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Algèbre commutative : Chapitres 5 à 7 = Commutative algebra : Chapters 5 to 7
The Mathematics Elements of Nicolas BOURBAKI aim to provide a rigorous, systematic presentation without prerequisites of mathematics from their foundations.This second volume of the Book of Commutative Algebra, Seventh Book of the treatise, introduces two fundamental notions in commutative algebra, that of algebraic integer and that of valuation, which have many applications in number theory and algebraic geometry.
Algèbre commutative : Chapitres 1à 4 = = Commutative algebra : Chapters 1 to 4
Nicolas BOURBAKI's Elements of Mathematics aim to provide a rigorous, systematic presentation without prerequisites of mathematics from their foundations. This first volume of the Book of Commutative Algebra, the seventh Book of the treatise, is devoted to the fundamental concepts of commutative algebra. It includes the chapters, Flat modules, Localization, Graduations, filtrations and topologies, First associated ideals and primary decomposition, It also contains historical notes. This volume is a reprint of the 1969 edition.
Algèbre : Chapitre 10 : Algèbre homologique = Algebra : Chapter 10 : Homological algebra
The Mathematics Elements of Nicolas BOURBAKI aim to provide a rigorous, systematic presentation without prerequisites of mathematics from their foundations. This tenth chapter of the Book of Algebra, the second Book of the treatise, lays the foundations of the homological calculus.
Algebras, Rings and Modules: Vol.1
Covers the major topics in ring and module theory and includes both fundamental classical results and more developments. This book is devoted to a study of special classes of rings and algebras, such as serial rings, hereditary rings, semidistributive rings and tiled orders.
Algebras, Rings and Modules ; Vol.2
This book provides both the classical aspects of the theory of groups and their representations as well as a general introduction to the modern theory of representations including the representations of quivers and finite partially ordered sets and their applications to finite dimensional algebras.
Algebraic Theory of Locally Nilpotent Derivations
This book explores the theory and application of locally nilpotent derivations, which is a subject of growing interest and importance not only among those in commutative algebra and algebraic geometry, but also in fields such as Lie algebras and differential equations. The author provides a unified treatment of the subject, beginning with 16 First Principles on which the entire theory is based. These are used to establish classical results, such as Rentschler’s Theorem for the plane, right up to the most recent results, such as Makar-Limanov’s Theorem for locally nilpotent derivations of polynomial rings.
Algebraic Multiplicity of Eigenvalues of Linear Operators
This book brings together all the most important known results of research into the theory of algebraic multiplicities, from well-known classics like the Jordan Theorem to recent developments such as the uniqueness theorem and the construction of multiplicity for non-analytic families.
Algebraic Groups and Lie Groups with Few Factors
Algebraic groups are treated in this volume from a group theoretical point of view and the obtained results are compared with the analogous issues in the theory of Lie groups. The main body of the text is devoted to a classification of algebraic groups and Lie groups having only few subgroups or few factor groups of different type. In particular, the diversity of the nature of algebraic groups over fields of positive characteristic and over fields of characteristic zero is emphasized. This is revealed by the plethora of three-dimensional unipotent algebraic groups over a perfect field of positive characteristic, as well as, by many concrete examples which cover an area systematically. In the final section, algebraic groups and Lie groups having many closed normal subgroups are determined.
Algebraic Geometry and Number Theory : In Honor of Vladimir Drinfeld's 50th Birthday
One of the most creative mathematicians of our times, Vladimir Drinfeld received the Fields Medal in 1990 for his groundbreaking contributions to the Langlands program and to the theory of quantum groups.These ten original articles by prominent mathematicians, dedicated to Drinfeld on the occasion of his 50th birthday, broadly reflect the range of Drinfeld's own interests in algebra, algebraic geometry, and number theory.
Algebraic Geometry and Geometric Modeling
Algebraic Geometry provides an impressive theory targeting the understanding of geometric objects defined algebraically. Geometric Modeling uses every day, in order to solve practical and difficult problems, digital shapes based on algebraic models. In this book, we have collected articles bridging these two areas. The confrontation of the different points of view results in a better analysis of what the key challenges are and how they can be met. We focus on the following important classes of problems: implicitization, classification, and intersection. The combination of illustrative pictures, explicit computations and review articles will help the reader to handle these subjects.
Algebraic Geometry : An Introduction
The book starts with easily-formulated problems with non-trivial solutions – for example, Bézout’s theorem and the problem of rational curves – and uses these problems to introduce the fundamental tools of modern algebraic geometry: dimension; singularities; sheaves; varieties; and cohomology. The treatment uses as little commutative algebra as possible by quoting without proof (or proving only in special cases) theorems whose proof is not necessary in practice, the priority being to develop an understanding of the phenomena rather than a mastery of the technique. A range of exercises is provided for each topic discussed, and a selection of problems and exam papers are collected in an appendix to provide material for further study.
