The book is a keeper.  Some changes for next time: go slightly faster
in the beginning, cover Euler's function and include RSA handout when
one covers Fermat's little theorem, in the beginning of Chapter 6 add
something about rings, and go slower with the group theory.  The
students would like more examples; be sure to give lots of examples in
class.  End with a blurb about Galios groups and solvable by
radicals. Keep things concrete.


WEEK 1 - January 13 - 15

Wed. - 1.1: Introduction
       Start Appendix F: Mathematical Induction
       HW Due Monday, January 18 - 1.1: 4-7, 14-17

Fri. - Appendix F: Mathematical Induction
       HW Due Wednesday, January 20 - Appendix F: 2,4,6,7,9,11,12,14


WEEK 2 - January 18 - 22

Mon. - 2.1: Complex Numbers
       HW Due Friday, January 22 - 2.1: 1-25 odd, 26-31, 36  
            delayed to Monday

Wed. - 2.2: Complex Roots
       HW Due Monday, January 25 - 2.2: 1, 13, 19, 21, 23, 27, 28
       NOTE: In #'s 19 and 21, it should be assumed that ``w'' is a cube
             root of unity.
       Take-home Quiz 1 Given Out - Due on Friday

Fri. - 2.2: Finish Complex Roots
       HW Due Wednesday, January 27 - 2.2: 5, 8, 15
       Read Section 2.3 for Monday


WEEK 3 - January 25 - 29

Mon. - 2.3: Solvability by Radicals and Algebraic Expressions
       HW Due Friday, January 29 - NONE

Wed. - 2.3:  Ruler and Compass Constructions
       HW Due Monday, February 1 - 2.3: 1-13, 15,18
       Take-home Quiz 2 Given Out - Due on Friday

Fri. - 2.4: Ruler and Compass Constructions
       HW Due Wednesday, February 3 - 2.4: 9, 11, 12, 13, 16, 19


WEEK 4 - February 1 - 5

Mon. - 2.4: Ruler and Compass Constructibility 
       Start reading Chapter 3
       HW Due Friday, February - 2.4: 3,6,21,23

Wed. - 2.5:  Orders of root of Unity
       HW Due Monday, February 1 - 2.5: 3,5,9,11,13,15,18
       Take-home Quiz 3 Given Out - Due on Friday

Fri. - 3.1: The cubic Formula
       In class presentations
       HW Due Wednesday, February 8 - 3.1: 1,5,10,11.
       (Section 2 skipped this Section).

WEEK 5 - February 8 - 12

Mon. - 4.1: Modular Arithmetic
       HW Due Friday, February 12 - 4.1: 3, 6 and 7 (only with respect
to #3), 9, 11, 15.

Wed. - 4.2: The Euclidean Algorithm
       HW Due Monday, February 15 - 4.2: 1, 2, 3, 5, 21, 22, 23, 25. 
       Take-home Quiz 4 Given Out - Due on Friday

Fri. - 4.2: Modular Inverses (and 4.3: Modular roots?)
       HW Due Wednesday, February 16 - 4.2: 11, 13, 17, 7, 15 (try in
          the above order)
       Group Presentations - 3.1: 15
        Next Group Projects 3.2: 24 and 26, 30.

WEEK 6 - February 15 - 19

Mon. - 5.1: The Binomial Theorem
       HW Due Friday, February 19 - 5.1: 1,5,7,15,23.

Wed. - 5.2: Fermat's Theorem 
       HW Due Wednesday, February 24 - 5.2: 1,3,7,9,12.
       Take-home Quiz 5 Given Out - Due on Friday

Fri. - 5.2: Fermat's Theorem -- orders of roots
       HW Due Wednesday, February 24 - 5.2: 17, 22, 25, 27. 
       Group Presentations - 3.2: 24 and 26, 30.
       No new group projects.

WEEK 7 - February 22 - 26

Mon. - Quick Review and Question and Answer session. 

Wed. - In-class exam.

Fri. - 6.1: Fields and Polynomials: 6.1
       HW Due Wednesday March 3  - 6.1: 1,3,4,5,7,11,18,21,22.

WEEK 8 - March 1 - 5

Mon. - 6.2:  Factorization of Polynomials
          HW Due Friday, March 5 - 6.2:  3,5,6,10,12 (Hint: see #10), 13

Wed. - 6.3:  The Euclidean Algorithm (again)
          HW Due Wednesday, March 17 - 6.3:  1, 3, 7, 8, 9, 21 
          Take-home quiz (due Friday)

Fri. -  6.4:  Elementary Symmetric Polynomials of degree 3  
         No HW  Due; Try  6.4: 3,5 9,11

WEEK 9 - March 15 -- 19 

Mon. - 7.1: Galois Fields:
       HW due Friday March 19 -- 7.1: 11,12,18-21,25.
       Group Projects for Friday March 26 7.1: 26,29.

Wed. - 7.1 and 7.2: Orders in Galois Fields: 
       HW due Monday March 22 -- 7.1: 1,2,5  
        and 7.2: 4 (hint look at problem 7.1.5).

Fri. - 7.2 and 7.3: More on orders: 
       HW Due Wednesday March 24  - 7.2: 1,3,10,11 and
        7.3: 2,3,5 (hint see problem 7.1.2), 7 (hint look 
         at problem 7.1.5), 13.  


WEEK 10 - March 22 -- 26 

Mon. - 7.4: Solutions of P(x) in GF(p,P(x))
            RSA scheme (applied example)
       HW due Friday March 26 -- 7.4: 5 and problem on RSA handout

Wed. - 8.2:  Permutations
       HW due Monday, March 29 -- Handout of problems for 8.2

Fri. - 8.2:  Group Projects and Permutations II
       HW due Wednesday, March 31 -- 8.2: 1, 3, 6, 8, 9, 11, 13, 22, 30, 31


WEEK 11 - March 29 -- 31 

Mon. - 8.4: Transposition and parity
        HW due Wednesday, April 7 -- 8.4:1,3,7,9,11,12,13. 

Wed. - 9.1 and 9.2:  Definition of a group, subgroup, order and examples.
        HW du Friday, April 9 -- 9.1: 1-6, 35 and 9.2:1-4.  
        Take-home Quiz due Wednesday after break.

Fri - NO CLASS - EASTER BREAK

WEEK 12 - April 7--9

Mon. - NO CLASS - EASTER BREAK!!

Wed. - 9.1 and 9.2: More examples of groups
         HW due Wednesday, April 14 -- 9.2: 28, 37 and 9.3: 17, 19, 22

Fri. - 9.3: Isomorphisms of groups
          HW due Wednesday, April 14 -- 9.3: 2, 3
          Practice Exam for Exam 2 given out

WEEK 13 - April 12-16

Mon. - Review for exam.

Wed. - In-class exam.

Fri. - 9.3: Isomorphisms and 9.4: Subgroups
       Homework Due Wednesday, April 21 - 9.3: 9-16 and 9.4: 1, 2, 6
WEEK 14 - April 19 - 23

Mon. - 9.4: Subgroups and cosets
       Homework Due Friday, April 23 - 9.4: 11, 13, 15, 28, 31, 32,
       33, 36, 61
       Quiz 11 Given Out.

Wed. - 9.5: Cyclic groups and 9.6: Cayley's Theorem:
       Homework Due Monday, April 26 - 9.4: 41, 56 and 9.5: 2, 3, 4,
        10, 13, 15, 16, 17.

Fri. - Catch-up on chapter 9.
       Homework Due Wednesday, April 28 - 9.5: 26 and 9.6: 1-4 (last
       homework assignment)
       Quiz 12 Given Out