Michael Monagan, Simon Fraser University (4 lectures, 8 hours)
Lecture 1 : Varieties and ideals in polynomial rings. Video
Lecture 2A : Monomial orderings, lexicographical order, graded lexicographical order. Video
Lecture 2B : The division algorithm. Ideal membership. VideoLecture 3A : Monomial ideals and Dixon's lemma. Video
Lecture 3B : The Hilbert basis theorem and Groebner bases. VideoLecture 4A : Buchberger's algorithm. Minimal and reduced Groebner bases. Video
Lecture 4B : Applications of Groebner bases.
Testing if a polynomial system is consistent and Hilbert's Nullstellensatz.
Solving polynomial systems. The elimination theorem.
Groebner bases in Maple. Video
Reference: Ideals, Varieties and Algorithms by Cox, Little, and O'Shea.