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Classical Abstract Algebra
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Book Synopsis A Book of Abstract Algebra by : Charles C Pinter
Download or read book A Book of Abstract Algebra written by Charles C Pinter and published by Courier Corporation. This book was released on 2010-01-14 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
Book Synopsis Classical Abstract Algebra by : Richard A. Dean
Download or read book Classical Abstract Algebra written by Richard A. Dean and published by HarperCollins Publishers. This book was released on 1990 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: A text designed in two parts. The first introduces the main concepts and constructs and requires only the facility gained from a good course in high school algebra II or from a standard course in calculus. The second part discusses topics of intermediate sophistication which are often contained in first-year graduate courses in algebra. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis A History of Abstract Algebra by : Israel Kleiner
Download or read book A History of Abstract Algebra written by Israel Kleiner and published by Springer Science & Business Media. This book was released on 2007-10-02 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the history of abstract algebra. It shows how abstract algebra has arisen in attempting to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved.
Book Synopsis Elements of Abstract Algebra by : Allan Clark
Download or read book Elements of Abstract Algebra written by Allan Clark and published by Courier Corporation. This book was released on 2012-07-06 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lucid coverage of the major theories of abstract algebra, with helpful illustrations and exercises included throughout. Unabridged, corrected republication of the work originally published 1971. Bibliography. Index. Includes 24 tables and figures.
Book Synopsis Groups and Characters by : Larry C. Grove
Download or read book Groups and Characters written by Larry C. Grove and published by John Wiley & Sons. This book was released on 2011-09-26 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authoritative, full-year course on both group theory and ordinary character theory--essential tools for mathematics and the physical sciences One of the few treatments available combining both group theory and character theory, Groups and Characters is an effective general textbook on these two fundamentally connected subjects. Presuming only a basic knowledge of abstract algebra as in a first-year graduate course, the text opens with a review of background material and then guides readers carefully through several of the most important aspects of groups and characters, concentrating mainly on finite groups. Challenging yet accessible, Groups and Characters features: * An extensive collection of examples surveying many different types of groups, including Sylow subgroups of symmetric groups, affine groups of fields, the Mathieu groups, and symplectic groups * A thorough, easy-to-follow discussion of Polya-Redfield enumeration, with applications to combinatorics * Inclusive explorations of the transfer function and normal complements, induction and restriction of characters, Clifford theory, characters of symmetric and alternating groups, Frobenius groups, and the Schur index * Illuminating accounts of several computational aspects of group theory, such as the Schreier-Sims algorithm, Todd-Coxeter coset enumeration, and algorithms for generating character tables As valuable as Groups and Characters will prove as a textbook for mathematicians, it has broader applications. With chapters suitable for use as independent review units, along with a full bibliography and index, it will be a dependable general reference for chemists, physicists, and crystallographers.
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 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: Great book! The author's teaching experinece shows in every chapter. --Efim Zelmanov, University of California, San Diego Vinberg has written an algebra book that is excellent, both as a classroom text or for self-study. It is plain that years of teaching abstract algebra have enabled him to say the right thing at the right time. --Irving Kaplansky, MSRI This is a comprehensive text on modern algebra written for advanced undergraduate and basic graduate algebra classes. The book is based on courses taught by the author at the Mechanics and Mathematics Department of Moscow State University and at the Mathematical College of the Independent University of Moscow. The unique feature of the book is that it contains almost no technically difficult proofs. Following his point of view on mathematics, the author tried, whenever possible, to replace calculations and difficult deductions with conceptual proofs and to associate geometric images to algebraic objects. Another important feature is that the book presents most of the topics on several levels, allowing the student to move smoothly from initial acquaintance to thorough study and deeper understanding of the subject. Presented are basic topics in algebra such as algebraic structures, linear algebra, polynomials, groups, as well as more advanced topics like affine and projective spaces, tensor algebra, Galois theory, Lie groups, associative algebras and their representations. Some applications of linear algebra and group theory to physics are discussed. Written with extreme care and supplied with more than 200 exercises and 70 figures, the book is also an excellent text for independent study.
