Math 582 - Abstract Algebra III
Spring 2006
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Course Materials Assignments Exam Dates and Materials Carmen
Course Information (call number 12822-9)
Instructor: 
Office: 
Phone: 
Email:  		 Angela Barnhill
MW 536
292-5251
abarnhill@math.ohio-state.edu
Office Hours: Mondays 2:30 - 4:00 pm
Tuesdays 11:30 am - 1:00 pm 
Or by appointment
Lectures:  Mondays, Wednesdays, and Fridays, 1:30 pm - 2:18 pm (room UH 151).
Text:   Abstract Algebra by Ronald Solomon, Brooks/Cole, 2003, ISBN 0-534-39996-7. 
Homework: Weekly problem sets will generally be due at the beginning of class on Wednesdays.  (All required problems will be collected although not all will necessarily be graded.)  The first problem set is due on Wednesday, April 5.  Late homework will not be accepted.

Important Dates: 

Make-up exams will only be given in the case of documented extraordinary circumstances.
Examinations will not be rescheduled because of travel arrangements -- it is your responsibility to schedule travel appropriately.

Grading:

Homework: 20%
Midterms: 20% each
Final exam: 40%

Remarks on written work: You are encouraged to discuss the course material with other students.  However, anything that you turn in must be your own work.  Work must be neat and legible in order to be graded. Also, remember that when you are writing up your solutions, your goal is not only to convey that you know how to solve a problem but also to communicate your solution effectively.  Could your solution be understood by a mathematician who has never before solved the problem?  If not, then it is not a complete solution.  Keep this in mind!

Course Materials

Note:   Some course materials will be posted in PDF format.  If you do not already have the capability to view such documents, then in order to open these files, you will need to install Adobe Acrobat Reader (a free program).

Syllabus

Carmen   (Check your grades, view course announcements, see solutions to past assignments, etc.)

 Class Schedule and Homework Assignments
 (This schedule is tentative and subject to change.   Please check back regularly for current lecture and homework information.)
Class Dates
 Major Topics
 Reading Assignment
(Discussed in class on)
 Assignment
Due Date
March 27, 29, 31
  • Constructions
  • Constructibility of numbers
  • Constructibility of polygons
  • Constructing the pentagon
  • pages 170-172 
Problem Set 1
Due Wed. 4/5
April 3, 5, 7
  • Gauss' Approach
  • Constructibility of the heptagon?
  • Constructing the mn-gon
  • The 17-gon
  • Gauss maps
  • Vector spaces
  • pages 172-173 (Mon)
  • pages 174-175 (Wed)
  • pages 177-178 (Fri)
 Problem Set 2
Due Wed. 4/12
April 10, 12, 14
  • The 17-gon and Gauss maps
  • Back to vector spaces
  • Extension fields
  • Basis
  • Linear independence
  • Vector space isomorphisms
  • Dimension
  • Splitting Fields
  • pages 178-181 (Wed)
  • pages 182-183 (Fri) 
 Problem Set 3
Due Wed. 4/19
April 17, 19, 21 Q&A in class (Wednesday)
Midterm 1 (Friday)		   Problem Set 4
Due Wed. 4/26
April 24, 26, 28
  • Minimum polynomials
  • Content
  • Gauss' Lemma
  • Irreducibility of  cyclotomic polynomials
  • Eisenstein's Criterion
  • pages 182-185 (Wed)
  • pages 186-188 (Fri)
 MT 1 Extra Credit
Due Mon. 5/1

Problem Set 5
Due Wed. 5/3
May 1, 3, 5
  •  The Tower Law
  • Constructible numbers
  • Non-constructible polygons
  • Quotient Rings
  • pages 191-194 (Mon)
  • pages 194-195, 184, 187 (Wed)
  • pages 198-199 (Fri)
 Optional Group Project
Due Wed. 5/31

Problem Set 6
Due Thurs. 5/11
May 8, 10, 12
  • More with quotient rings
  • Galois groups
MT2 Information Sheet
MT2 Practice Problems
Q&A in class (Friday)
  • pages 199-200 (Mon)
  • page 208 (Wed)
 Study for Midterm 2
May 15, 17, 19 Midterm 2 (Monday)
  • Galois groups
  • Galois automorphisms
  • page 208 (Wed)
  • pages 209-210 (Fri)
MT 2 Extra Credit
Due Mon. 5/22

Problem Set 7
Due Fri. 5/26
May 22, 24, 26
  • Examples of Galois groups
  • Main Theorem on Galois Automorphisms
  • Galois Correspondence
  • pages 209-210 (Mon)
  • page 213 (Wed)
  • page 216 (Fri)
 Study for Final
May 31, June 2 Memorial Day (Monday)  
  • Constructibility of p-gons
Final Exam Information Sheet
Q&A in class (Friday)		   Study for Final 
June 7 Final Exam (Wednesday)