Math 375 Section 1 - Calendar- Spring 2011

Last Updated: Sunday, June 26 2011 at 03:57 AM
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Numbers indicate sections from Contemporary Abstract Algebra- 7th Edition.
Numbers in parenthesis indicate sections from Contemporary Abstract Algebra- 6th Edition.

R is for the reading assignment
C is for exercises that are assigned and will be collected
G is for exercises that are to be done in your groups and will be collected
NC is for exercises that are assigned but will not be collected

Tuesday

Thursday
Jan. 25
Lecture #1:
Introduction to Algebraic Systems
Symmetries of the Square

Homework #1:
 R Chapter 0
 C Additional Problems:
Solutions Additional Problem Solutions:
 NC Chapter 0: 1,2
 		Jan. 27
Lecture #2:
Dihedral Group
Binary Operators

Homework #2:
 R Chapter 1
 C Chapter 1: 1,2,3,6,8,22(first row)
C Additional Problems:
 NC Chapter 1: 9,13,15,22(rest)
Feb. 1
Homework Due:
Last Week's Homework
Lecture #3:
Group Definition
Group Examples

Homework #3:
 R Chapter 2
 C Additional Problems:
 		Feb. 3
Lecture #4:
General Linear Groups
Properties of Groups
Four Element Groups
Z_n

Homework #4:
 R Chapter 3
 C Chapter 2: 4,14
C Additional Problems:
 NC Chapter 2: 1,3
Feb. 8
Homework Due:
Last Week's Homework
Lecture #5:
Associativity
U(n)

Homework #5:
 C Chapter 2: 11,12,15,18,22,35
(Hint for 11. Do 3 on extra problems for 2/10 first)
(Hint for 12. Do 2 on extra problems for 2/10 first)
 NC Chapter 2: 7,13,16,28
 		Feb. 10
Lecture #6:
U(n) examples
Subgroups

Homework #6:
 C Chapter 3: 1,4,6,18
C Additional Problems:
 NC Chapter 3: 2,3,5,9
Feb. 15
Homework Due:
Last Week's Homework
Lecture #7:
One and Two Step Subgroup Test
Cyclic Subgroups
Center and Centralizer

Homework #7:
 R Chapter 4
 G Chapter 3: 12(10),19(15),23(17),51(43),59ab(51ab)
G Additional Problems:
 NC Chapter 3: 27,28,53
 		Feb. 17
Quiz 1
Hint: It will contain at least one definition
 Lecture #8:
Examples of Cyclic Subgroups and Center
Finite Cyclic Groups

Homework #8:
 C Chapter 3: 57(49),46(38),48(40)
C Chapter 4: 1,2
C Additional Problems:
 NC Chapter 3: 31(25),38(30),39(31)
Feb. 22
Homework Due:
Last Week's Homework
Lecture #9:
Orders of Cyclic Subgroups

Homework #9:
 R Chapter 5
 G Chapter 4: 13,17,23,29
G Additional Problems:
 NC Chapter 4: 11,15,18,26,43,45
 		Feb. 24
Lecture #10:
Fundamental Theorem of Cyclic Groups
Permutations of a set

Homework #10:
 G Chapter 4: 12
G Chapter 5: 4,17
G Additional Problems:
March 1
Homework Due:
Last Week's Homework
Lecture #11:
The symmetric Group
Cyclic Notation
Questions for Midterm

Homework #11:
 C Additional Problems:
 		March 3
Exam 1
Homework #12:
 G Chapter 5: 1,2,3abd
G Additional Problems:
 NC Chapter 5: 3cef,5
March 8
Homework Due:
Last Week's Homework
Lecture #12:
Transpositions
Even and Odd Permutation
Alternating Groups

Homework #13:
 R Chapter 6
 G Chapter 5: 5,9,12,13,15,18
G Additional Problems:
 NC Chapter 5: 11,21,27,28
 		March 10
Lecture #13:
A_n
Symmetries of Tetrahedron

