Hilbert functions and resolutions are both central objects in commutative algebra and fruitful tools in the fields of algebraic geometry, combinatorics, commuta

The study of free resolutions is a core and beautiful area in Commutative Algebra. The main goal of this book is to inspire the readers and develop their intuit

"The Hilbert function for any graded module over a field k is defined by the dimension of all of the summands M_b, where b indicates the graded component being

The most important invariant of a topological space is its fundamental group. When this is trivial, the resulting homotopy theory is well researched and familia

Hilbert Functions play major roles in Algebraic Geometry and Commutative Algebra, and are becoming increasingly important also in Computational Algebra. They ca