Math 765 - Computational Commutative Algebra

January 9 - Monomial Orders and Multivariate Polynomial Division
	Getting Started
	Multivariate Polynomial Division
January 11 – Groebner Bases and Buchberger\'s Algorithm
	Groebner Bases
	Buchberger\'s Algorithm
January 14 – An Introduction to Macaulay2
	Sample Macaulay2 Session
January 16 – Introduction to Affine Algebraic Geometry
	Affine Varieties
	Groebner Bases and Elimination Ideals
January 18 – First Macaulay2 Hands-On Session
	Problem 1
	Problem 2
	Problem 3
January 23 - R-modules
January 25 - More on Graded Modules, Minimal Free Resolutions, Betti Numbers
January 28 - Betti Diagrams, The Koszul Complex for R/m, Proof of Hilbert Syzygy Theorem
January 30 - Projective Geometry, Hilbert Functions
February 1 - Worksheet 2
February 4
	The Hilbert Function, Series, and Polynomial
February 6 - Algorithms for minimal free resolutions
	More general terms orders:
February 8
	Schreyer Resolutions and Schreyer Frames
February 11 - Example of Computing a Schreyer Frame
February 13 - Example of Computing a Schreyer Resolution
February 15 - An Algorithm for Computing a Schreyer Resolution
February 18
February 20 - Worksheet Day
February 22 - More on Hilbert Functions, Points in Projective Space
	Geometric Information from the Hilbert Function
February 25 - Points in Projective Space, Regularity, Resolutions, Examples
	Imposed Conditions
February 27 - Some background towards (stating and) proving the theorem
March 1 - Worksheet Day - Writing your own Macaulay2 functions.
March 4 - Regularity, Depth, and Local Cohomology
	Local Cohomology
March 6
March 8
March 18
	Completing the Proof from Last Time:
	Applications of the theorem:
March 20
March 22: Loading Packages, Depth in Macaulay2
	Problem 1
	Problem 2
Week of March 25 - 29: Simplicial Complexes Worksheet
	Problem 1
	Problem 2
	Problem 3
	Problem 4
Week of April 1: Alexander Duality
	Problem 1
	Problem 2
	Problem 3