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Selected Topics In Algebra
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Book Synopsis Universal Algebra by : Clifford Bergman
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 Mathematics++ written by Ida Kantor and published by American Mathematical Soc.. This book was released on 2015-08-27 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics++ is a concise introduction to six selected areas of 20th century mathematics providing numerous modern mathematical tools used in contemporary research in computer science, engineering, and other fields. The areas are: measure theory, high-dimensional geometry, Fourier analysis, representations of groups, multivariate polynomials, and topology. For each of the areas, the authors introduce basic notions, examples, and results. The presentation is clear and accessible, stressing intuitive understanding, and it includes carefully selected exercises as an integral part. Theory is complemented by applications--some quite surprising--in theoretical computer science and discrete mathematics. The chapters are independent of one another and can be studied in any order. It is assumed that the reader has gone through the basic mathematics courses. Although the book was conceived while the authors were teaching Ph.D. students in theoretical computer science and discrete mathematics, it will be useful for a much wider audience, such as mathematicians specializing in other areas, mathematics students deciding what specialization to pursue, or experts in engineering or other fields.
Book Synopsis Topics in Algebra by : I. N. Herstein
Download or read book Topics in Algebra written by I. N. Herstein and published by John Wiley & Sons. This book was released on 1991-01-16 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: New edition includes extensive revisions of the material on finite groups and Galois Theory. New problems added throughout.
Book Synopsis Categorical Foundations by : Maria Cristina Pedicchio
Download or read book Categorical Foundations written by Maria Cristina Pedicchio and published by Cambridge University Press. This book was released on 2004 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description
Book Synopsis Some Topics in Algebra by : Michel Broué
Download or read book Some Topics in Algebra written by Michel Broué and published by Springer Science & Business Media. This book was released on 2013-10-29 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the springs of 2011 and 2012, the author was invited by Peking University to give an advanced undergraduate algebra course (once a week over two months each year). This book was written during and for that course. By no way does it claim to be too exhaustive. It was originally intended as a brief introduction to algebra for an extremely pleasant and passionate audience. It certainly reflects some of the author’s own tastes, and it was influenced by the feelings and the reactions of the students. Nevertheless, the result covers some advanced undergraduate algebra (rings, ideals, basics of fields theory, algebraic integers, modules, hom and tensor functors, projective modules, etc.) illustrated by numerous examples, counterexamples and exercises. Following a worldwide tradition, the author had planned to conclude by lecturing on the structure of finitely generated modules over principal ideal domains. But during the course, after explaining that the notion of projective modules is more natural than the notion of free modules, it became clear that principal ideal domains needed to be replaced by Dedekind rings; this is much less traditional in the literature — but not more difficult.
Book Synopsis TOPICS IN ALGEBRA, 2ND ED by : I.N.Herstein
Download or read book TOPICS IN ALGEBRA, 2ND ED written by I.N.Herstein and published by John Wiley & Sons. This book was released on 2006 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: About The Book: This book on algebra includes extensive revisions of the material on finite groups and Galois Theory. Further more the book also contains new problems relating to Algebra.
Book Synopsis Certain Number-Theoretic Episodes In Algebra, Second Edition by : R Sivaramakrishnan
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 444 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.
Book Synopsis Advanced Topics in Linear Algebra by : Kevin O'Meara
Download or read book Advanced Topics in Linear Algebra written by Kevin O'Meara and published by OUP USA. This book was released on 2011-09-16 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops the Weyr matrix canonical form, a largely unknown cousin of the Jordan form. It explores novel applications, including include matrix commutativity problems, approximate simultaneous diagonalization, and algebraic geometry. Module theory and algebraic geometry are employed but with self-contained accounts.
Book Synopsis A Course in Algebra by : Ėrnest Borisovich Vinberg
Download or read book A Course in Algebra written by Ėrnest Borisovich Vinberg and published by American Mathematical Soc.. This book was released on 2003-04-10 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents modern algebra. This book includes such topics as affine and projective spaces, tensor algebra, Galois theory, Lie groups, and associative algebras and their representations. It is suitable for independent study for advanced undergraduates and graduate students.
Download or read book Modern Algebra written by Seth Warner and published by Courier Corporation. This book was released on 2012-08-29 with total page 852 pages. Available in PDF, EPUB and Kindle. Book excerpt: Standard text provides an exceptionally comprehensive treatment of every aspect of modern algebra. Explores algebraic structures, rings and fields, vector spaces, polynomials, linear operators, much more. Over 1,300 exercises. 1965 edition.
