Applied Algebra for the Computer Sciences (Prentice-Hall series in automatic computation) (Hardcover) ~ Grimaldi R.Details
# Hardcover: 416 pages # Publisher: Pearson Education Australia (February 1976) # Language: English # ISBN-10: 0130392227 # ISBN-13: 978-0130392220Description
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Tensors in Image Processing and Computer Vision (Advances in Pattern Recognition) (Hardcover)
~ Aja-Fernandez S., et al.
# Hardcover: 470 pages
# Publisher: Springer; 1 edition (July 14, 2009)
# Language: English
# ISBN-10: 1848822987
# ISBN-13: 978-1848822986
Tensor signal processing is an emerging field with important applications to computer vision and image processing.
This book presents the state of the art in this new branch of signal processing, offering a great deal of research and discussions by leading experts in the area. The wide-ranging volume offers an overview into cutting-edge research into the newest tensor processing techniques and their application to different domains related to computer vision and image processing.
This comprehensive text will prove to be an invaluable reference and resource for researchers, practitioners and advanced students working in the area of computer vision and image processing.
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Integers, Polynomials, and Rings: A Course in Algebra (Undergraduate Texts in Mathematics) (Hardcover)
~ Irving R.
# Hardcover: 284 pages
# Publisher: Springer; 1 edition (January 8, 2004)
# Language: English
# ISBN-10: 0387403973
# ISBN-13: 978-0387403977
Mathematics is often regarded as the study of calculation, but in fact, mathematics is much more. It combines creativity and logic in order to arrive at abstract truths. This book is intended to illustrate how calculation, creativity, and logic can be combined to solve a range of problems in algebra. Originally conceived as a text for a course for future secondary-school mathematics teachers, this book has developed into one that could serve well in an undergraduate course in abstract algebra or a course designed as an introduction to higher mathematics. Not all topics in a traditional algebra course are covered. Rather, the author focuses on integers, polynomials, their ring structure, and fields, with the aim that students master a small number of serious mathematical ideas. The topics studied should be of interest to all mathematics students and are especially appropriate for future teachers.
One nonstandard feature of the book is the small number of theorems for which full proofs are given. Many proofs are left as exercises, and for almost every such exercise a detailed hint or outline of the proof is provided. These exercises form the heart of the text. Unwinding the meaning of the hint or outline can be a significant challenge, and the unwinding process serves as the catalyst for learning.
Ron Irving is the Divisional Dean of Natural Sciences at the University of Washington. Prior to assuming this position, he served as Chair of the Department of Mathematics. He has published research articles in several areas of algebra, including ring theory and the representation theory of Lie groups and Lie algebras. In 2001, he received the University of Washington's Distinguished Teaching Award for the course on which this book is based.
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Topics in Algebra (Paperback)
# Paperback: 400 pages
# Publisher: Wiley; 2 edition (June 20, 1975)
# Language: English
# ISBN-10: 0471010901
# ISBN-13: 978-0471010906
New edition includes extensive revisions of the material on finite groups and Galois Theory. New problems added throughout.
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Algebras, Rings and Modules: Volume 2 (Mathematics and Its Applications) (Hardcover)
~ Michiel Hazewinkel (Author), Nadiya Gubareni (Author), V.V. Kirichenko (Author)
# Hardcover: 400 pages
# Publisher: Springer; 1 edition (October 23, 2007)
# Language: English
# ISBN-10: 1402051409
# ISBN-13: 978-1402051401
As a natural continuation of the first volume of Algebras, Rings and Modules, this book provides both the classical aspects of the theory of groups and their representations as well as a general introduction to the modern theory of representations including the representations of quivers and finite partially ordered sets and their applications to finite dimensional algebras.
Detailed attention is given to special classes of algebras and rings including Frobenius, quasi-Frobenius, right serial rings and tiled orders using the technique of quivers. The most important recent developments in the theory of these rings are examined.
The Cartan Determinant Conjecture and some properties of global dimensions of different classes of rings are also given. The last chapters of this volume provide the theory of semiprime Noetherian semiperfect and semidistributive rings.
Of course, this book is mainly aimed at researchers in the theory of rings and algebras but graduate and postgraduate students, especially those using algebraic techniques, should also find this book of interest.
