Download or read book The Elements of Universal Mathematics Or Algebra written by Willem Jacob van's Gravesande and published by . This book was released on 1728 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Elements of Algebra written by Leonhard Euler and published by . This book was released on 1810 with total page 960 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Course in Universal Algebra written by S. Burris and published by Springer. This book was released on 2011-10-21 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Universal algebra has enjoyed a particularly explosive growth in the last twenty years, and a student entering the subject now will find a bewildering amount of material to digest. This text is not intended to be encyclopedic; rather, a few themes central to universal algebra have been developed sufficiently to bring the reader to the brink of current research. The choice of topics most certainly reflects the authors' interests. Chapter I contains a brief but substantial introduction to lattices, and to the close connection between complete lattices and closure operators. In particular, everything necessary for the subsequent study of congruence lattices is included. Chapter II develops the most general and fundamental notions of uni versal algebra-these include the results that apply to all types of algebras, such as the homomorphism and isomorphism theorems. Free algebras are discussed in great detail-we use them to derive the existence of simple algebras, the rules of equational logic, and the important Mal'cev conditions. We introduce the notion of classifying a variety by properties of (the lattices of) congruences on members of the variety. Also, the center of an algebra is defined and used to characterize modules (up to polynomial equivalence). In Chapter III we show how neatly two famous results-the refutation of Euler's conjecture on orthogonal Latin squares and Kleene's character ization of languages accepted by finite automata-can be presented using universal algebra. We predict that such "applied universal algebra" will become much more prominent.
Download or read book Universal Algebra written by Clifford Bergman and published by CRC Press. This book was released on 2011-09-20 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with the most basic notions, Universal Algebra: Fundamentals and Selected Topics introduces all the key elements needed to read and understand current research in this field. Based on the author’s two-semester course, the text prepares students for research work by providing a solid grounding in the fundamental constructions and concepts of universal algebra and by introducing a variety of recent research topics. The first part of the book focuses on core components, including subalgebras, congruences, lattices, direct and subdirect products, isomorphism theorems, a clone of operations, terms, free algebras, Birkhoff’s theorem, and standard Maltsev conditions. The second part covers topics that demonstrate the power and breadth of the subject. The author discusses the consequences of Jónsson’s lemma, finitely and nonfinitely based algebras, definable principal congruences, and the work of Foster and Pixley on primal and quasiprimal algebras. He also includes a proof of Murskiĭ’s theorem on primal algebras and presents McKenzie’s characterization of directly representable varieties, which clearly shows the power of the universal algebraic toolbox. The last chapter covers the rudiments of tame congruence theory. Throughout the text, a series of examples illustrates concepts as they are introduced and helps students understand how universal algebra sheds light on topics they have already studied, such as Abelian groups and commutative rings. Suitable for newcomers to the field, the book also includes carefully selected exercises that reinforce the concepts and push students to a deeper understanding of the theorems and techniques.
Download or read book Elements of Number Theory written by John Stillwell and published by Springer Science & Business Media. This book was released on 2012-11-12 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solutions of equations in integers is the central problem of number theory and is the focus of this book. The amount of material is suitable for a one-semester course. The author has tried to avoid the ad hoc proofs in favor of unifying ideas that work in many situations. There are exercises at the end of almost every section, so that each new idea or proof receives immediate reinforcement.
Download or read book The Elements of Universal Mathematics Or Algebra written by Willem Jacob 's Gravesande and published by . This book was released on 1728 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Elements of Algebra written by Arthur Schultze and published by . This book was released on 1918 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Elements of Algebra written by John Stillwell and published by Springer Science & Business Media. This book was released on 2001-07-20 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra is abstract mathematics - let us make no bones about it - yet it is also applied mathematics in its best and purest form. It is not abstraction for its own sake, but abstraction for the sake of efficiency, power and insight. Algebra emerged from the struggle to solve concrete, physical problems in geometry, and succeeded after 2000 years of failure by other forms of mathematics. It did this by exposing the mathematical structure of geometry, and by providing the tools to analyse it. This is typical of the way algebra is applied; it is the best and purest form of application because it reveals the simplest and most universal mathematical structures. The present book aims to foster a proper appreciation of algebra by showing abstraction at work on concrete problems, the classical problems of construction by straightedge and compass. These problems originated in the time of Euclid, when geometry and number theory were paramount, and were not solved until th the 19 century, with the advent of abstract algebra. As we now know, alge bra brings about a unification of geometry, number theory and indeed most branches of mathematics. This is not really surprising when one has a historical understanding of the subject, which I also hope to impart.
