This textbook offers a thorough, modern introduction into commutative algebra. It is intented mainly to serve as a guide for a course of one or two semesters, or for self-study. The carefully selected subject matter concentrates on the concepts and results at the center of the field. The book maintains a constant view on the natural geometric context, enabling the reader to gain a deeper understanding of the material. Although it emphasizes theory, three chapters are devoted to computational aspects. Many illustrative examples and exercises enrich the text.

This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Groebner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be of more than passing interest. More than ten years after the first publication of the book, the second edition now provides a major update and covers many recent developments in the field. Among the roughly 100 added pages there are two appendices, authored by Vladimi r Popov, and an addendum by Norbert A'Campo and Vladimir Popov.

This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Groebner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be of more than passing interest. More than ten years after the first publication of the book, the second edition now provides a major update and covers many recent developments in the field. Among the roughly 100 added pages there are two appendices, authored by Vladimi r Popov, and an addendum by Norbert A'Campo and Vladimir Popov.

This book, the first volume of a subseries on "Invariant Theory and Algebraic Transformation Groups," provides a comprehensive and up-to-date overview of the algorithmic aspects of invariant theory. Numerous illustrative examples and a careful selection of proofs make the book accessible to non-specialists.

Lineare Algebra auf den Punkt gebracht Dieses Buch ist bestens geeignet fur Studierende als Begleitlekture und fur Lehrende als Grundlage zur Vorlesungsplanung. Es zeichnet sich aus durch eine prazise Darstellung ohne Ausschweifungen. Einzigartig ist die Kombination dreier "Handlungsstrange" Lineare Algebra (als Hauptstrang), diskrete Mathematik und Mengenlehre. Dabei kann der Hauptstrang unabhangig von den beiden anderen Strangen gelesen werden, die jeweils eine solide Einfuhrung in ihre Stoffgebiete beinhalten. Auf diese Weise lassen sich die Nebenstrange in eine gemeinsame Vorlesung mit der Linearen Algebra integrieren oder bleiben ein optionales Zusatzangebot zur Linearen Algebra fur Erganzungen oder Seminare. Mit uber 350 Aufgaben bietet das Buch bei jedem Themengebiet die Gelegenheit zur aktiven Auseinandersetzung mit dem Stoff an. Die Bandbreite umfasst neben vorlesungsbegleitenden UEbungsaufgaben auch typische Klausuraufgaben und groessere Aufgabenprojekte. Fur einige der Aufgaben sind zudem Loesungsvideos verfugbar.