Professor of Mathematics
Department of Mathematics
Northern
Highland Heights
859-572-6672
FAX: 859-572-6097
E-mail christensen@nku.edu
Here is a copy of the syllabus for MAT 415 – 001.
Here is a copy of the Departmental syllabus that applies to all MAT and STA courses.
Monday, January 12
Section 7.1 Introduction to rings and field.
Wednesday, January 14
Units and zero divisors.
Friday, January 16
Quadratic integer rings – especially the Gaussian integers.
Monday, January 19
Holiday
Wednesday, January 21
Polynomial rings and matrix rings.
Friday, January 23
Ring homorphisms and (two-sided) ideals
Monday, January 26
Ideals and quotient rings
Wednesday, January 28
Classes cancelled because of weather.
Friday, January 30
Ideal properties
Monday, February 2
Maximal ideals
Wednesday, February 4
Friday, February 6
Ideal M is maximal if and only if R/M is a field.
Monday, February 9
Ideal P is prime if and only if R/P is an integral domain.
Wednesday, February 11
Construction of a quotient field
Friday, February 13
Euclidean domains and principal ideal domains
Monday, February 16
Prime ideals are maximal ideals in a PID
Wednesday, February 18
Primes and irreducible
Friday, February 20
UFDs
Monday, February 23
Gauss’ lemma
Wednesday, February 25
Irreducibility tests
Friday, February 27
Mod p test
Monday, March 2
Eisenstein’s criterion
Wednesday, March 4 and Friday, March 6
Spring break
Monday, March 16
Introduction to fields: characteristic and extension
Wednesday, March 18
Kronecker construction
Friday, March 20
Finite fields
Monday, March 23
Kronecker construction
Wednesday, March 25
Simple extension
Friday, March 27
No Class
Monday, March 30
Simple algebraic extension
Wednesday, April 1
Simple plus finite is algebraic. Finite implies algebraic.
Friday, April 3
[L:k] = [L:K][K:k]
Monday, April 6
Finitely generated by algebraic elements implies finite.
Wednesday, April 8
The rational numbers … and more are constructible.
Friday, April 10
The Greek construction problems are impossible
Monday, April 13
Splitting field
Wednesday, April 15
Hints for test three
Algebraic closure
Friday, April 17
Separable polynomial
Monday, April 20
Roots of unity
Wednesday, April 22
Primitive nth roots of unity and cyclotomic polynomials
Friday, April 24
Cyclotomic polynomials
Exam Do 7 problems. Due no later than noon on Friday, May 8.
Monday, April 27
Cyclotomic polynomials are irreducible
Wednesday, April 29
Introduction to Galois theory
Friday, May 1
Construction of regular n-gons