Author: K. Elayn Martin-Gay
Publisher: Pearson
ISBN: 9780134582771
Category :
Languages : en
Pages :

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Author: R.L. Cignoli
Publisher: Springer Science & Business Media
ISBN: 9401594805
Category : Mathematics
Languages : en
Pages : 238

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This unique textbook states and proves all the major theorems of many-valued propositional logic and provides the reader with the most recent developments and trends, including applications to adaptive error-correcting binary search. The book is suitable for self-study, making the basic tools of many-valued logic accessible to students and scientists with a basic mathematical knowledge who are interested in the mathematical treatment of uncertain information. Stressing the interplay between algebra and logic, the book contains material never before published, such as a simple proof of the completeness theorem and of the equivalence between Chang's MV algebras and Abelian lattice-ordered groups with unit - a necessary prerequisite for the incorporation of a genuine addition operation into fuzzy logic. Readers interested in fuzzy control are provided with a rich deductive system in which one can define fuzzy partitions, just as Boolean partitions can be defined and computed in classical logic. Detailed bibliographic remarks at the end of each chapter and an extensive bibliography lead the reader on to further specialised topics.

Author: Samuel Eilenberg
Publisher: Princeton University Press
ISBN: 1400877490
Category : Mathematics
Languages : en
Pages : 345

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The need for an axiomatic treatment of homology and cohomology theory has long been felt by topologists. Professors Eilenberg and Steenrod present here for the first time an axiomatization of the complete transition from topology to algebra. Originally published in 1952. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author: Dietmar Hildenbrand
Publisher: Springer Science & Business Media
ISBN: 3642317944
Category : Computers
Languages : en
Pages : 217

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The author defines “Geometric Algebra Computing” as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry. The related technology is driven by the invention of conformal geometric algebra as a 5D extension of the 4D projective geometric algebra and by the recent progress in parallel processing, and with the specific conformal geometric algebra there is a growing community in recent years applying geometric algebra to applications in computer vision, computer graphics, and robotics. This book is organized into three parts: in Part I the author focuses on the mathematical foundations; in Part II he explains the interactive handling of geometric algebra; and in Part III he deals with computing technology for high-performance implementations based on geometric algebra as a domain-specific language in standard programming languages such as C++ and OpenCL. The book is written in a tutorial style and readers should gain experience with the associated freely available software packages and applications. The book is suitable for students, engineers, and researchers in computer science, computational engineering, and mathematics.

Author: Egidio Astesiano
Publisher: Springer Science & Business Media
ISBN: 364259851X
Category : Computers
Languages : en
Pages : 626

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This IFIP report is a collection of fundamental, high-quality contributions on the algebraic foundations of system specification. The contributions cover and survey active topics and recent advances, and address such subjects as: the role of formal specification, algebraic preliminaries, partiality, institutions, specification semantics, structuring, refinement, specification languages, term rewriting, deduction and proof systems, object specification, concurrency, and the development process. The authors are well-known experts in the field, and the book is the result of IFIP WG 1.3 in cooperation with Esprit Basic Research WG COMPASS, and provides the foundations of the algebraic specification language CASL designed in the CoFI project. For students, researchers, and system developers.

Author: John Browne
Publisher: John M Browne
ISBN: 1479197637
Category : Mathematics
Languages : en
Pages : 589

