Undergraduate Algebra
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| Author | : Serge Lang |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 380 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 1475768982 |
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
| Author | : Matej Brešar |
| Publisher | : Springer |
| Total Pages | : 316 |
| Release | : 2019-05-20 |
| Genre | : Mathematics |
| ISBN | : 9783030140526 |
This textbook offers an innovative approach to abstract algebra, based on a unified treatment of similar concepts across different algebraic structures. This makes it possible to express the main ideas of algebra more clearly and to avoid unnecessary repetition. The book consists of two parts: The Language of Algebra and Algebra in Action. The unified approach to different algebraic structures is a primary feature of the first part, which discusses the basic notions of algebra at an elementary level. The second part is mathematically more complex, covering topics such as the Sylow theorems, modules over principal ideal domains, and Galois theory. Intended for an undergraduate course or for self-study, the book is written in a readable, conversational style, is rich in examples, and contains over 700 carefully selected exercises.
| Author | : Miles Reid |
| Publisher | : Cambridge University Press |
| Total Pages | : 172 |
| Release | : 1995-11-30 |
| Genre | : Mathematics |
| ISBN | : 9780521458894 |
Commutative algebra is at the crossroads of algebra, number theory and algebraic geometry. This textbook is affordable and clearly illustrated, and is intended for advanced undergraduate or beginning graduate students with some previous experience of rings and fields. Alongside standard algebraic notions such as generators of modules and the ascending chain condition, the book develops in detail the geometric view of a commutative ring as the ring of functions on a space. The starting point is the Nullstellensatz, which provides a close link between the geometry of a variety V and the algebra of its coordinate ring A=k[V]; however, many of the geometric ideas arising from varieties apply also to fairly general rings. The final chapter relates the material of the book to more advanced topics in commutative algebra and algebraic geometry. It includes an account of some famous 'pathological' examples of Akizuki and Nagata, and a brief but thought-provoking essay on the changing position of abstract algebra in today's world.
| Author | : Ėrnest Borisovich Vinberg |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 532 |
| Release | : 2003-04-10 |
| Genre | : Mathematics |
| ISBN | : 9780821834138 |
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.
| Author | : Rudolf Lidl |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 500 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 1475729413 |
Accessible to junior and senior undergraduate students, this survey contains many examples, solved exercises, sets of problems, and parts of abstract algebra of use in many other areas of discrete mathematics. Although this is a mathematics book, the authors have made great efforts to address the needs of users employing the techniques discussed. Fully worked out computational examples are backed by more than 500 exercises throughout the 40 sections. This new edition includes a new chapter on cryptology, and an enlarged chapter on applications of groups, while an extensive chapter has been added to survey other applications not included in the first edition. The book assumes knowledge of the material covered in a course on linear algebra and, preferably, a first course in (abstract) algebra covering the basics of groups, rings, and fields.
| Author | : Charles C Pinter |
| Publisher | : Courier Corporation |
| Total Pages | : 402 |
| Release | : 2010-01-14 |
| Genre | : Mathematics |
| ISBN | : 0486474178 |
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.
| Author | : Thomas S. Shores |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 394 |
| Release | : 2007-03-12 |
| Genre | : Mathematics |
| ISBN | : 0387489479 |
This new book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence. Intended for a one-semester course, Applied Linear Algebra and Matrix Analysis places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects. While the flavor is heavily computational and experimental, the text is independent of specific hardware or software platforms. Throughout the book, significant motivating examples are woven into the text, and each section ends with a set of exercises.
| Author | : Thomas W. Hungerford |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 523 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461261015 |
Finally a self-contained, one volume, graduate-level algebra text that is readable by the average graduate student and flexible enough to accommodate a wide variety of instructors and course contents. The guiding principle throughout is that the material should be presented as general as possible, consistent with good pedagogy. Therefore it stresses clarity rather than brevity and contains an extraordinarily large number of illustrative exercises.
| Author | : David R. Finston |
| Publisher | : Springer |
| Total Pages | : 194 |
| Release | : 2014-08-29 |
| Genre | : Mathematics |
| ISBN | : 3319044982 |
This text seeks to generate interest in abstract algebra by introducing each new structure and topic via a real-world application. The down-to-earth presentation is accessible to a readership with no prior knowledge of abstract algebra. Students are led to algebraic concepts and questions in a natural way through their everyday experiences. Applications include: Identification numbers and modular arithmetic (linear) error-correcting codes, including cyclic codes ruler and compass constructions cryptography symmetry of patterns in the real plane Abstract Algebra: Structure and Application is suitable as a text for a first course on abstract algebra whose main purpose is to generate interest in the subject or as a supplementary text for more advanced courses. The material paves the way to subsequent courses that further develop the theory of abstract algebra and will appeal to students of mathematics, mathematics education, computer science, and engineering interested in applications of algebraic concepts.
| Author | : Serge Lang |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 300 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461210704 |
This is a short text in linear algebra, intended for a one-term course. In the first chapter, Lang discusses the relation between the geometry and the algebra underlying the subject, and gives concrete examples of the notions which appear later in the book. He then starts with a discussion of linear equations, matrices and Gaussian elimination, and proceeds to discuss vector spaces, linear maps, scalar products, determinants, and eigenvalues. The book contains a large number of exercises, some of the routine computational type, while others are conceptual.
