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Number Theory
This two-volume book is a modern introduction to the theory of numbers, emphasizing its connections with other branches of mathematics. Part A is accessible to first-year undergraduates and deals with elementary number theory. Part B is more advanced and gives the reader an idea of the scope of mathematics today. The connecting theme is the theory of numbers. By exploring its many connections with other branches a broad picture is obtained. The book contains a treasury of proofs, several of which are gems seldom seen in number theory books.
Non-Associative Algebra and Its Applications
With contributions derived from presentations at an international conference, Non-Associative Algebra and Its Applications explores a wide range of topics focusing on Lie algebras, nonassociative rings and algebras, quasigroups, loops, and related systems as well as applications of nonassociative algebra to geometry, physics, and natural sciences. This book covers material such as Jordan superalgebras, nonassociative deformations, nonassociative generalization of Hopf algebras, the structure of free algebras, derivations of Lie algebras, and the identities of Albert algebra. It also includes applications of smooth quasigroups and loops to differential geometry and relativity.
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.
Geometry of Principal Sheaves
The book provides a detailed introduction to the theory of connections on principal sheaves in the framework of Abstract Differential Geometry (ADG). This is a new approach to differential geometry based on sheaf theoretic methods, without use of ordinary calculus. This point of view complies with the demand of contemporary physics to cope with non-smooth models of physical phenomena and spaces with singularities. Starting with a brief survey of the required sheaf theory and cohomology, the exposition then moves on to differential triads (the abstraction of smooth manifolds) and Lie sheaves of groups (the abstraction of Lie groups). Having laid the groundwork, the main part of the book is de...
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Optical Communication Technology
The optical world is continuously and rapidly evolving, and new challenges arise every day. As a result of these rapid changes, the need for up-to-date texts that address this growing field from an interdisciplinary perspective persists. This book presents an overview of new optical communication technologies and a bird's-eye view of some of the more promising technologies among them. The book covers the theoretical but also the practical aspects of technology implementation in a way that is suitable for undergraduate- and graduate-level students, as well as researchers and professional engineers.
Agricultural Engineering
A broad coverage of basic & applied research projects dealing with the application of engineering principles to both food production & processing. Land and water use; Agricultural buildings; Agricultural mechanisation; Power & processing; Management & ergonomics. About 450 papers from over 50 countries worlwide.
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...
Advanced Signal Analysis and its Applications to Mathematical Physics
The mathematical tools used in signal analysis involve differential and difference equations, integral equations, matrix algebra and calculus, complex analysis and probability theory and random processes. This book applies these tools to problems in various branches of physics like fluid dynamics, electromagnetism and quantum theory. The book will be of use to research workers in signal processing as well as to research workers in physics and applied mathematics. Partial differential equations have been introduced here as an additional tool in signal analysis since they are used to describe quantum, electromagnetic and fluid dynamical phenomena not to forget Einstein’s equations of gravitation. The book will be of use to signal processing experts who are interested in developing tools for the analysis of signals arising in real systems.
