Mathematics 5332  Abstract Algebra II Schedule/Homework

Fall 2009

 

Date

Section/Topic

Homework

8/24/09 Algebraic Foundations--Groups Hw # 1
8/26/09 Algebraic Foundations--Group homomorphisms and rings HW # 2
8/31/09 Algebraic Foundations-Quotient rings HW # 3
9/2/09 Algebraic Foundations--Polynomials HW # 4
9/7/09 Algebraic Foundations--Field extensions HW#5 Review vector spaces
9/14/09 Algebraic Foundations-Simple Extensions HW # 6
9/16/09 Algebraic Foundations-Splitting fields
Classwork
HW # 7
9/21/09 Structure of finite fields HW # 8

HW # 9 Due On 9/30
2.3, 3.1 (ii), 3.2 (ii), 4.1, 6.3, 7.1,7.2, 7.3, 7.4
9/30/09 Class presentations-Sections 1-7  
10/5/09 Structure of finite fields HW # 10
10/7/09 Roots of irreducible polynomials HW # 11
10/12/09 Trace HW # 12
10/14/09 Norm
Click here for the link to the page mentioned in class.
HW # 13
10/19/09 Basis of field extensions-I HW # 14
10/21/09 Basis of field extensions-II
First project Report Due
HW # 15
10/26/09 Cyclotomic extensions HW # 16
10/28/09 Class presentations-Sections 10-11 HW # 17
11/02/09 Class presentations-Sections 12-15
Dual basis computation
HW # 18
11/04/09 Roots of unity in finite fields HW # 19
11/09/09 Primitive roots of unity;
Representation of elements of finite fields, I
Second project Report Due
HW # 20
11/11/09 Representation of elements of finite fields, II
Cyclotomic polynomials and Wedderburn's Theorem
HW # 21
11/16/09 Order of polynomials and Primitive polynomials HW # 22
11/18/09 Irreducible polynomials
Third project Report Due
HW # 23
11/23/09 Class presentations-Theoretical applications of Finite Fields
     Angie Brown--Finite Geometries
     Stephanie Lane--Combinatorics
 
11/25/09 Class presentations/discussion  
11/30/09 Class presentations
     Linlin Chen--Linear Modular Systems
     David Carreno--Linear Codes
 
12/02/09 Class presentations
     Scott Lacy--Cyclic Codes
     Kelly Aman--Goppa Codes
 
12/07/09 Final Exam--Class presentations
     Justin Sanches--Cryptology
     Daniel Dawson--Stream Cyphers
     Justin Ahrens-- Further Cryptosystems