Book Synopsis Exercises in Classical Ring Theory by : T.Y. Lam
Download or read book Exercises in Classical Ring Theory written by T.Y. Lam and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based in large part on the comprehensive "First Course in Ring Theory" by the same author, this book provides a comprehensive set of problems and solutions in ring theory that will serve not only as a teaching aid to instructors using that book, but also for students, who will see how ring theory theorems are applied to solving ring-theoretic problems and how good proofs are written. The author demonstrates that problem-solving is a lively process: in "Comments" following many solutions he discusses what happens if a hypothesis is removed, whether the exercise can be further generalized, what would be a concrete example for the exercise, and so forth. The book is thus much more than a solution manual.
Book Synopsis A History of Abstract Algebra by : Israel Kleiner
Download or read book A History of Abstract Algebra written by Israel Kleiner and published by Springer Science & Business Media. This book was released on 2007-09-20 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book does nothing less than provide an account of the intellectual lineage of abstract algebra. The development of abstract algebra was propelled by the need for new tools to address certain classical problems that appeared insoluble by classical means. A major theme of the book is to show how abstract algebra has arisen in attempting to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved. Mathematics instructors, algebraists, and historians of science will find the work a valuable reference.
Book Synopsis Classical Algebra by : Roger L. Cooke
Download or read book Classical Algebra written by Roger L. Cooke and published by John Wiley & Sons. This book was released on 2008-05-16 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This insightful book combines the history, pedagogy, and popularization of algebra to present a unified discussion of the subject. Classical Algebra provides a complete and contemporary perspective on classical polynomial algebra through the exploration of how it was developed and how it exists today. With a focus on prominent areas such as the numerical solutions of equations, the systematic study of equations, and Galois theory, this book facilitates a thorough understanding of algebra and illustrates how the concepts of modern algebra originally developed from classical algebraic precursors. This book successfully ties together the disconnect between classical and modern algebraand provides readers with answers to many fascinating questions that typically go unexamined, including: What is algebra about? How did it arise? What uses does it have? How did it develop? What problems and issues have occurred in its history? How were these problems and issues resolved? The author answers these questions and more, shedding light on a rich history of the subject—from ancient and medieval times to the present. Structured as eleven "lessons" that are intended to give the reader further insight on classical algebra, each chapter contains thought-provoking problems and stimulating questions, for which complete answers are provided in an appendix. Complemented with a mixture of historical remarks and analyses of polynomial equations throughout, Classical Algebra: Its Nature, Origins, and Uses is an excellent book for mathematics courses at the undergraduate level. It also serves as a valuable resource to anyone with a general interest in mathematics.
Book Synopsis A Classical Introduction to Modern Number Theory by : Kenneth Ireland
Download or read book A Classical Introduction to Modern Number Theory written by Kenneth Ireland and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: This well-developed, accessible text details the historical development of the subject throughout. It also provides wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. This second edition contains two new chapters that provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers and an overview of recent progress on the arithmetic of elliptic curves.
Book Synopsis Abstract Algebra by : Gregory T. Lee
Download or read book Abstract Algebra written by Gregory T. Lee and published by Springer. This book was released on 2018-04-13 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields. The first two chapters present preliminary topics such as properties of the integers and equivalence relations. The author then explores the first major algebraic structure, the group, progressing as far as the Sylow theorems and the classification of finite abelian groups. An introduction to ring theory follows, leading to a discussion of fields and polynomials that includes sections on splitting fields and the construction of finite fields. The final part contains applications to public key cryptography as well as classical straightedge and compass constructions. Explaining key topics at a gentle pace, this book is aimed at undergraduate students. It assumes no prior knowledge of the subject and contains over 500 exercises, half of which have detailed solutions provided.
