Download or read book Certain Number Theoretic Episodes In Algebra written by Sivaramakrishnan R and published by CRC Press. This book was released on 2006-09-22 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Certain Number Theoretic Episodes In Algebra Second Edition written by R Sivaramakrishnan and published by CRC Press. This book was released on 2019-03-19 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Invariant Descriptive Set Theory written by Su Gao and published by CRC Press. This book was released on 2008-09-03 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Universal Algebra written by Clifford Bergman and published by CRC Press. This book was released on 2011-09-20 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Representation Theory and Higher Algebraic K Theory written by Aderemi Kuku and published by CRC Press. This book was released on 2016-04-19 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book The Separable Galois Theory of Commutative Rings written by Andy R. Magid and published by CRC Press. This book was released on 2014-07-14 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 n
Download or read book Geomathematically Oriented Potential Theory written by Willi Freeden and published by CRC Press. This book was released on 2012-10-30 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Quadratic Irrationals written by Franz Halter-Koch and published by CRC Press. This book was released on 2013-06-17 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Matrix Theory written by Robert Piziak and published by CRC Press. This book was released on 2007-02-22 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algorithmic Lie Theory for Solving Ordinary Differential Equations written by Fritz Schwarz and published by CRC Press. This book was released on 2007-10-02 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite the fact that Sophus Lie's theory was virtually the only systematic method for solving nonlinear ordinary differential equations (ODEs), it was rarely used for practical problems because of the massive amount of calculations involved. But with the advent of computer algebra programs, it became possible to apply Lie theory to concrete proble
Download or read book Metaharmonic Lattice Point Theory written by Willi Freeden and published by CRC Press. This book was released on 2011-05-09 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Measure and Integral written by Richard L. Wheeden and published by CRC Press. This book was released on 2015-04-24 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Classification of Lipschitz Mappings written by Lukasz Piasecki and published by CRC Press. This book was released on 2016-04-19 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classification of Lipschitz Mappings presents a systematic, self-contained treatment of a new classification of Lipschitz mappings and its application in many topics of metric fixed point theory. Suitable for readers interested in metric fixed point theory, differential equations, and dynamical systems, the book only requires a basic background in
Download or read book Uncertain Dynamical Systems written by A.A. Martynyuk and published by CRC Press. This book was released on 2011-11-28 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained book provides systematic instructive analysis of uncertain systems of the following types: ordinary differential equations, impulsive equations, equations on time scales, singularly perturbed differential equations, and set differential equations. Each chapter contains new conditions of stability of unperturbed motion of the abo
Download or read book The Divergence Theorem and Sets of Finite Perimeter written by Washek F. Pfeffer and published by CRC Press. This book was released on 2016-02-03 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to a detailed development of the divergence theorem. The framework is that of Lebesgue integration- no generalized Riemann integrals of Henstock-Kurzweil variety are involved.In Part I the divergence theorem is established by a combinatorial argument involving dyadic cubes. Only elementary properties of the Lebesgue integral an
Download or read book Weakly Connected Nonlinear Systems written by Anatoly Martynyuk and published by CRC Press. This book was released on 2016-04-19 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Weakly Connected Nonlinear Systems: Boundedness and Stability of Motion provides a systematic study on the boundedness and stability of weakly connected nonlinear systems, covering theory and applications previously unavailable in book form. It contains many essential results needed for carrying out research on nonlinear systems of weakly connected
Download or read book Differential Equations with Maxima written by Drumi D. Bainov and published by CRC Press. This book was released on 2011-04-28 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations with "maxima"-differential equations that contain the maximum of the unknown function over a previous interval-adequately model real-world processes whose present state significantly depends on the maximum value of the state on a past time interval. More and more, these equations model and regulate the behavior of various tec
