Monomial Ideals and Their Decompositions (Universitext)

December 5, 2020
Monomial Ideals and Their Decompositions (Universitext)

Includes tutorials and exercises for Macaulay 2Provides hands-on experience with over 600 exercisesBroadens understanding of monomial ideals in polynomialringsThis textbook on combinatorial commutative algebra focuses onproperties of monomial ideals in polynomial rings and theirconnections with other areas of mathematics such as combinatorics,electrical engineering, topology, geometry, and homologicalalgebra. Aimed toward advanced undergraduate students and graduatestudents who have taken a basic course in abstract algebra thatincludes polynomial rings and ideals, this book serves as a coretext for a course in combinatorial commutative algebra or aspreparation for more advanced courses in the area. The textcontains over 600 exercises to provide readers with a hands-onexperience working with the material; the exercises includecomputations of specific examples and proofs of general results.Readers will receive a firsthand introduction to the computeralgebra system Macaulay2 with tutorials and exercises for mostsections of the text, preparing them for significant computationalwork in the area. Connections to non-monomial areas of abstractalgebra, electrical engineering, combinatorics and other areas ofmathematics are provided which give the reader a sense of how theseideas reach into other areas.