Math 581 - Algebra 2
Winter 2006

Course Materials Assignments Exam/Paper 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: Tuesdays 1:30 - 3:00 pm 
Wednesday 10:00 - 11:30 am
Or by appointment

Lectures:  Mondays, Wednesdays, and Fridays, 1:30 pm - 2:18 pm (room CL 137).

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 required problems will be collected although not all will necessarily be graded.)  The first homework is due on Wednesday, January 11.  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%
Midterm: 20%
Paper:  20%
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).


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
(Read before class on)
Assignments
Jan. 4, 6
  • Permutations
  • Orbits
  • Stabilizers
  • Lagrange's Orbit-Stabilizer Theorem
pp 80-82 (Wed)
pp 83-85 (Fri)
Problem Set 1
(due 1/11)
Jan. 9, 11, 13
  • Cauchy's Counting Formula
  • Finite subgroups of SO(3)
  • Platonic Solids
pp 86-88 (Mon)
pp 89-91 (Wed)
pp 92-93 (Fri) 
Problem Set 2
(due 1/18)
Jan. 18, 20 No class on Monday
  • Finite subgroups of SO(3), cont'd
  • Division Algorithm
  • Euclidean Algorithm
  • Golden Ratio
pp 90-93 (Wed)
pp 102-107 (Fri)
 Problem Set 3
(due 1/27)
Jan. 23, 25, 27
  • Greatest Common Divisors
  • Euclid's Lemma
  • Fundamental Theorem of Arithmetic
  • Algorithms for polynomials
pp 107-109 (Mon)
pp 109-111 (Wed/Fri)
 Problem Set 4
(due 2/1)
Jan. 30, Feb. 1, 3
  • Polynomial Rings
  • Domains and Fields
In-class review (Wednesday)
Midterm Exam (Friday)
Midterm Information Sheet
(List of Proofs to Know is on Carmen)
 Review rings on page 66
pp 113-117 (Mon)
   Problem Set 5
(due 2/8)
Feb. 6, 8, 10
  • Algorithms for polynomials
  • Euclid's Lemma for polynomials
  • Unique factorization for polynomials
  • Fermat's Little Theorem
  • The Binomial Theorem
Paper Topic Due (no later than Friday)
(Submit your topic in the Dropbox of Carmen)
   pp 117-118 (Mon)
pp 118-119 (Wed)
pp 119-124 (Fri)
   Problem Set 6
(due 2/15) 
Feb. 13, 15, 17
  •  Modular Arithmetic
  • Euler's phi Function
  • Euler-Fermat Theorem
  • Euler's Theorem
  • o(g) divides |G|
  • The Group of Units U_n
pp 124-125 (Mon)
pp 125-127 (Wed)
pp 128-130 (Fri) 
Problem Set 7
(due 2/22)  
Feb. 20, 22, 24
  • The ring of integers modulo n
  • More polynomials
  • Cyclotomic polynomials
  • Generators of U_p
  • More with Euler's phi Function
Paper Due (Friday)
pp 128-129 (Mon)
pp 132-133 (Wed)
pp 133-134 (Fri) 
 Problem Set 8
(due 3/1) 
Feb. 27, March 1, 3
  • Another description of Z_n
  • Cosets and equivalence relations
  • Lagrange's Theorem
  • Cauchy's Theorem
  pp 129-130 (Mon)
pp 136-137 (Wed)
pp 138-141 (Fri)
Problem Set 9
(due 3/8)   
March 8, 10, 12 Finish Cauchy's Thoerem (Monday)
In-class problems (Wednesday)
Q&A style in-class review (Friday)
     
March 15 Final Exam (Monday)