concrete abstract algebra from numbers to grobner bases

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Concrete Abstract Algebra

Author : Niels Lauritzen
ISBN : 0521534100
Genre : Mathematics
File Size : 39. 65 MB
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This 2003 book presents abstract algebra based on concrete examples and applications. All the traditional material with exciting directions.

Concrete Abstract Algebra

Author : Niels Lauritzen
ISBN : 9781139936613
Genre : Mathematics
File Size : 54. 61 MB
Format : PDF, ePub, Mobi
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Concrete Abstract Algebra develops the theory of abstract algebra from numbers to Gröbner bases, whilst taking in all the usual material of a traditional introductory course. In addition there is a rich supply of topics like cryptography, factoring algorithms for integers, quadratic residues, finite fields, factoring algorithms for polynomials and systems of non-linear equations. A special feature is that Gröbner bases do not appear as an isolated example. They are fully integrated as a subject that can be successfully taught in an undergraduate context. Lauritzen's approach to teaching abstract algebra is based on an extensive use of examples, applications and exercises. The basic philosophy is that inspiring, non-trivial applications and examples give motivation and ease the learning of abstract concepts. This book is built on several years of experience teaching introductory abstract algebra at Aarhus, where the emphasis on concrete and inspiring examples has improved student performance significantly. Solutions to the exercises are available to lecturers from [email protected]

Concrete Abstract Algebra

Author : Niels Lauritzen
ISBN : 0521826799
Genre : Mathematics
File Size : 86. 2 MB
Format : PDF
Download : 672
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Concrete Abstract Algebra develops the theory of abstract algebra from numbers to Gr"obner bases, while takin in all the usual material of a traditional introductory course. In addition, there is a rich supply of topics such as cryptography, factoring algorithms for integers, quadratic residues, finite fields, factoring algorithms for polynomials, and systems of non-linear equations. A special feature is that Gr"obner bases do not appear as an isolated example. They are fully integrated as a subject that can be successfully taught in an undergraduate context. Lauritzen's approach to teaching abstract algebra is based on an extensive use of examples, applications, and exercises. The basic philosophy is that inspiring, non-trivial applications and examples give motivation and ease the learning of abstract concepts. This book is built on several years of experienced teaching introductory abstract algebra at Aarhus, where the emphasis on concrete and inspiring examples has improved student performance significantly.

E Study Guide For Concrete Abstract Algebra From Numbers To Grobner Bases By Niels Lauritzen Isbn 9780521826792

Author : Cram101 Textbook Reviews
ISBN : 9781478401056
Genre : Education
File Size : 52. 6 MB
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Never Highlight a Book Again! Just the FACTS101 study guides give the student the textbook outlines, highlights, practice quizzes and optional access to the full practice tests for their textbook.

Gr Bner Bases

Author : Thomas Becker
ISBN : 9781461209133
Genre : Mathematics
File Size : 45. 56 MB
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The origins of the mathematics in this book date back more than two thou sand years, as can be seen from the fact that one of the most important algorithms presented here bears the name of the Greek mathematician Eu clid. The word "algorithm" as well as the key word "algebra" in the title of this book come from the name and the work of the ninth-century scientist Mohammed ibn Musa al-Khowarizmi, who was born in what is now Uzbek istan and worked in Baghdad at the court of Harun al-Rashid's son. The word "algorithm" is actually a westernization of al-Khowarizmi's name, while "algebra" derives from "al-jabr," a term that appears in the title of his book Kitab al-jabr wa'l muqabala, where he discusses symbolic methods for the solution of equations. This close connection between algebra and al gorithms lasted roughly up to the beginning of this century; until then, the primary goal of algebra was the design of constructive methods for solving equations by means of symbolic transformations. During the second half of the nineteenth century, a new line of thought began to enter algebra from the realm of geometry, where it had been successful since Euclid's time, namely, the axiomatic method.