Download or read book Abstract Algebra written by Thomas Judson and published by Orthogonal Publishing L3c. This book was released on 2023-08-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract Algebra: Theory and Applications is an open-source textbook that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many non-trivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.
Book Synopsis Selected Exercises in Algebra by : Rocco Chirivì
Download or read book Selected Exercises in Algebra written by Rocco Chirivì and published by Springer Nature. This book was released on 2020-01-29 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the first of two volumes, contains over 250 selected exercises in Algebra which have featured as exam questions for the Arithmetic course taught by the authors at the University of Pisa. Each exercise is presented together with one or more solutions, carefully written with consistent language and notation. A distinguishing feature of this book is the fact that each exercise is unique and requires some creative thinking in order to be solved. The themes covered in this volume are: mathematical induction, combinatorics, modular arithmetic, Abelian groups, commutative rings, polynomials, field extensions, finite fields. The book includes a detailed section recalling relevant theory which can be used as a reference for study and revision. A list of preliminary exercises introduces the main techniques to be applied in solving the proposed exam questions. This volume is aimed at first year students in Mathematics and Computer Science.
Book Synopsis Linear Algebra and Matrices by : Helene Shapiro
Download or read book Linear Algebra and Matrices written by Helene Shapiro and published by American Mathematical Soc.. This book was released on 2015-10-08 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear algebra and matrix theory are fundamental tools for almost every area of mathematics, both pure and applied. This book combines coverage of core topics with an introduction to some areas in which linear algebra plays a key role, for example, block designs, directed graphs, error correcting codes, and linear dynamical systems. Notable features include a discussion of the Weyr characteristic and Weyr canonical forms, and their relationship to the better-known Jordan canonical form; the use of block cyclic matrices and directed graphs to prove Frobenius's theorem on the structure of the eigenvalues of a nonnegative, irreducible matrix; and the inclusion of such combinatorial topics as BIBDs, Hadamard matrices, and strongly regular graphs. Also included are McCoy's theorem about matrices with property P, the Bruck-Ryser-Chowla theorem on the existence of block designs, and an introduction to Markov chains. This book is intended for those who are familiar with the linear algebra covered in a typical first course and are interested in learning more advanced results.
Book Synopsis Selected topics in discrete mathematics: Proceedings of the Moscow Discrete Mathematics Seminar, 1972-1990 by : Alexander K. Kelmans
Download or read book Selected topics in discrete mathematics: Proceedings of the Moscow Discrete Mathematics Seminar, 1972-1990 written by Alexander K. Kelmans and published by American Mathematical Soc.. This book was released on 1994-02-18 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of translations of a variety of papers on discrete mathematics by members of the Moscow Seminar on Discrete Mathematics. This seminar, begun in 1972, was marked by active participation and intellectual ferment. Mathematicians in the USSR often encountered difficulties in publishing, so many interesting results in discrete mathematics remained unknown in the West for some years, and some are unknown even to the present day. To help fill this communication gap, this collection offers papers that were obscurely published and very hard to find. Among the topics covered here are: graph theory, network flow and multicommodity flow, linear programming and combinatorial optimization, matroid theory and submodular systems, matrix theory and combinatorics, parallel computing, complexity of algorithms, random graphs and statistical mechanics, coding theory, and algebraic combinatorics and group theory.
Book Synopsis Introduction To Commutative Algebra by : Michael F. Atiyah
Download or read book Introduction To Commutative Algebra written by Michael F. Atiyah and published by CRC Press. This book was released on 2018-03-09 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Published in 2018. This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization.
Book Synopsis Selected Topics in the Teaching of Mathematics by : National Council of Teachers of Mathematics
Download or read book Selected Topics in the Teaching of Mathematics written by National Council of Teachers of Mathematics and published by . This book was released on 1928 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fundamental Concepts of Algebra by : Bruce Elwyn Meserve
Download or read book Fundamental Concepts of Algebra written by Bruce Elwyn Meserve and published by Courier Corporation. This book was released on 1982-01-01 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncommonly interesting introduction illuminates complexities of higher mathematics while offering a thorough understanding of elementary mathematics. Covers development of complex number system and elementary theories of numbers, polynomials and operations, determinants, matrices, constructions and graphical representations. Several exercises — without solutions.