Homework #14:
 C Chapter 5: 20,23,30,43,44
C Additional Problems:
 NC Chapter 5: 24,25,38
March 15
Spring Break 		March 17
Spring Break
March 22
Homework Due:
Last Week's Homework
Lecture #14:
Isomorphisms
Cayley's Theorem

Homework #15:
 G Chap. 6:1,7,24(22),26(24)
G Additional Problems:
 NC Chap. 6: 3,4,5
 		March 24
Quiz 2 on Permutations
Lecture #15:
Properties of Isomorphisms
Automorphisms

Homework #16:
 R Chapter 7
 G Chapter 6: 3,20(18),21(19),22(20),25(23)
G Additional Problems:
 NC Chapter 6: 27(25),32(30),38(36)
March 29
Homework Due:
Last Week's Homework
Lecture #16:
Inner Automorphisms
Cosets of a subgroup

Homework #17:
 G Chapter 7: 1,4,5,7
G Additional Problems:
 NC Chapter 7: 2,3,6
 		March 31
Lecture #17:
Cayley's Theorem
Fermat's Little Theorem
External Direct Product

Homework #18:
 R Chapter 8
 G Chapter 7: 13,15,16,23(21),26(24),28(26)
G Chapter 8: 1
 NC Chapter 7: 8,9,12
April 5
Homework Due:
Last Week's Homework
Lecture #18:
Direct Product of Groups
Vernam

Homework #19:
 R Chapter 9
 G Chapter 8:4,6,8,9,13,14,45(41)
G Additional Problems:
 NC Chapter 8:2,14,26(22),27(23),28(24),46(43)
 		April 7
Quiz 3
Lecture #19:
Factor Groups

Homework #20:
 G Chapter 8: 25(21)
G Chapter 9: 2,4,6,10
G Additional Problems:
 NC Chapter 8: 29(25),53(49)
April 12
Homework Due:
Last Week's Homework
Lecture #20:
More Factor Groups
Exam Review

Homework #21:
 C Study for Exam
 NC Additional Problems:
 		April 14
Exam 2
 Homework #22:
 R Chapter 10
 G Chapter 9: 14,19,48(44)
G Additional Problems:
 NC Chapter 9: 18,22,23
April 19
Homework Due:
Last Week's Homework
Lecture #21:
Applications of Factor Groups
Group Homomorphisms

Homework #23:
 Due April 28
G Chapter 9: 21,24
G Chapter 10: 2,4,6,8
G Additional Problems:
 NC Chapter 9: 39
NC Chapter 10: 1,3,5,7 		April 21
Easter Break
April 26
Lecture #22:
Properties of Homorphisms
First Isomorphism Theorem

Homework #24:
 R Chapter 12
 G Chapter 10: 12,16,19,24,26,33,35
 NC Chapter 10: 18,21,32,36
 		April 28
Homework Due:
Last Week's Homework
Lecture #23:
Rings

Homework #25:
 R Chapter 13
 G Chapter 12: 5,6,11
G Additional Problems:
 NC Chapter 12: 7,8,9
May 3
Homework Due:
Last Week's Homework
Lecture #24:
Integral Domains
Ideals and Factor Rings

Homework #26:
 R Chapters 14,15
 G Chapter 12: 15,46,47
G Chapter 13: 4,5,6,16,20(18)
 NC Chapter 13: 1,2,15,21(19),27(25)
 		May 5
Lecture #25:
Ring Homomorphisms
Polynomial Rings

Homework #27:
 R Chapter 15,16
 G Chapter 14: 5,10
G Chapter 15: 6
G Chapter 16: 2,6,12,13
NC Chapter 16: 1,3,8,11
May 10
Homework Due:
Last Week's Homework
Lecture #26:
Division Algorthms for Polynomials

Homework #28:
 I Additional Problems:
Final Exam
 Thursday, May 19 at 8 AM

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