Theory and Applications of Finite Groups
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The Theory of Equations
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An Introduction to Algebra
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Test Problems in Algebra
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Relative Nonhomogeneous Koszul Duality
This research monograph develops the theory of relative nonhomogeneous Koszul duality. Koszul duality is a fundamental phenomenon in homological algebra and related areas of mathematics, such as algebraic topology, algebraic geometry, and representation theory. Koszul duality is a popular subject of contemporary research. This book, written by one of the world's leading experts in the area, includes the homogeneous and nonhomogeneous quadratic duality theory over a nonsemisimple, noncommutative base ring, the Poincare-Birkhoff-Witt theorem generalized to this context, and triangulated equivalences between suitable exotic derived categories of modules, curved DG comodules, and curved DG contramodules. The thematic example, meaning the classical duality between the ring of differential operators and the de Rham DG algebra of differential forms, involves some of the most important objects of study in the contemporary algebraic and differential geometry. For the first timein the history of Koszul duality the derived D-\Omega duality is included into a general framework. Examples highly relevant for algebraic and differential geometry are discussed in detail.
A Text Book of Algebra
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Principles of the Algebra of Physics
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A Practical System of Algebra in Theory and Practice in Two Parts
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High School Algebra
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High School Algebra
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An Introduction to the Elements of Algebra
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High School Algebra
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The Elements of Algebra. Designed for the Use of Students in the University
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An Elementary Exposition of Grassmann’s Ausdehnungslehre
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The Theory of Equations
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The Elements of Algebra. Designed for the Use of Students in the University
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Elements of Algebra
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Elements of Algebra
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High School Algebra
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High School Algebra
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An Elementary Exposition of Grassmann's Ausdehnungslehre
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The Theory of Determinants in the Historical Order of Development
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Memoir On The Theory Of The Partitions Of Numbers; Volume 1
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The Theory of Equations
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A Drill-Book in Algebra
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Introduction to Higher Algebra
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The Theory of Determinants in the Historical Order of Development
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Elements of Quaternions
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A Treatise On Algebra
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Bridging Gaps In Elementary Mathematics
We cannot get away from Mathematics in our daily lives. It is omnipresent. Whatever the path we choose, we are likely to encounter Mathematics, in some form.This study supplement was created to improve upon the appreciation, and fundamental understanding of Mathematics, by employing the "WHY" of the Mathematics approach. It was also created to ensure that those who did not have an opportunity in their earlier years to study mathematics, or those who did but need better understanding, would be able to "BRIDGE" the gap formed in their education.The material covers topics found in the curriculum at the Primary to the pre-Junior High School level. It is not intended to substitute for formally prescribed schooling study materials and textbooks. Still, it is a supplement that provides a more profound understanding, real-life applications and different perspectives of the universal elements of the Mathematics curriculum. It effectively approaches the subject from the root to help make it less abstract.
A Primer of Quaternions
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An Exercise Book in Algebra
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Algebra for Beginners
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Elements of Quaternions
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Theory and Applications of Finite Groups
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The Absolute Galois Group of a Semi-Local Field
This book is devoted to the structure of the absolute Galois groups of certain algebraic extensions of the field of rational numbers. Its main result, a theorem proved by the authors and Florian Pop in 2012, describes the absolute Galois group of distinguished semi-local algebraic (and other) extensions of the rational numbers as free products of the free profinite group on countably many generators and local Galois groups. This is an instance of a positive answer to the generalized inverse problem of Galois theory. Adopting both an arithmetic and probabilistic approach, the book carefully sets out the preliminary material needed to prove the main theorem and its supporting results. In addition, it includes a description of Melnikov's construction of free products of profinite groups and, for the first time in book form, an account of a generalization of the theory of free products of profinite groups and their subgroups. The book will be of interest to researchers in field arithmetic, Galois theory and profinite groups.
Structure and Regularity of Group Actions on One-Manifolds
This book presents the theory of optimal and critical regularities of groups of diffeomorphisms, from the classical work of Denjoy and Herman, up through recent advances. Beginning with an investigation of regularity phenomena for single diffeomorphisms, the book goes on to describes a circle of ideas surrounding Filipkiewicz's Theorem, which recovers the smooth structure of a manifold from its full diffeomorphism group. Topics covered include the simplicity of homeomorphism groups, differentiability of continuous Lie group actions, smooth conjugation of diffeomorphism groups, and the reconstruction of spaces from group actions. Various classical and modern tools are developed for controlling the dynamics of general finitely generated group actions on one-dimensional manifolds, subject to regularity bounds, including material on Thompson's group F, nilpotent groups, right-angled Artin groups, chain groups, finitely generated groups with prescribed critical regularities, and applications to foliation theory and the study of mapping class groups. The book will be of interest to researchers in geometric group theory.
The Complete Algebra
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Lectures on Fundamental Concepts of Algebra and Geometry
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Advanced Algebra
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