3.7, 3.8; Class notes: 10/19 - 11/13; Homework: 8 - 10. Solutions.      
      Week 15     23     M     7.4     The Sylow Theorems.          
                  No class.     Thanksgiving holiday: 11/25 - 11/29.      
      Week 16     30     M                  
      December  
      2     W                  
      4     F                  
      Finals week     8     Tues     Final guide. Review: LC303B, Mon., Dec. 7, 7:00 pm.     Final Exam, 9 - 12. Solutions.     Cumulative.