Algebraic Cycles, Sheaves, Shtukas, and Moduli : Impanga Lecture Notes
The articles in this volume are devoted to: - moduli of coherent sheaves. - principal bundles and sheaves and their moduli. - new insights into Geometric Invariant Theory. - stacks of shtukas and their compactifications. - algebraic cycles vs. commutative algebra. - Thom polynomials of singularities. - zero schemes of sections of vector bundles.
Algebraic Combinatorics : Lectures at a Summer School in Nordfjordeid, Norway, June 2003
This book is based on two series of lectures given at a summer school on algebraic combinatorics at the Sophus Lie Centre in Nordfjordeid, Norway, in June 2003, one by Peter Orlik on hyperplane arrangements, and the other one by Volkmar Welker on free resolutions.
Algebraic Cobordism
Algebraic Cobordism: is a theory satisfies the analogues of Quillen's theorems: the cobordism of the base field is the Lazard ring and the cobordism of a smooth variety is generated over the Lazard ring by the elements of positive degrees.
Algebraic Analysis of Differential Equations : from Microlocal Analysis to Exponential Asymptotics Festschrift in Honor of Takahiro Kawai Editors
This volume contains 23 articles on algebraic analysis of differential equations and related topics, most of which were presented as papers at the international conference "Algebraic Analysis of Differential Equations – from Microlocal Analysis to Exponential Asymptotics" at Kyoto University in 2005. Microlocal analysis and exponential asymptotics are intimately connected and provide powerful tools that have been applied to linear and non-linear differential equations as well as many related fields such as real and complex analysis, integral transforms, spectral theory, inverse problems, integrable systems, and mathematical physics. The articles contained here present many new results and ideas, providing interested researchers and students with valuable suggestions and instructive guidance for their work.
Algebra : Fields with structure, algebras and advanced topics
The present textbook is a lively, problem-oriented and carefully written introduction to classical modern algebra. The author leads the reader through interesting subject matter, while assuming only the background provided by a first course in linear algebra. The first volume focuses on field extensions. Galois theory and its applications are treated more thoroughly than in most texts. It also covers basic applications to number theory, ring extensions and algebraic geometry. The main focus of the second volume is on additional structure of fields and related topics. Much material not usually covered in textbooks appears here, including real fields and quadratic forms, the Tsen rank of a field, the calculus of Witt vectors, the Schur group of a field, and local class field theory.
African Cultural Astronomy : Current Archaeoastronomy and Ethnoastronomy research in Africa
Astronomy is the science of studying the sky using telescopes and light collectors such as photographic plates or CCD detectors. However, people have always studied the sky and continue to study the sky without the aid of instruments this is the realm of cultural astronomy. This is the first scholarly collection of articles focused on the cultural astronomy of Africans. It weaves together astronomy, anthropology, and Africa. The volume includes African myths and legends about the sky, alignments to celestial bodies found at archaeological sites and at places of worship, rock art with celestial imagery, and scientific thinking revealed in local astronomy traditions including ethnomathematics and the creation of calendars. Authors include astronomers Kim Malville, Johnson Urama, and Thebe Medupe; archaeologist Felix Chami, and geographer Michael Bonine, and many new authors.
Affine Density in Wavelet Analysis
Provides the first thorough and comprehensive treatment of irregular wavelet frames by introducing and employing a new notion of affine density as a highly effective tool for examining the geometry of sequences of time-scale indices.
Affect and Mathematics Education : Fresh Perspectives on Motivation, Engagement, and Identity
Presents the latest trends in research in the area. Following an introduction and a survey chapter providing a concise overview of the state-of-art in the field of mathematics-related affect, the book is divided into three main sections: motivation and values, engagement, and identity in mathematics education. Each section comprises several independent chapters based on original research, as well as a reflective commentary by an expert in the area. Collectively, the chapters present a rich methodological spectrum, from narrative analysis to structural equation modelling.
Advancing Human Assessment : The Methodological, Psychological and Policy Contributions of ETS
Describes the extensive contributions made toward the advancement of human assessment by scientists from one of the world’s leading research institutions, Educational Testing Service. The book’s four major sections detail research and development in measurement and statistics, education policy analysis and evaluation, scientific psychology, and validity. Many of the developments presented have become de-facto standards in educational and psychological measurement, including in item response theory (IRT), linking and equating, differential item functioning (DIF), and educational surveys like the National Assessment of Educational Progress (NAEP), the Programme of international Student Assessment (PISA), the Progress of International Reading Literacy Study (PIRLS) and the Trends in Mathematics and Science Study (TIMSS). In addition to its comprehensive coverage of contributions to the theory and methodology of educational and psychological measurement and statistics,
