Arjeh M. Cohen - Böcker

From 1-4 April 1986 a Symposium on Algebraic Groups was held at the University of Utrecht, The Netherlands, in celebration of the 350th birthday of the University and the 60th of T.A. Springer. Recognized leaders in the field of algebraic groups and related areas gave lectures which covered wide and central areas of mathematics. Though the fourteen papers in this volume are mostly original research contributions, some survey articles are included. Centering on the Symposium subject, such diverse topics are covered as Discrete Subgroups of Lie Groups, Invariant Theory, D-modules, Lie Algebras, Special Functions, Group Actions on Varieties.

This book arose from a series of courses on computer algebra which were given at Eindhoven Technical University. Its chapters present a variety of topics in computer algebra at an accessible (upper undergraduate/graduate) level with a view towards recent developments. For those wanting to acquaint themselves somewhat further with the material, the book also contains seven 'projects', which could serve as practical sessions related to one or more chapters. The contributions focus on topics like Grobner bases, real algebraic geometry, Lie algebras, factorisation of polynomials, integer programming, permutation groups, differential equations, coding theory, automatic theorem proving, and polyhedral geometry. This book is a must-read for everybody interested in computer algebra.

Algebra Interactive! is an HTML-based course for undergraduate students in all fields of science, e.g. mathematics, computer science, physics and (electrical) engineering. The novel features of Algebra Interactive are the interactive examples and tools for computing in the various structures. Many of these tools and examples use the computer package GAP, which comes with Algebra Interactive, as a back engine. Moreover, abstract notations are enlivened by Java applets, which go beyond the classical examples given in traditional textbooks. The course contains numerous exercises. Apart from the classical type of exercise (with hints and solutions), the product also presents interactive multiple-choice questions on each page and at the end of each chapter. A comprehensive accompanying printed book summarizes the contents of Algebra Interactive.

In the years 1994, 1995, two EIDMA mini courses on Computer Algebra were given at the Eindhoven University of Technology by, apart from ourselves, various invited lecturers. When discussing these courses in comparison with other kinds of courses one might give in a week's time, Joachim Neubüser referred to our courses as 'tapas'.

This book provides a self-contained introduction to diagram geometry. Polar geometry is motivated by polarities on diagram geometries and the complete classification of those polar geometries whose projective planes are Desarguesian is given. Group theorists will find examples of the use of diagram geometry.

This book provides a self-contained introduction to diagram geometry.  Tight connections with group theory are shown. It treats thin geometries (related to Coxeter groups) and thick buildings from a diagrammatic perspective. Projective and affine geometry are main examples.  Polar geometry is motivated by polarities on diagram geometries and the complete classification of those polar geometries whose projective planes are Desarguesian is given. It differs from Tits' comprehensive treatment in that it uses Veldkamp's embeddings. The book intends to be a basic reference for those who study diagram geometry.  Group theorists will find examples of the use of diagram geometry.  Light on matroid theory is shed from the point of view of geometry with linear diagrams.  Those interested in Coxeter groups and those interested in buildings will find brief but self-contained introductions into these topics from the diagrammatic perspective.  Graph theorists will find many highly regular graphs.The text is written so graduate students will be able to follow the arguments without needing recourse to further literature.A strong point of the book is the density of examples.

Ever since the discovery of the five platonic solids in ancient times, the study of symmetry and regularity has been one of the most fascinating aspects of mathematics. Quite often the arithmetical regularity properties of an object imply its uniqueness and the existence of many symmetries. This interplay between regularity and symmetry properties of graphs is the theme of this book. Starting from very elementary regularity properties, the concept of a distance-regular graph arises naturally as a common setting for regular graphs which are extremal in one sense or another. Several other important regular combinatorial structures are then shown to be equivalent to special families of distance-regular graphs. Other subjects of more general interest, such as regularity and extremal properties in graphs, association schemes, representations of graphs in euclidean space, groups and geometries of Lie type, groups acting on graphs, and codes are covered independently. Many new results and proofs and more than 750 references increase the encyclopaedic value of this book.