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Algebras, Rings and Modules: Volume 1 (Mathematics and Its Applications) (Hardcover)
~ Michiel Hazewinkel (Author), Nadiya Gubareni (Author)
# Hardcover: 380 pages
# Publisher: Springer; 1 edition (December 20, 2004)
# Language: English
# ISBN-10: 1402026900
# ISBN-13: 978-1402026904
The text of the first volume of the book covers the major topics in ring and module theory and includes both fundamental classical results and more recent developments. The basic tools of investigation are methods from the theory of modules, which allow a very simple and clear approach both to classical and new results. An unusual main feature of this book is the use of the technique of quivers for studying the structure of rings. A considerable part of the first volume of the book is devoted to a study of special classes of rings and algebras, such as serial rings, hereditary rings, semidistributive rings and tiled orders. Many results of this text until now have been available in journal articles only.
This book is aimed at graduate and post-graduate students and for all mathematicians who use algebraic techniques in their work.
This is a self-contained book which is intended to be a modern textbook on the structure theory of associative rings and algebras and is suitable for independent study.
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A radical approach to algebra (Addison-Wesley series in mathematics) (Hardcover)
~ Mary W Gray (Author)
# Hardcover: 232 pages
# Publisher: Addison-Wesley Pub. Co (1970)
# Language: English
# ASIN: B0006CK840
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Modern Algebra with Applications (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts) by William J. Gilbert and W. Keith Nicholson
# Hardcover: 352 pages
# Publisher: Wiley-Interscience; 2 edition (November 5, 2003)
# Language: English
# ISBN-10: 0471414514
# ISBN-13: 978-0471414513
Praise for the first edition
"This book is clearly written and presents a large number of examples illustrating the theory . . . there is no other book of comparable content available. Because of its detailed coverage of applications generally neglected in the literature, it is a desirable if not essential addition to undergraduate mathematics and computer science libraries."
–CHOICE
As a cornerstone of mathematical science, the importance of modern algebra and discrete structures to many areas of science and technology is apparent and growing–with extensive use in computing science, physics, chemistry, and data communications as well as in areas of mathematics such as combinatorics.
Blending the theoretical with the practical in the instruction of modern algebra, Modern Algebra with Applications, Second Edition provides interesting and important applications of this subject–effectively holding your interest and creating a more seamless method of instruction.
Incorporating the applications of modern algebra throughout its authoritative treatment of the subject, this book covers the full complement of group, ring, and field theory typically contained in a standard modern algebra course. Numerous examples are included in each chapter, and answers to odd-numbered exercises are appended in the back of the text.
Chapter topics include:
* Boolean Algebras
* Polynomial and Euclidean Rings
* Groups
* Quotient Rings
* Quotient Groups
* Field Extensions
* Symmetry Groups in Three Dimensions
* Latin Squares
* Pólya—Burnside Method of Enumeration
* Geometrical Constructions
* Monoids and Machines
* Error-Correcting Codes
* Rings and Fields
In addition to improvements in exposition, this fully updated Second Edition also contains new material on order of an element and cyclic groups, more details about the lattice of divisors of an integer, and new historical notes.
Filled with in-depth insights and over 600 exercises of varying difficulty, Modern Algebra with Applications, Second Edition can help anyone appreciate and understand this subject.
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Contemporary Abstract Algebra (Hardcover)
~ Joseph Gallian (Author)
# Hardcover: 574 pages
# Publisher: Brooks Cole; 7 edition (January 8, 2009)
# Language: English
# ISBN-10: 0547165099
# ISBN-13: 978-0547165097
Contemporary Abstract Algebra 7e, written by Joseph Gallian, a well-known active researcher and award-winning teacher upholds the text's reputation for providing students a solid introduction to traditional abstract algebra topics. The text includes concepts and methodologies used by working mathematicians, computer scientists, physicists and chemists.
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A First Course in Abstract Algebra, 7th Edition (Hardcover)
~ Fraleigh J.B.
# Hardcover: 590 pages
# Publisher: Addison Wesley; 7 edition (November 16, 2002)
# Language: English
# ISBN-10: 0201763907
# ISBN-13: 978-0201763904
This is an in-depth introduction to abstract algebra. Focused on groups, rings and fields, it should give students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures. Features include: a classical approach to abstract algebra focussing on applications; an accessible pedagogy including historical notes written by Victor Katz; and a study of group theory.
