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A Course in Abstract Algebra,
The book starts with a brief introduction to results from Set theory and Number theory. It then goes on to cover Groups, Rings, Fields and Linear Algebra. The topics under groups include Subgroups, Finitely generated abelian groups, Group actions, Solvable and Nilpotent groups. The course in ring theory covers Ideals, Embedding of rings, Euclidean domains, PIDs, UFDs, Polynomial rings and Noetherian (Artinian) rings. Topics in field include Algebraic extensions, Splitting fields, Normal extensions, Separable extensions, Algebraically closed fields, Galois extensions, and Construction by ruler and compass. The portion on linear algebra deals with Vector spaces, Linear transformations, Eigen spaces, Diagonalizable operators, Inner product spaces, Dual spaces, Operators on inner product spaces etc. The theory has been strongly supported by numerous examples and workedout problems. There is also a plenty of scope for the readers to try and solve problems on their own. The book is designed for undergraduate and postgraduate students of mathematics. It can also be used by those preparing for various competitive examinations.
Lie Algebras and Algebraic Groups
Devoted to the theory of Lie algebras and algebraic groups, this book includes a large amount of commutative algebra and algebraic geometry so as to make it as self-contained as possible. The aim of the book is to assemble in a single volume the algebraic aspects of the theory, so as to present the foundations of the theory in characteristic zero. Detailed proofs are included, and some recent results are discussed in the final chapters.
Topics in Quaternion Linear Algebra
Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetri...
Podręcznik do egzaminu B2 z języka angielskiego
Podręcznik do egzaminu B2 z języka angielskiego to e-book zawierający cały potrzebny materiał do nauki dla osób przygotowujących się do egzaminu na poziomie B2, ale także dla osób, które uczą się samodzielnie języka angielskiego. E-book zawiera słowa i zwroty niezbędne do zdania tego egzaminu poprzez naukę wg. wypróbowanej i skutecznej metody opracowanej przez autora oraz pełny przegląd gramatyki angielskiej. Podręcznik jest przystosowany do używania na komputerach i tabletach.
Modern Algebra, 9e
The book starts from set theory and covers an advanced course in group theory and ring theory. A detailed study of field theory and its application to geometry is undertaken after a brief and concise account of vector spaces and linear transformations. One of the chapters discusses rings with chain conditions and Hilbert’s basis theorem. The book is replete with solved examples to provide ample opportunity to students to comprehend the subject.
Arithmetic and Analytic Theories of Quadratic Forms and Clifford Groups
The two main themes of the book are (1) quadratic Diophantine equations; (2) Euler products and Eisenstein series on orthogonal groups and Clifford groups. Whereas the latest chapters of the book contain new results, a substantial portion of it is devoted to expository material related to these themes, such as Witt's theorem and the Hasse principle on quadratic forms, algebraic theory of Clifford algebras, spin groups, and spin representations. The starting point of the first main theme is the result of Gauss that the number of primitive representations of an integer as the sum of three squares is essentially the class number of primitive binary quadratic forms. A generalization of this fact...
Basic Concepts in Organic Stereochemistry
This book discusses essential stereochemical concepts associated with organic molecules (natural or synthetic), as reflected in the course of their many reactions, their mechanisms, their asymmetric synthesis, biosynthesis, and biological activities. This treatise provides useful insights and understanding of the chiral/achiral designations (nomenclatures), the stereochemical features, and related properties of the natural and synthetic products. Without having an adequate knowledge of stereochemical concepts, it will not be possible to understand and appreciate the stereochemistry of natural or synthetic products. Thus, essential static and dynamic aspects of stereochemistry with sufficient illustrative examples along with discussions are presented. The structure of the monograph allows for easy selection of separate topics for reading and teaching. This book will also provide an idea of basic stereochemical concepts, as applied to organic molecules in general as well as to organic ligands in coordination complexes, and will, therefore, be valuable resources to teachers and students of advanced undergraduates and post-graduates, researchers, and professionals.
