Certain Number Theoretic Episodes In Algebra Second Edition
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Certain Number-Theoretic Episodes In Algebra by Sivaramakrishnan R,R Sivaramakrishnan Pdf
Many basic ideas of algebra and number theory intertwine, making it ideal to explore both at the same time. Certain Number-Theoretic Episodes in Algebra focuses on some important aspects of interconnections between number theory and commutative algebra. Using a pedagogical approach, the author presents the conceptual foundations of commutati
Certain Number-Theoretic Episodes In Algebra, Second Edition by R Sivaramakrishnan Pdf
The book attempts to point out the interconnections between number theory and algebra with a view to making a student understand certain basic concepts in the two areas forming the subject-matter of the book.
Certain Number-Theoretic Episodes In Algebra, Second Edition by R Sivaramakrishnan Pdf
The book attempts to point out the interconnections between number theory and algebra with a view to making a student understand certain basic concepts in the two areas forming the subject-matter of the book.
The Separable Galois Theory of Commutative Rings, Second Edition by Andy R. Magid Pdf
The Separable Galois Theory of Commutative Rings, Second Edition provides a complete and self-contained account of the Galois theory of commutative rings from the viewpoint of categorical classification theorems and using solely the techniques of commutative algebra. Along with updating nearly every result and explanation, this edition contains a new chapter on the theory of separable algebras. The book develops the notion of commutative separable algebra over a given commutative ring and explains how to construct an equivalent category of profinite spaces on which a profinite groupoid acts. It explores how the connection between the categories depends on the construction of a suitable separable closure of the given ring, which in turn depends on certain notions in profinite topology. The book also discusses how to handle rings with infinitely many idempotents using profinite topological spaces and other methods.
Representation Theory and Higher Algebraic K-Theory by Aderemi Kuku Pdf
Representation Theory and Higher Algebraic K-Theory is the first book to present higher algebraic K-theory of orders and group rings as well as characterize higher algebraic K-theory as Mackey functors that lead to equivariant higher algebraic K-theory and their relative generalizations. Thus, this book makes computations of higher K-theory of grou
Presents Results from a Very Active Area of ResearchExploring an active area of mathematics that studies the complexity of equivalence relations and classification problems, Invariant Descriptive Set Theory presents an introduction to the basic concepts, methods, and results of this theory. It brings together techniques from various areas of mathem
Now considered a classic text on the topic, Measure and Integral: An Introduction to Real Analysis provides an introduction to real analysis by first developing the theory of measure and integration in the simple setting of Euclidean space, and then presenting a more general treatment based on abstract notions characterized by axioms and with less
Starting with the most basic notions, Universal Algebra: Fundamentals and Selected Topics introduces all the key elements needed to read and understand current research in this field. Based on the author’s two-semester course, the text prepares students for research work by providing a solid grounding in the fundamental constructions and concepts of universal algebra and by introducing a variety of recent research topics. The first part of the book focuses on core components, including subalgebras, congruences, lattices, direct and subdirect products, isomorphism theorems, a clone of operations, terms, free algebras, Birkhoff’s theorem, and standard Maltsev conditions. The second part covers topics that demonstrate the power and breadth of the subject. The author discusses the consequences of Jónsson’s lemma, finitely and nonfinitely based algebras, definable principal congruences, and the work of Foster and Pixley on primal and quasiprimal algebras. He also includes a proof of Murskiĭ’s theorem on primal algebras and presents McKenzie’s characterization of directly representable varieties, which clearly shows the power of the universal algebraic toolbox. The last chapter covers the rudiments of tame congruence theory. Throughout the text, a series of examples illustrates concepts as they are introduced and helps students understand how universal algebra sheds light on topics they have already studied, such as Abelian groups and commutative rings. Suitable for newcomers to the field, the book also includes carefully selected exercises that reinforce the concepts and push students to a deeper understanding of the theorems and techniques.
