Math 5332 – Abstract Algebra II – Schedule/Homework – Fall 2009

DateSection/TopicHomework
8/24/09Algebraic Foundations–GroupsHw # 1
8/26/09Algebraic Foundations–Group homomorphisms and ringsHW # 2
8/31/09Algebraic Foundations-Quotient ringsHW # 3
9/2/09Algebraic Foundations–PolynomialsHW # 4
9/7/09Algebraic Foundations–Field extensionsHW#5 Review vector spaces
9/14/09Algebraic Foundations-Simple ExtensionsHW # 6
9/16/09Algebraic Foundations-Splitting fields
Classwork		HW # 7
9/21/09Structure of finite fieldsHW # 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
9/30/09Class presentations-Sections 1-7 
10/5/09Structure of finite fieldsHW # 10
10/7/09Roots of irreducible polynomialsHW # 11
10/12/09TraceHW # 12
10/14/09Norm
Click here for the link to the page mentioned in class.		HW # 13
10/19/09Basis of field extensions-IHW # 14
10/21/09Basis of field extensions-II
First project Report Due		HW # 15
10/26/09Cyclotomic extensionsHW # 16
10/28/09Class presentations-Sections 10-11HW # 17
11/02/09Class presentations-Sections 12-15
Dual basis computation		HW # 18
11/04/09Roots of unity in finite fieldsHW # 19
11/09/09Primitive roots of unity;
Representation of elements of finite fields, I
Second project Report Due		HW # 20
11/11/09Representation of elements of finite fields, II
Cyclotomic polynomials and Wedderburn’s Theorem		HW # 21
11/16/09Order of polynomials and Primitive polynomialsHW # 22
11/18/09Irreducible polynomials
Third project Report Due		HW # 23
11/23/09Class presentations-Theoretical applications of Finite Fields
     Angie Brown–Finite Geometries
     Stephanie Lane–Combinatorics		 
11/25/09Class presentations/discussion 
11/30/09Class presentations
     Linlin Chen–Linear Modular Systems
     David Carreno–Linear Codes		 
12/02/09Class presentations
     Scott Lacy–Cyclic Codes
     Kelly Aman–Goppa Codes		 
12/07/09Final Exam–Class presentations
     Justin Sanches–Cryptology
     Daniel Dawson–Stream Cyphers
     Justin Ahrens– Further Cryptosystems