applied abstract algebra undergraduate texts in mathematics

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Applied Abstract Algebra

Author : Rudolf Lidl
ISBN : 9781475729412
Genre : Mathematics
File Size : 57. 47 MB
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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.

Abstract Algebra

Author : Ronald Solomon
ISBN : 0821847953
Genre : Mathematics
File Size : 30. 48 MB
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This undergraduate text takes a novel approach to the standard introductory material on groups, rings, and fields. At the heart of the text is a semi-historical journey through the early decades of the subject as it emerged in the revolutionary work of Euler, Lagrange, Gauss, and Galois. Avoiding excessive abstraction whenever possible, the text focuses on the central problem of studying the solutions of polynomial equations. Highlights include a proof of the Fundamental Theorem of Algebra, essentially due to Euler, and a proof of the constructability of the regular 17-gon, in the manner of Gauss. Another novel feature is the introduction of groups through a meditation on the meaning of congruence in the work of Euclid. Everywhere in the text, the goal is to make clear the links connecting abstract algebra to Euclidean geometry, high school algebra, and trigonometry, in the hope that students pursuing a career as secondary mathematics educators will carry away a deeper and richer understanding of the high school mathematics curriculum. Another goal is to encourage students, insofar as possible in a textbook format, to build the course for themselves, with exercises integrally embedded in the text of each chapter.

Undergraduate Algebra

Author : Serge Lang
ISBN : 9780387274751
Genre : Mathematics
File Size : 71. 49 MB
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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

Discrete Mathematics

Author : L. Lovász
ISBN : 0387955852
Genre : Mathematics
File Size : 26. 94 MB
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Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to problems. Numerous examples, figures, and exercises are spread throughout the book.

A First Course In Analysis

Author : George Pedrick
ISBN : 0387941088
Genre : Mathematics
File Size : 27. 40 MB
Format : PDF
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This text on advanced calculus discusses such topics as number systems, the extreme value problem, continuous functions, differentiation, integration and infinite series. The reader will find the focus of attention shifted from the learning and applying of computational techniques to careful reasoning from hypothesis to conclusion. The book is intended both for a terminal course and as preparation for more advanced studies in mathematics, science, engineering and computation.

Topics In Applied Abstract Algebra

Author : S. R. Nagpaul
ISBN : 0821874292
Genre : Mathematics
File Size : 66. 78 MB
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This book presents interesting applications of abstract algebra to practical real-world problems. Especially for those whose interest in algebra is not confined to abstract theory, the text makes the study of abstract algebra more exciting and meaningful. The book is appropriate as either a text for an applied abstract algebra course or as a supplemental text for a standard course in abstract algebra. While fully developed, the algebraic theory presented is just what is required for the applications discussed in the book. This book is included in the Brooks/Cole Series in Advanced Mathematics (Series Editor: Paul Sally, Jr.).

Lineare Algebra

Author : Gilbert Strang
ISBN : 9783642556319
Genre : Mathematics
File Size : 45. 76 MB
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Diese Einführung in die lineare Algebra bietet einen sehr anschaulichen Zugang zum Thema. Die englische Originalausgabe wurde rasch zum Standardwerk in den Anfängerkursen des Massachusetts Institute of Technology sowie in vielen anderen nordamerikanischen Universitäten. Auch hierzulande ist dieses Buch als Grundstudiumsvorlesung für alle Studenten hervorragend lesbar. Darüber hinaus gibt es neue Impulse in der Mathematikausbildung und folgt dem Trend hin zu Anwendungen und Interdisziplinarität. Inhaltlich umfasst das Werk die Grundkenntnisse und die wichtigsten Anwendungen der linearen Algebra und eignet sich hervorragend für Studierende der Ingenieurwissenschaften, Naturwissenschaften, Mathematik und Informatik, die einen modernen Zugang zum Einsatz der linearen Algebra suchen. Ganz klar liegt hierbei der Schwerpunkt auf den Anwendungen, ohne dabei die mathematische Strenge zu vernachlässigen. Im Buch wird die jeweils zugrundeliegende Theorie mit zahlreichen Beispielen aus der Elektrotechnik, der Informatik, der Physik, Biologie und den Wirtschaftswissenschaften direkt verknüpft. Zahlreiche Aufgaben mit Lösungen runden das Werk ab.

Abstract Algebra

Author : Clive Reis
ISBN : 9789814335645
Genre : Mathematics
File Size : 20. 89 MB
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Suitable for second to fourth year undergraduates, this title contains several applications: Polya-Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space.

Applied Linear Algebra And Matrix Analysis

Author : Thomas S. Shores
ISBN : 0387331956
Genre : Mathematics
File Size : 52. 92 MB
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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. The student will develop a solid foundation in the following topics *Gaussian elimination and other operations with matrices *basic properties of matrix and determinant algebra *standard Euclidean spaces, both real and complex *geometrical aspects of vectors, such as norm, dot product, and angle *eigenvalues, eigenvectors, and discrete dynamical systems *general norm and inner-product concepts for abstract vector spaces For many students, the tools of matrix and linear algebra will be as fundamental in their professional work as the tools of calculus; thus it is important to ensure that students appreciate the utility and beauty of these subjects as well as the mechanics. By including applied mathematics and mathematical modeling, this new textbook will teach students how concepts of matrix and linear algebra make concrete problems workable. Thomas S. Shores is Professor of Mathematics at the University of Nebraska, Lincoln, where he has received awards for his teaching. His research touches on group theory, commutative algebra, mathematical modeling, numerical analysis, and inverse theory.

Exploring Abstract Algebra With Mathematica

Author : Allen C. Hibbard
ISBN : 0387986197
Genre : Computers
File Size : 28. 14 MB
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This work is intended as an upper-division laboratory supplement for courses in abstract algebra. It consists of several Mathematica packages that the authors have programmed as a foundation with two collections of labs for group theory and ring theory built on this base. Additionally, there is a "users guide" which illustrates the functionality of the underlying code. The lab portion of the book reflects the contents of the Mathematica-based electronic notebooks. Students interact with both the printed and electronic versions of the material in the laboratory, and the students can look up details and reference information in the Users Guide. Exercises occur in the stream of the text of the lab, which provides a context within which to answer. Questions are designed so that they either be written into the electronic notebook, or on paper, whichever the instructor prefers. The notebooks are available for all versions of Mathematica and run across all platforms for which Mathematica exists. Exploring Abstract Algebra with Mathematica is a very timely addition to the undergraduate abstract algebra curriculum. This work is unique, filling a tremendous void in the literature. It offers an environment for studying algebraic structures using Mathematica, to write computer labs in which students can explore the ideas in abstract algebra computationally and visually, and it provides a Users Guide for the data structures and commands of this package. Flexibility of use, and the intention of the authors to make this work highly visual, e.g., with the inclusion of a fullcolor insert of significant algebraic concepts/images, make this publication pedagogically useful to both instructors and students alike. For more information on the underlying software packages, please go to the website

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