Download or read book Official Summary of Security Transactions and Holdings Reported to the Securities and Exchange Commission Under the Securities Exchange Act of 1934 and the Public Utility Holding Company Act of 1935 written by United States. Securities and Exchange Commission and published by . This book was released on 1988 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Elements of Mathematics written by John Stillwell and published by Princeton University Press. This book was released on 2016 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exciting look at the world of elementary mathematics Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics--but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become "elementary." Stillwell examines elementary mathematics from a distinctive twenty-first-century viewpoint and describes not only the beauty and scope of the discipline, but also its limits. From Gaussian integers to propositional logic, Stillwell delves into arithmetic, computation, algebra, geometry, calculus, combinatorics, probability, and logic. He discusses how each area ties into more advanced topics to build mathematics as a whole. Through a rich collection of basic principles, vivid examples, and interesting problems, Stillwell demonstrates that elementary mathematics becomes advanced with the intervention of infinity. Infinity has been observed throughout mathematical history, but the recent development of "reverse mathematics" confirms that infinity is essential for proving well-known theorems, and helps to determine the nature, contours, and borders of elementary mathematics. Elements of Mathematics gives readers, from high school students to professional mathematicians, the highlights of elementary mathematics and glimpses of the parts of math beyond its boundaries.
Download or read book The Shape of Algebra in the Mirrors of Mathematics written by Gabriel Katz and published by World Scientific. This book was released on 2012 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Shape of Algebra is the authors' attempt to share their mathematical experiences with readers who have more than a passing interest in mathematics, but have only a traditional exposure to elementary algebra. Secondary school and college teachers and students who want to expand their horizons in the field will find a fresh presentation of familiar concepts and some unexpected results. This book serves as a text for an "appreciation" course in modern mathematics designed for non-mathematics majors or for first-year students who are considering the possibility of studying mathematics or related disciplines. It can also serve as a source of computer-supported activities that could supplement traditional courses in algebra, multivariable calculus, and complex variable. This book gives the reader a sense of the visual nature of mathematics. Mathematical experiments with universal mapping software VisuMatica, designed by Vladimir Nodel'man, form the very core of the book. Readers are encouraged to reproduce, play with, and expand on these experiments. Numerous problems are interspersed throughout the text to guide the reader. Our treatment of standard algebra is visual and computational. By introducing visual computational environments like VisuMatica, our book promotes this geometric approach to algebra and makes it accessible to readers a great deal earlier. The book will enable our readers to approach its content on three levels: the first one which requires only some fluency with elementary algebraic manipulations; the second one which also presumes familiarity with the notions of derivatives and tangent lines to plane curves, and the third one which uses some basic concepts of multivariable calculus. All three levels are clearly marked in the text, and will allow for a smooth reading and virtual experiments, regardless of the level that our readers will find comfortable.
Download or read book Euclid s Elements written by Euclid and published by . This book was released on 2002 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The book includes introductions, terminology and biographical notes, bibliography, and an index and glossary" --from book jacket.
Download or read book An Introduction to Algebraic Structures written by Joseph Landin and published by Courier Corporation. This book was released on 2012-08-29 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained text covers sets and numbers, elements of set theory, real numbers, the theory of groups, group isomorphism and homomorphism, theory of rings, and polynomial rings. 1969 edition.
Download or read book Finite Semigroups And Universal Algebra written by Jorge Almeida and published by World Scientific. This book was released on 1995-01-27 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by applications in theoretical computer science, the theory of finite semigroups has emerged in recent years as an autonomous area of mathematics. It fruitfully combines methods, ideas and constructions from algebra, combinatorics, logic and topology. In simple terms, the theory aims at a classification of finite semigroups in certain classes called “pseudovarieties”. The classifying characteristics have both structural and syntactical aspects, the general connection between them being part of universal algebra. Besides providing a foundational study of the theory in the setting of arbitrary abstract finite algebras, this book stresses the syntactical approach to finite semigroups. This involves studying (relatively) free and profinite free semigroups and their presentations. The techniques used are illustrated in a systematic study of various operators on pseudovarieties of semigroups.
Download or read book Euclid in the Rainforest written by Joseph Mazur and published by Penguin. This book was released on 2006-07-25 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like Douglas Hofstadter’s Gödel, Escher, Bach, and David Berlinski’s A Tour of the Calculus, Euclid in the Rainforest combines the literary with the mathematical to explore logic—the one indispensable tool in man’s quest to understand the world. Underpinning both math and science, it is the foundation of every major advancement in knowledge since the time of the ancient Greeks. Through adventure stories and historical narratives populated with a rich and quirky cast of characters, Mazur artfully reveals the less-than-airtight nature of logic and the muddled relationship between math and the real world. Ultimately, Mazur argues, logical reasoning is not purely robotic. At its most basic level, it is a creative process guided by our intuitions and beliefs about the world.
Download or read book Category Theory in Context written by Emily Riehl and published by Courier Dover Publications. This book was released on 2017-03-09 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.
Download or read book Basic Algebra written by Anthony W. Knapp and published by Springer Science & Business Media. This book was released on 2007-07-28 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems.
