This book is the third of a three-volume set of books on the theory of algebras, a study that provides a consistent framework for understanding algebraic systems, including groups, rings, modules, semigroups and lattices. Volume I, first published in the 1980s, built the foundations of the theory and is considered to be a classic in this field. The long-awaited volumes II and III are now available. Taken together, the three volumes provide a comprehensive picture of the state of art in general algebra today, and serve as a valuable resource for anyone working in the general theory of algebraic systems or in related fields. The two new volumes are arranged around six themes first introduced in Volume I. Volume II covers the Classification of Varieties, Equational Logic, and Rudiments of Model Theory, and Volume III covers Finite Algebras and their Clones, Abstract Clone Theory, and the Commutator. These topics are presented in six chapters with independent expositions, but are linked by themes and motifs that run through all three volumes.
This book presents the foundations of a general theory of algebras. Often called “universal algebra”, this theory provides a common framework for all algebraic systems, including groups, rings, modules, fields, and lattices. Each chapter is replete with useful illustrations and exercises that solidify the reader's understanding. The book begins by developing the main concepts and working tools of algebras and lattices, and continues with examples of classical algebraic systems like groups, semigroups, monoids, and categories. The essence of the book lies in Chapter 4, which provides not only basic concepts and results of general algebra, but also the perspectives and intuitions shared by practitioners of the field. The book finishes with a study of possible uniqueness of factorizations of an algebra into a direct product of directly indecomposable algebras. There is enough material in this text for a two semester course sequence, but a one semester course could also focus primarily on Chapter 4, with additional topics selected from throughout the text.
Who was Paul; what did he do, what did he write? Walter F. Taylor sets out to bring together a wealth of contemporary perspectives in a clear and accessible synthesis, bringing to bear on his subject the best of recent social-scientific and cultural-anthropological thinking on Paul. An appendix presents a clear summary of issues related to Pauls thought on gender and sexuality.
From the reviews: ".. An excellent reference on undergraduate mathematical computing." (American Mathematical Monthly) "... manuals for such systems (Maple and MATLAB) tend to use trivial examples, making it difficult for new users of such systems to quickly apply their power to real problems. The authors have written a good book to address this need. ... the book is worth buying if you want guidance in applying Maple and MATLAB to problems in the workplace..." (Computing Reviews) ".. The presentation is unique, and extremely interesting. I was thrilled to read this text, and to learn the powerful problem-solving skills presented by these authors. I recommend the text highly, as a learning experience, not only to engineering students, but also to anyone interested in computation." (Mathematics of Computation)
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