Elementary Number Theory by Charles Vanden Eynden Pdf
This practical and versatile text evolved from the author’s years of teaching experience and the input of his students. Vanden Eynden strives to alleviate the anxiety that many students experience when approaching any proof-oriented area of mathematics, including number theory. His informal yet straightforward writing style explains the ideas behind the process of proof construction, showing that mathematicians develop theorems and proofs from trial and error and evolutionary improvement, not spontaneous insight. Furthermore, the book includes more computational problems than most other number theory texts to build students’ familiarity and confidence with the theory behind the material. The author has devised the content, organization, and writing style so that information is accessible, students can gain self-confidence with respect to mathematics, and the book can be used in a wide range of courses—from those that emphasize history and type A problems to those that are proof oriented.
Geomathematically Oriented Potential Theory by Willi Freeden,Christian Gerhards Pdf
As the Earth`s surface deviates from its spherical shape by less than 0.4 percent of its radius and today's satellite missions collect their gravitational and magnetic data on nearly spherical orbits, sphere-oriented mathematical methods and tools play important roles in studying the Earth's gravitational and magnetic field. Geomathematically Orien
Incorporating a number of the author’s recent ideas and examples, Dynamic Programming: Foundations and Principles, Second Edition presents a comprehensive and rigorous treatment of dynamic programming. The author emphasizes the crucial role that modeling plays in understanding this area. He also shows how Dijkstra’s algorithm is an excellent example of a dynamic programming algorithm, despite the impression given by the computer science literature. New to the Second Edition Expanded discussions of sequential decision models and the role of the state variable in modeling A new chapter on forward dynamic programming models A new chapter on the Push method that gives a dynamic programming perspective on Dijkstra’s algorithm for the shortest path problem A new appendix on the Corridor method Taking into account recent developments in dynamic programming, this edition continues to provide a systematic, formal outline of Bellman’s approach to dynamic programming. It looks at dynamic programming as a problem-solving methodology, identifying its constituent components and explaining its theoretical basis for tackling problems.
Quadratic Irrationals: An Introduction to Classical Number Theory gives a unified treatment of the classical theory of quadratic irrationals. Presenting the material in a modern and elementary algebraic setting, the author focuses on equivalence, continued fractions, quadratic characters, quadratic orders, binary quadratic forms, and class groups.T
Metaharmonic Lattice Point Theory by Willi Freeden Pdf
Metaharmonic Lattice Point Theory covers interrelated methods and tools of spherically oriented geomathematics and periodically reflected analytic number theory. The book establishes multi-dimensional Euler and Poisson summation formulas corresponding to elliptic operators for the adaptive determination and calculation of formulas and identities of
Topological Vector Spaces by Lawrence Narici,Edward Beckenstein Pdf
With many new concrete examples and historical notes, Topological Vector Spaces, Second Edition provides one of the most thorough and up-to-date treatments of the Hahn-Banach theorem. This edition explores the theorem's connection with the axiom of choice, discusses the uniqueness of Hahn-Banach extensions, and includes an entirely new chapter on v
In 1990, the National Science Foundation recommended that every college mathematics curriculum should include a second course in linear algebra. In answer to this recommendation, Matrix Theory: From Generalized Inverses to Jordan Form provides the material for a second semester of linear algebra that probes introductory linear algebra concepts while also exploring topics not typically covered in a sophomore-level class. Tailoring the material to advanced undergraduate and beginning graduate students, the authors offer instructors flexibility in choosing topics from the book. The text first focuses on the central problem of linear algebra: solving systems of linear equations. It then discusses LU factorization, derives Sylvester's rank formula, introduces full-rank factorization, and describes generalized inverses. After discussions on norms, QR factorization, and orthogonality, the authors prove the important spectral theorem. They also highlight the primary decomposition theorem, Schur's triangularization theorem, singular value decomposition, and the Jordan canonical form theorem. The book concludes with a chapter on multilinear algebra. With this classroom-tested text students can delve into elementary linear algebra ideas at a deeper level and prepare for further study in matrix theory and abstract algebra.