Book Synopsis Modern Classical Homotopy Theory by : Jeffrey Strom
Download or read book Modern Classical Homotopy Theory written by Jeffrey Strom and published by American Mathematical Society. This book was released on 2023-01-19 with total page 862 pages. Available in PDF, EPUB and Kindle. Book excerpt: The core of classical homotopy theory is a body of ideas and theorems that emerged in the 1950s and was later largely codified in the notion of a model category. This core includes the notions of fibration and cofibration; CW complexes; long fiber and cofiber sequences; loop spaces and suspensions; and so on. Brown's representability theorems show that homology and cohomology are also contained in classical homotopy theory. This text develops classical homotopy theory from a modern point of view, meaning that the exposition is informed by the theory of model categories and that homotopy limits and colimits play central roles. The exposition is guided by the principle that it is generally preferable to prove topological results using topology (rather than algebra). The language and basic theory of homotopy limits and colimits make it possible to penetrate deep into the subject with just the rudiments of algebra. The text does reach advanced territory, including the Steenrod algebra, Bott periodicity, localization, the Exponent Theorem of Cohen, Moore, and Neisendorfer, and Miller's Theorem on the Sullivan Conjecture. Thus the reader is given the tools needed to understand and participate in research at (part of) the current frontier of homotopy theory. Proofs are not provided outright. Rather, they are presented in the form of directed problem sets. To the expert, these read as terse proofs; to novices they are challenges that draw them in and help them to thoroughly understand the arguments.
Book Synopsis Basic Abstract Algebra by : Robert B. Ash
Download or read book Basic Abstract Algebra written by Robert B. Ash and published by Courier Corporation. This book was released on 2013-06-17 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Relations between groups and sets, results and methods of abstract algebra in terms of number theory and geometry, and noncommutative and homological algebra. Solutions. 2006 edition.
Book Synopsis Abstract Algebra by : John W. Lawrence
Download or read book Abstract Algebra written by John W. Lawrence and published by Cambridge University Press. This book was released on 2021-04-15 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through this book, upper undergraduate mathematics majors will master a challenging yet rewarding subject, and approach advanced studies in algebra, number theory and geometry with confidence. Groups, rings and fields are covered in depth with a strong emphasis on irreducible polynomials, a fresh approach to modules and linear algebra, a fresh take on Gröbner theory, and a group theoretic treatment of Rejewski's deciphering of the Enigma machine. It includes a detailed treatment of the basics on finite groups, including Sylow theory and the structure of finite abelian groups. Galois theory and its applications to polynomial equations and geometric constructions are treated in depth. Those interested in computations will appreciate the novel treatment of division algorithms. This rigorous text 'gets to the point', focusing on concisely demonstrating the concept at hand, taking a 'definitions first, examples next' approach. Exercises reinforce the main ideas of the text and encourage students' creativity.
Book Synopsis Representations and Invariants of the Classical Groups by : Roe Goodman
Download or read book Representations and Invariants of the Classical Groups written by Roe Goodman and published by Cambridge University Press. This book was released on 2000-01-13 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: More than half a century has passed since Weyl's 'The Classical Groups' gave a unified picture of invariant theory. This book presents an updated version of this theory together with many of the important recent developments. As a text for those new to the area, this book provides an introduction to the structure and finite-dimensional representation theory of the complex classical groups that requires only an abstract algebra course as a prerequisite. The more advanced reader will find an introduction to the structure and representations of complex reductive algebraic groups and their compact real forms. This book will also serve as a reference for the main results on tensor and polynomial invariants and the finite-dimensional representation theory of the classical groups. It will appeal to researchers in mathematics, statistics, physics and chemistry whose work involves symmetry groups, representation theory, invariant theory and algebraic group theory.
Book Synopsis Undergraduate Algebra by : Serge Lang
Download or read book Undergraduate Algebra written by Serge Lang and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The companion title, Linear Algebra, has sold over 8,000 copies The writing style is very accessible The material can be covered easily in a one-year or one-term course Includes Noah Snyder's proof of the Mason-Stothers polynomial abc theorem New material included on product structure for matrices including descriptions of the conjugation representation of the diagonal group
Book Synopsis Algebra: Chapter 0 by : Paolo Aluffi
Download or read book Algebra: Chapter 0 written by Paolo Aluffi and published by American Mathematical Soc.. This book was released on 2021-11-09 with total page 713 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.