An Introduction To Gr Bner Bases

Author : Ralf Fröberg
ISBN : 0471974420
Genre : Mathematics
File Size : 26. 38 MB
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As algebra becomes more widely used in a variety of applicationsand computers are developed to allow efficient calculations in thefield, so there becomes a need for new techniques to further thisarea of research. Gröbner Bases is one topic which hasrecently become a very popular and important area of modernalgebra. This book provides a concrete introduction to commutativealgebra through Gröbner Bases. The inclusion of exercises,lists of further reading and related literature make this apractical approach to introducing Gröbner Bases. The authorpresents new concepts and results of recent research in the areaallowing students and researchers in technology, computer scienceand mathematics to gain a basic understanding of the technique. Afirst course in algebra is the only prior knowledge required forthis introduction. Chapter titles include: * Monomial ldeas * Gröbner Bases * Algebraic Sets * Solving Systems of Polynomial Equations * Applications of Gröbner Bases * Homogeneous Algebra * Hilbert Series * Variations of Gröbner Bases * Improvements to Buchberger's Algorithms * Software

Introduction To Algebraic Geometry

Author : Brendan Hassett
ISBN : 9781139464598
Genre : Mathematics
File Size : 80. 90 MB
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Algebraic geometry, central to pure mathematics, has important applications in such fields as engineering, computer science, statistics and computational biology, which exploit the computational algorithms that the theory provides. Users get the full benefit, however, when they know something of the underlying theory, as well as basic procedures and facts. This book is a systematic introduction to the central concepts of algebraic geometry most useful for computation. Written for advanced undergraduate and graduate students in mathematics and researchers in application areas, it focuses on specific examples and restricts development of formalism to what is needed to address these examples. In particular, it introduces the notion of Gröbner bases early on and develops algorithms for almost everything covered. It is based on courses given over the past five years in a large interdisciplinary programme in computational algebraic geometry at Rice University, spanning mathematics, computer science, biomathematics and bioinformatics.

A Concrete Approach To Abstract Algebra Student Solutions Manual E Only

Author : Jeffrey Bergen
ISBN : 0123846811
Genre : Mathematics
File Size : 75. 11 MB
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A Concrete Approach to Abstract Algebra begins with a concrete and thorough examination of familiar objects like integers, rational numbers, real numbers, complex numbers, complex conjugation and polynomials, in this unique approach, the author builds upon these familar objects and then uses them to introduce and motivate advanced concepts in algebra in a manner that is easier to understand for most students. The text will be of particular interest to teachers and future teachers as it links abstract algebra to many topics wich arise in courses in algebra, geometry, trigonometry, precalculus and calculus. The final four chapters present the more theoretical material needed for graduate study.

Gr Bner Bases In Commutative Algebra

Author : Viviana Ene
ISBN : 9780821872871
Genre : Mathematics
File Size : 54. 47 MB
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This book provides a concise yet comprehensive and self-contained introduction to Grobner basis theory and its applications to various current research topics in commutative algebra. It especially aims to help young researchers become acquainted with fundamental tools and techniques related to Grobner bases which are used in commutative algebra and to arouse their interest in exploring further topics such as toric rings, Koszul and Rees algebras, determinantal ideal theory, binomial edge ideals, and their applications to statistics. The book can be used for graduate courses and self-study. More than 100 problems will help the readers to better understand the main theoretical results and will inspire them to further investigate the topics studied in this book.

A Singular Introduction To Commutative Algebra

Author : Gert-Martin Greuel
ISBN : 9783662049631
Genre : Mathematics
File Size : 28. 99 MB
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This book can be understood as a model for teaching commutative algebra, and takes into account modern developments such as algorithmic and computational aspects. As soon as a new concept is introduced, the authors show how the concept can be worked on using a computer. The computations are exemplified with the computer algebra system Singular, developed by the authors. Singular is a special system for polynomial computation with many features for global as well as for local commutative algebra and algebraic geometry. The book includes a CD containing Singular as well as the examples and procedures explained in the book.

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