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MTH721 : Commutative Algebra

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Course Info

Course Category

Mathematics

Course Level

Graduate

Credit Hours

3

Pre-requisites

N/A

Instructor

Dr. Sarfraz Ahmad
Postdoc (Combinatorics & Commutative Algebra)
Philipps-Universität Marburg, Germany

Course Contents

Introduction to Groups, Introduction to Rings, Polynomial Rings, Ideals, Operations of Ideals, Primary decomposition, Krull dimension, Graded Rings, Hilbert Function and Hilbert Series, Monomial Ideals, Macualay Bases Theorem, Hilbert Basis Theorem, Monomial Ordering, Division algorithms, Grobner Bases, Buchberger’s algorithm, Applications of Grobner Bases, Simplicial Complexes, Clique Complex, f and h vectors, Stanley Reisner Rings.