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This course will be an introduction to commutative algebra, with elementary applications to combinatorics and computational algebra.
The first part of the course will treat basic notions and results---chain conditions, prime ideals, flatness, Krull dimension, Hilbert functions. The other half of the course will study in more detail rings of polynomials and its geometry, and Gr\"{o}bner bases. It will open the door to computational methods in algebra (a few will be studied). Some other applications will deal with counting solutions of certain linear diophantine equations.
An useful reference will be David Eisenbud's Commutative Algebra with a view toward Algebraic Geometry, Springer.
The pre-requisite is a previous graduate course in abstract algebra. If in doubt, please talk to me in Hill 228.
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