This introduction to polynomial rings, Gröbner bases and applications bridges the gap in the literature between theory and actual computation. It details numerous applications, covering fields as disparate as algebraic geometry and financial markets. To aid in a full understanding of these applications, more than 40 tutorials illustrate how the theory can be used. The book also includes many exercises, both theoretical and practical.
Whereas in the first volume gardening and chess playing were not treated, in this volume they are. This is a book for learning, teaching, reading, and most of all, enjoying the topic at hand.
Whereas in the first volume gardening and chess playing were not treated, in this volume they are. This is a book for learning, teaching, reading, and most of all, enjoying the topic at hand.
This book completes a trilogy initiated by the uncharacteristically witty books Computational Commutative Algebra 1 and 2 by the same authors. The material treated here is not available in book form, and much of it is not available at all.
Written by pioneers in this exciting new field, Algebraic Statistics introduces the application of polynomial algebra to experimental design, discrete probability, and statistics.
From the reviews of the hardcover edition: "... Many parts of the book can be read by anyone with a basic abstract algebra course.
Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory.
Gröbner, W. (1970). Algebraische Geometrie, Vol. II. Bibliographisches Institut, Mannheim. Hartshorne, R. (1977). Algebraic Geometry. Graduate Texts in Mathematics 52, Springer-Verlag, New York. Hense, K. (1908).
... 576 Apéry, R., 542 apparently silly definition, 506 approximate root, 183, 209 Arabic, article in, 576 Artin, E., ... N., 576 branch of a plane curve, 129, 185 Brieskorn, E., 515 Brouwer, L.E.J., 214 Bruhat decomposition, 369 Bruns, ...
Table of contents
This book can be understood as a model for teaching commutative algebra, and takes into account modern developments such as algorithmic and computational aspects.