Math 580 - Algebra 1
Fall 2005
Course Materials Assignments Exam Dates and Materials WebCT
Course Information (call number 12822-9)
Instructor: 
Office: 
Phone: 
Email:  		 Angela Barnhill
MW 536
292-5251
abarnhill@math.ohio-state.edu
Office Hours: Monday 2:30 pm - 4:00 pm
Tuesday 11 am - noon
Wednesday 10:30 am  - 11:30 am
Or by appointment
Lectures:  Mondays, Wednesdays, and Fridays, 1:30 pm - 2:18 pm (room CL 109).
Prerequisites:  Math 568 (may be taken concurrently) and Math 345.  Not open to students with credit for Math H590.

Course description: The algebra sequence 580-581-582 includes elementary number theory, group theory, vector spaces, linear transformations, and field theory.  It gives a historical introduction to many of the major ideas in modern algebra.  This quarter, we will cover Chapters 0--7 of the text.  We will start with a study of congruence and symmetry that will introduce the concept of a group.  Then, we will move on to solving polynomial equations, a topic that will lead us to rings and fields.

Text:   Abstract Algebra by Ronald Solomon, Brooks/Cole, 2003, ISBN 0-534-39996-7. 
Homework: Weekly homework assignments will generally be due at the beginning of class on Wednesdays.  (All problems will be collected although not all will necessarily be graded.)  The first homework is due on Wednesday, September 28.  Late homework will not be accepted.

Exams: There will be two midterms and a cumulative final.

There will be no make-up exams. Examinations will not be rescheduled because of travel arrangements -- it is your responsibility to schedule travel appropriately.

Grading:

Homework: 100 points
First and second exams: 200 points (100 points each)
Final exam: 200 points
Total Possible:  500 points

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).
Midterm 1 Review Sheet          Review Sheet Solutions         Extra Credit  for Midterm 1 (due 11/2)

Midterm 2 Review Sheet      Review Sheet Solutions          Extra Credit  for Midterm 2 (due 11/28)

Final Exam Information Sheet   Practice Problems
Syllabus (as handed out on the first day of class, except that the Midterm 2 date has been changed as announced in class)

Supplementary Material for the text (as handed out on the first day of class)

Check your grades on WebCT.

 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
 Homework
 Solutions
 (WebCT)
September 21, 23
  • Functions
  • Isometries
pages 1-17
 HW 1
(due 9/28)
  Set 1
September 26, 28, 30
  • Isometries of the real line
  • Equivalence Relations
  • Groups
 pages 18-21
 HW 2
(due 10/5)
  Set 2
October  3, 5, 7
  • Groups
  • Matrices and linear transformations
  • Isometries of the real plane
 (Review matrices and
linear transformations)
pages 22-27
 HW 3
(due 10/12)
  Set 3
October 10, 12, 14
  • O(2)
  • Eigenvalues
  • Symmetry groups
 (Review eigenvalues)
pages 28-31
 HW 4
optional
(due 10/19)
  Set 4
October 17, 19, 21
  • Permutations
  • The symmetric group
 pages 31-32
pages 78-81


 HW 5
(due 10/26)
 Set 5
October 24, 26, 28
  • Dihedral groups
  • Isomorphisms
  • SO(2)
  • Cyclic groups
  • Finite subgroups of O(2)
 pages 33-41
 HW 6
(due 11/2)

Extra Credit  for Midterm 1
(due 11/4) 		Set 6
October 31
November 2, 4
  • Cubic equations
  • Cardano's Formula
  • Introduction to rings and fields
 pages 46 - 52
 HW 7
(due 11/10) 		Set 7
November 7, 9
  • Factor Theorem
  • Viete's method
  • Ferrari's method
No class on Veteran's Day (Friday)
 pages 53 - 58
 Review for Midterm
November 14, 16, 18
 Q&A in class (Monday)
Midterm 2 (Wednesday)
Midterm 2 Review Sheet
Review Sheet Solutions
  • Complex numbers
  • DeMoivre's formula
 pages 59-63
 HW 8
(due 11/23) 		Set 8
November 21, 23
  • More on Homomorphisms
  • Roots of Unity
  • Gaussian integers
Thanksgiving (No class  on Friday)
 pages 63-67
 Extra Credit  for Midterm 2 (due 11/28)

HW 9
(due 11/30) 		Set 9
November 28, 30, December 2
  • Fundamental Theorem of Algebra
  • Irreducible polynomials
Q&A in class (Friday)
 pages 68-73
 Final Extra Credit
(due 12/02)
December 7
 Final Exam
Final Exam Information Sheet
Practice Problems

Solutions to final review and practice problems