Courses:
Math 8250 T Th 2:30-3:45pm
Lecture notes:
Lecture 1: Flatness and completion
;
Lecture 2: I-adic completion, Artin-Rees lemma
;
Lecture 3: Krull's Theorem
;
Lecture 4: Going-down theorem and normal rings
;
Lecture 5: Affine domains, valuation rings
;
Lecture 6: Characterization of normal rings, Dedekind rings
;
Lecture 7: Graded rings and modules, the Hilbert function
;
Lecture 8; The Hilbert polynomial, the Hilbert-Samuel function and polynomial
;
Math 8240 M W 2:00-3:15pm
Syllabus
Lecture notes:
Lecture 1: Polynomial rings, Grobner bases
;
Lecture 2: Noetherian and Artinian ring and modules
;
Lecture 3: Krull's Intersection Theorem
;
Lecture 4: Artinian rings
;
Lecture 5: Finite length modules
;
Lecture 6: Rings of fractions
;
Lecture 7: Modules of fractions
;
Lecture 8: Associated primes and the prime filtration
;
Lecture 9: Primary decomposition
;
Lecture 10: Affine algebraic geometry
;
Lecture 11: Affine algebraic geometry II
;
Lecture 12: Integral extensions
;
Lecture 13: Integral extensions, Noether normalization, Nullstellensatz
;
Math 7610 GOML only: Problem Solving Strategies
Past courses
Math 4442/6442 Modern Algebra II Tu Th 1-2:15pm
Syllabus
Math 4441/6441 Modern Algebra I MW 3-4:15pm
Syllabus
Math 7610 (GOML): Problem Solving Strategies.
Math 8220 Abstract Algebra I MW 1:30-2:45pm
Syllabus
Courses for Spring 2012:
Math 8221 Abstract Algebra II Tu Th 4-5:15pm
Syllabus
Courses for Fall 2012:
Math 4441/6441 Modern Algebra I MW 12-1:15pm
Syllabus
Math 8220 Abstract Algebra I MW 1:30-2:45pm
Syllabus
HON 1000 Tu 10:00-10:50am
Syllabus
Commutative Algebra Lectures
These lectures are based upon a two semester course at Georgia State University: Math 8240 (Spring 2010) and Math 8250 (Fall 2010). They represent a preliminary version of the notes. They will undergo revisions periodically.
Math 8240
Math 8250
Lecture 14
;
Lecture 15
(revised 10/11/2010);
Lecture 16
;
Lecture 17
;
Lecture 18
;
Lecture 19
;
Lecture 20
;
Lecture 21
;
Courses for Fall 2010:
Math 4444/6444 Polynomials 2:30-3:45pm
Syllabus
Lecture 1
;
Lecture 2
;
Lecture 3
;
Lecture 4
;
Lecture 5
;
Lecture 6
;
Lecture 7
;
Lecture 8
;
Lecture 9
;
Lecture 10
;
Lecture 11
;
Lecture 12
;
Homework 1
;
Solutions Homework 1
;
Homework 2
;
Solutions Homework 2
;
Homework 3
;
Solutions Homework 3
;
Homework 4
;
Solutions Homework 4
;
Homework 5
;
Solutions Homework 5
;
Homework 6
;
Solutions Homework 6
;
Courses for Summer 2010:
Math 4441/6441 Modern Algebra I M W F 12:00-1:50pm
Math 1101 Intro to math modeling 10-10:50am
Courses for Summer 2009:
Math 4441/6441 Modern Algebra I M W F 12:00-1:50pm
Courses for Spring 2009:
Math 8221 Abstract Algebra II Tu Th 4:00-5:15pm Syllabus
Math 8801 Research topics in algebra
Courses for Fall 2008:
Math 8220 Tu Th 4:00-5:15pm
Math 4441/6441-Modern Algebra I MW 12-1:15pm
Syllabus
Hon 1000 Freshman Honors Seminar Tu 11-11:50am
Syllabus
Algebra Qualifying Examination - GSU Ph. D program
List of topics
Topics
List of review problems
Problems
Recent exams
2009
;
2010
;
2011