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Grassmann Algebra Volume 1: Foundations Exploring extended vector algebra with Mathematica Grassmann algebra extends vector algebra by introducing the exterior product to algebraicize the notion of linear dependence. With it, vectors may be extended to higher-grade entities: bivectors, trivectors, … multivectors. The extensive exterior product also has a regressive dual: the regressive product. The pair behaves a little like the Boolean duals of union and intersection. By interpreting one of the elements of the vector space as an origin point, points can be defined, and the exterior product can extend points into higher-grade located entities from which lines, planes and multiplanes can be defined. Theorems of Projective Geometry are simply formulae involving these entities and the dual products. By introducing the (orthogonal) complement operation, the scalar product of vectors may be extended to the interior product of multivectors, which in this more general case may no longer result in a scalar. The notion of the magnitude of vectors is extended to the magnitude of multivectors: for example, the magnitude of the exterior product of two vectors (a bivector) is the area of the parallelogram formed by them. To develop these foundational concepts, we need only consider entities which are the sums of elements of the same grade. This is the focus of this volume. But the entities of Grassmann algebra need not be of the same grade, and the possible product types need not be constricted to just the exterior, regressive and interior products. For example quaternion algebra is simply the Grassmann algebra of scalars and bivectors under a new product operation. Clifford, geometric and higher order hypercomplex algebras, for example the octonions, may be defined similarly. If to these we introduce Clifford's invention of a scalar which squares to zero, we can define entities (for example dual quaternions) with which we can perform elaborate transformations. Exploration of these entities, operations and algebras will be the focus of the volume to follow this. There is something fascinating about the beauty with which the mathematical structures that Hermann Grassmann discovered describe the physical world, and something also fascinating about how these beautiful structures have been largely lost to the mainstreams of mathematics and science. He wrote his seminal Ausdehnungslehre (Die Ausdehnungslehre. Vollständig und in strenger Form) in 1862. But it was not until the latter part of his life that he received any significant recognition for it, most notably by Gibbs and Clifford. In recent times David Hestenes' Geometric Algebra must be given the credit for much of the emerging awareness of Grass­mann's innovation. In the hope that the book be accessible to scientists and engineers, students and professionals alike, the text attempts to avoid any terminology which does not make an essential contribution to an understanding of the basic concepts. Some familiarity with basic linear algebra may however be useful. The book is written using Mathematica, a powerful system for doing mathematics on a computer. This enables the theory to be cross-checked with computational explorations. However, a knowledge of Mathematica is not essential for an appreciation of Grassmann's beautiful ideas.

Author: Elayn Martin-Gay
Publisher: Pearson
ISBN: 9780133975048
Category : Mathematics
Languages : en
Pages :

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Author: Elayn Martin-Gay
Publisher: Pearson
ISBN: 0321978927
Category : Mathematics
Languages : en
Pages : 1585

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NOTE: Before purchasing, check with your instructor to ensure you select the correct ISBN. Several versions of Pearson's MyLab & Mastering products exist for each title, and registrations are not transferable. To register for and use Pearson's MyLab & Mastering products, you may also need a Course ID, which your instructor will provide. Used books, rentals, and purchases made outside of Pearson If purchasing or renting from companies other than Pearson, the access codes for Pearson's MyLab & Mastering products may not be included, may be incorrect, or may be previously redeemed. Check with the seller before completing your purchase. -- Elayn Martin-Gay's developmental math program is motivated by her firm belief that every student can succeed. The new All in One, Algebra Foundations: Prealgebra, Introductory Algebra, & Intermediate Algebra, offers everything needed to teach the full developmental math sequence in one flexible course solution.Martin-Gay's focus on the student shapes her clear, accessible writing, inspires her constant pedagogical innovations, and contributes to the popularity and effectiveness of her video resources. This new All in One continues her focus on students and what they need to be successful.

Author: K. Elayn Martin-Gay
Publisher:
ISBN: 9781256123392
Category : Mathematics
Languages : en
Pages : 0

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Author: Elayn Martin-Gay
Publisher: Pearson
ISBN: 9780135239247
Category :
Languages : en
Pages : 1792

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For courses or sequences that cover topics from Prealgebra, Introductory Algebra, and Intermediate Algebra. The Martin-Gay principle: Every student can succeed Elayn Martin-Gay's student-centric approach is woven seamlessly throughout her texts and MyLab(tm) courses, giving students the optimal amount of support through effective video resources, an accessible writing style, and study skills support built into the program. This revision of Martin-Gay's worktext series continues her focus on students with new and improved resources to support student success. Algebra Foundations , 2nd Edition is a comprehensive All in One program that offers everything needed to teach Prealgebra, Introductory Algebra, and Intermediate Algebra in one easy-to-use solution. Three courses' worth of material, in one seamless MyLab Math course and text, allows instructors to pick and choose what content they want to cover and when they want to cover it. This content is designed to work for any course format, and can even be used in a corequisite course--giving instructors a library of review material to support a credit-level corequisite course. Two choices for a MyLab course provide options when it comes to assignments and interactivity; time-based access options make accessing the content flexible and keeps the course completely customizable. Elayn Martin-Gay's signature approach is integrated throughout the MyLab to ensure a completely consistent experience from print to MyLab. Also available with MyLab Math MyLab Math is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student. Note: You are purchasing a standalone product; MyLab Math does not come packaged with this content. Students, if interested in purchasing this title with MyLab Math, ask your instructor to confirm the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information.