Customarily, the framework of algebraic geometry has been worked over an algebraically closed field of characteristic zero, say, over the complex number field.
The purpose of this book is to present the classical analytic function theory of several variables as a standard subject in a course of mathematics after learning the elementary materials (sets, general topology, algebra, one complex variable).
This monograph contains an exposition of the theory of minimal surfaces in Euclidean space, with an emphasis on complete minimal surfaces of finite total curvature.
This book grew out of our lectures given in the Oberseminar on 'Cod- ing Theory and Number Theory' at the Mathematics Institute of the Wiirzburg University in the Summer Semester, 2001.
The already broad range of applications of ring theory has been enhanced in the eighties by the increasing interest in algebraic structures of considerable complexity, the so-called class of quantum groups.
The 12 lectures presented in Representation Theories and Algebraic Geometry focus on the very rich and powerful interplay between algebraic geometry and the representation theories of various modern mathematical structures, such as reductive groups, quantum groups, Hecke algebras, restricted Lie algebras, and their companions.
Recent major advances in model theory include connections between model theory and Diophantine and real analytic geometry, permutation groups, and finite algebras.
Algebraic K-theory is a modern branch of algebra which has many important applications in fundamental areas of mathematics connected with algebra, topology, algebraic geometry, functional analysis and algebraic number theory.
Automorphisms of Affine Spaces describes the latest results concerning several conjectures related to polynomial automorphisms: the Jacobian, real Jacobian, Markus-Yamabe, Linearization and tame generators conjectures.
This volume presents the lectures given during the second French-Uzbek Colloquium on Algebra and Operator Theory which took place in Tashkent in 1997, at the Mathematical Institute of the Uzbekistan Academy of Sciences.
The NATO Advanced Study Institute on "e;The Arithmetic and Geometry of Algebraic Cycles"e; was held at the Banff Centre for Conferences in Banff (Al- berta, Canada) from June 7 until June 19, 1998.
Geometric Methods in System Theory In automatic control there are a large number of applications of a fairly simple type for which the motion of the state variables is not free to evolve in a vector space but rather must satisfy some constraints.
An up-to-date report on the current status of important research topics in algebraic geometry and its applications, such as computational algebra and geometry, singularity theory algorithms, numerical solutions of polynomial systems, coding theory, communication networks, and computer vision.
The NATO Advanced Study Institute "e;Axiomatic, enriched and rna- tivic homotopy theory"e; took place at the Isaac Newton Institute of Mathematical Sciences, Cambridge, England during 9-20 September 2002.