We wrote this book to introduce undergraduates to some interesting ideas in algebraic
geometry and commutative algebra. For a long time, these topics involved a lot of abstract …

The main purpose of this book is to introduce algebraic, combinatorial, and computational
methods to study monomial algebras and their presentation ideals, including Stanley …

Hofstadter's Law: It always takes longer than you think it will take, even if you take into
account Hofstadter's Law.(Douglas R. Hofstadter) Dear Reader, what you are holding in …

From the reviews:"... Many parts of the book can be read by anyone with a basic abstract
algebra course... it was one of the author's intentions to equip students who are interested in …

In this paper we show how to use the knowledge of the Hilbert–Poincaré series of an idealIto
speed up the Buchberger algorithm for the computation of a Gröbner basis. The algorithm is …

This book starts with an overview of the research of Gröbner bases which have many
applications in various areas of mathematics since they are a general tool for the …

Toric ideals are binomial ideals which represent the algebraic relations of sets of power
products. They appear in many problems arising from different branches of mathematics. In …

We describe how to construct and enumerate Magic squares, Franklin squares, Magic
cubes, and Magic graphs as lattice points inside polyhedral cones using techniques from …

We present the design and implementation of a C++ class for reliability analysis of multi-
state systems using an algebraic approach based on monomial ideals. The class is …

How Many Squares Are There, Mr. Franklin?: Constructing and Enumerating Franklin Squares
Page 1 How Many Squares Are There, Mr. Franklin?: Constructing and Enumerating Franklin …