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A Gentle Introduction to Category Theory
~ Maarten M Fokkinga
Year of publication
1992
Editor
University of Utrecht
In these notes we present the important notions from category theory. The intention is to provide a fairly good skill in manipulating with those concepts formally. What you probably will not acquire from these notes is the ability to recognise the concepts in your daily work when that differs from algorithmics, since we give only a few examples and those are taken from algorithmics. For such an ability you need to work through many, very many examples, in diverse fields of applications.
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The Fundamental Theorem of Algebra (Undergraduate Texts in Mathematics) (Hardcover)
~ Benjamin Fine
# Hardcover: 208 pages
# Publisher: Springer; 1 edition (June 20, 1997)
# Language: English
# ISBN-10: 0387946578
# ISBN-13: 978-0387946573
The FUNDAMENTAL THEOREM OF ALGEBRA states that any complex polynomial must have a complex root. This basic result, whose first accepted proof was given by Gauss, lies really at the intersection of the theory of numbers and the theory of equations, and arises also in many other areas of mathematics. The purpose of this book is to examine three pairs of proofs of the theorem from three different areas of mathematics: abstract algebra, complex analysis and topology. The first proof in each pair is fairly straightforward and depends only on what could be considered elementary mathematics. However, each of these first proofs lends itself to generalizations, which in turn, lead to more general results from which the fundamental theorem can be deduced as a direct consequence. These general results constitute the second prooof in each pair. To arrive at each of the proofs, enough of the general theory of each relevant area is developed to understand the proof. In addition to the proofs and techniques themselves, many applications such as the insolvability of the quintic and the trascendence of e and pi are presented. Finally, a series of appendices give six additional proofs including a version of Gauss' original first proof.
The book is intended for junior/senior level undergraduate mathematics students or first year graduate students. It is ideal for a "capstone" course in mathematics. It could also be used as an alternative approach to an undergraduate abstract algebra course. Finally, because of the breadth of topics it covers it would also be ideal for a graduate course for mathmatics teachers.
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Abstract Algebra (Hardcover)
~ David S. Dummit (Author)
# Hardcover: 944 pages
# Publisher: Wiley; 3 edition (July 14, 2003)
# Language: English
# ISBN-10: 0471433349
# ISBN-13: 978-0471433347
Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings.
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First Course in the Theory of Equations (Paperback)
~ Leonard Eugene Dickson (Author)
# Paperback: 200 pages
# Publisher: CreateSpace (October 3, 2009)
# Language: English
# ISBN-10: 1449500498
# ISBN-13: 978-1449500498
This is a new printing of the classic book by Dickson. It was to meet the numerous needs of the student in regard to his earlier and future mathematical courses that the present book was planned with great care and after wide consultation. It differs essentially from the author's "Elementary Theory of Equations", both in regard to omissions and additions, and since it is addressed to younger students and may be used parallel with a course in differential calculus. Simpler and more detailed proofs are now employed. The exercises are simpler, more numerous, of greater variety, and involve more practical applications. There are more than 480 exercises for students to practice. Topics covered include complex numbers, roots of equations, the quadratic equation, graphical methods, cubic and quartic equations, numerical methods, systems of linear equations, etc. Answers to all the exercises are provided at the end of the book. This is a new, high quality, and affordable edition.
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The Rules of Algebra: (Ars Magna) (Dover Books on Mathematics) (Paperback)
~ Girolamo Cardano
Girolamo Cardano (Author)
# Paperback: 304 pages
# Publisher: Dover Publications (April 19, 2007)
# Language: English
# ISBN-10: 0486458733
# ISBN-13: 978-0486458731
First published in 1545, this cornerstone in the history of mathematics contains the first revelation of the principles for solving cubic and biquadratic equations. T. Richard Witmer's excellent translation from the Latin, adapted to modern mathematical syntax, will appeal to both mathematicians and historians. Foreword by Oystein Ore.
