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This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book. A comprehensive chart in the preface illustrates a variety of ways to proceed with the material once these chapters are covered. In addition to the fundamentals of algebraic geometry—the elimination theorem, the extension theorem, the closure theorem, and ...

Toric varieties form a beautiful and accessible part of modern algebraic geometry. This book covers the standard topics in toric geometry, a novel feature is that each of the first nine chapters contains an introductory section on the necessary background material in algebraic geometry.

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This book details the heart and soul of modern commutative and algebraic geometry. It covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. In addition to enhancing the text of the second edition, with over 200 pages reflecting changes to enhance clarity and correctness, this third edition of Ideals, Varieties and Algorithms includes: a significantly updated section o...

In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraic geometry. These algorithmic methods have also given rise to some exciting new applications of algebraic geometry. This book illustrates the many uses of algebraic geometry, highlighting some of the more recent applications o...

The discovery of new algorithms for dealing with polynomial equations, and their implementation on fast, inexpensive computers, has revolutionized algebraic geometry and led to exciting new applications in the field. This book details many uses of algebraic geometry and highlights recent applications of Grobner bases and resultants. This edition contains two new sections, a new chapter, updated references and many minor improvements throughout.

Consists of invited papers, from internationally recognized researchers, chosen for their quality as well as their overall unity. Describes current methods along with innovative research and presents new technologies for solving problems unique to establishment surveys. Stages of the survey process are addressed in the first five parts with cross-cutting topics in the last section.

An exciting approach to the history and mathematics of number theory ". . . the author's style is totally lucid and very easy to read . . . the result is indeed a wonderful story." -Mathematical Reviews Written in a unique and accessible style for readers of varied mathematical backgrounds, the Second Edition of Primes of the Form p = x2 + ny2 details the history behind how Pierre de Fermat's work ultimately gave birth to quadratic reciproci...

Praise for the First Edition ". . .will certainly fascinate anyone interested in abstract algebra: a remarkable book!" --Monatshefte fur Mathematik Galois theory is one of the most established topics in mathematics, with historical roots that led to the development of many central concepts in modern algebra, including groups and fields. Covering classic applications of the theory, such as solvability by radicals, geometric constructions, and...

Sir David Cox's most important papers, each the subject of a new commentary by Professor Cox.

This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book. A comprehensive chart in the preface illustrates a variety of ways to proceed with the material once these chapters are covered. In addition to the fundamentals of algebraic geometry—the elimination theorem, the extension theorem, the closure theorem, and ...

Sir David Cox's most important papers, each the subject of a new commentary by Professor Cox.

Sir David Cox's most important papers, each the subject of a new commentary by Professor Cox.