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Introduction to Algebra (Paperback)
~ Peter J. Cameron
# Paperback: 350 pages
# Publisher: Oxford University Press, USA; 2 edition (February 9, 2008)
# Language: English
# ISBN-10: 0198527934
# ISBN-13: 978-0198527930
Developed to meet the needs of modern students, this Second Edition of the classic algebra text by Peter Cameron covers all the abstract algebra an undergraduate student is likely to need. Starting with an introductory overview of numbers, sets and functions, matrices, polynomials, and modular arithmetic, the text then introduces the most important algebraic structures: groups, rings and fields, and their properties. This is followed by coverage of vector spaces and modules with applications to abelian groups and canonical forms before returning to the construction of the number systems, including the existence of transcendental numbers. The final chapters take the reader further into the theory of groups, rings and fields, coding theory, and Galois theory. With over 300 exercises, and web-based solutions, this is an ideal introductory text for Year 1 and 2 undergraduate students in mathematics.
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An Introductory Course in Commutative Algebra (Oxford Science Publications) (Paperback)
~ A. W. Chatters
A. W. Chatters (Author)
# Paperback: 160 pages
# Publisher: Oxford University Press, USA (July 16, 1998)
# Language: English
# ISBN-10: 0198501447
# ISBN-13: 978-0198501442
The authors provide a concise introduction to topics in commutative algebra, with an emphasis on worked examples and applications. Their treatment combines elegant algebraic theory with applications to number theory, problems in classical Greek geometry, and the theory of finite fields, which has important uses in other branches of science. Topics covered include rings and Euclidean rings, the four-squares theorem, fields and field extensions, finite cyclic groups and finite fields. The material can serve equally well as a textbook for an entire course or as preparation for the further study of abstract algebra.
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MODERN HIGHER ALGEBRA (Hardcover)
~ A. Adrian Albert (Author)
# Hardcover
# Publisher: Chicago: University of Chicago Pr (January 1, 1939)
# ASIN: B000L54Y8S
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Elliptic Curves: Number Theory and Cryptography (Discrete Mathematics and Its Applications)
by: Lawrence C. Washington
# Hardcover: 440 pages
# Publisher: Chapman & Hall/CRC; 1 edition (May 28, 2003)
# Language: English
# ISBN-10: 1584883650
# ISBN-13: 978-1584883654
Elliptic curves have played an increasingly important role in number theory and related fields over the last several decades, most notably in areas such as cryptography, factorization, and the proof of Fermat's Last Theorem. However, most books on the subject assume a rather high level of mathematical sophistication, and few are truly accessible to senior undergraduate or beginning graduate students.Assuming only a modest background in elementary number theory, groups, and fields, Elliptic Curves: Number Theory and Cryptography introduces both the cryptographic and number theoretic sides of elliptic curves, interweaving the theory of elliptic curves with their applications. The author introduces elliptic curves over finite fields early in the treatment, leading readers directly to the intriguing cryptographic applications, but the book is structured so that readers can explore the number theoretic aspects independently if desired.By side-stepping algebraic geometry in favor an approach based on basic formulas, this book clearly demonstrates how elliptic curves are used and opens the doors to higher-level studies. Elliptic Curves offers a solid introduction to the mathematics and applications of elliptic curves that well prepares its readers to tackle more advanced problems in cryptography and number theory.
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Problems and Solutions for Undergraduate Analysis
by: Rami Shakarchi, Serge Lang
# Paperback: 368 pages
# Publisher: Springer; 1 edition (December 19, 1997)
# Language: English
# ISBN-10: 0387982353
# ISBN-13: 978-0387982359
This volume contains all the exercises and their solutions for Lang's second edition of UNDERGRADUATE ANALYSIS. The wide variety of exercises, which range from computational to more conceptual and which are of varying difficulty, cover the following subjects and more: real numbers, limits, continuous functions, differentiation and elementary integration, normed vector spaces, compactness, series, integration in one variable, improper integrals, convolutions, Fourier series and the Fourier integral, functions in n-space, derivatives in vector spaces, inverse and implicit mapping theorem, ordinary differential equations, multiple integrals and differential forms. This volume also serves as an independent source of problems with detailed answers beneficial for anyone interested in learning analysis. Intermediary steps and original drawings provided by the author assists students in their mastery of problem solving techniques and increases their overall comprehension of the subject matter.
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