Download or read book Modern Algebraic Theories written by Leonard Eugene Dickson and published by . This book was released on 1930 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modern Algebraic Theories written by Leonard Eugene Dickson and published by . This book was released on 1926 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modern Algebraic Theories written by Leonard Eugene Dickson and published by . This book was released on 1926 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic Theories written by Leonard Dickson and published by Courier Corporation. This book was released on 2014-03-05 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This in-depth introduction to classical topics in higher algebra provides rigorous, detailed proofs for its explorations of some of mathematics' most significant concepts, including matrices, invariants, and groups. Algebraic Theories studies all of the important theories; its extensive offerings range from the foundations of higher algebra and the Galois theory of algebraic equations to finite linear groups (including Klein's "icosahedron" and the theory of equations of the fifth degree) and algebraic invariants. The full treatment includes matrices, linear transformations, elementary divisors and invariant factors, and quadratic, bilinear, and Hermitian forms, both singly and in pairs. The results are classical, with due attention to issues of rationality. Elementary divisors and invariant factors receive simple, natural introductions in connection with the classical form and a rational, canonical form of linear transformations. All topics are developed with a remarkable lucidity and discussed in close connection with their most frequent mathematical applications.
Download or read book Introduction to Modern Number Theory written by Yu. I. Manin and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edition has been called ‘startlingly up-to-date’, and in this corrected second printing you can be sure that it’s even more contemporaneous. It surveys from a unified point of view both the modern state and the trends of continuing development in various branches of number theory. Illuminated by elementary problems, the central ideas of modern theories are laid bare. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories.
Download or read book The K book written by Charles A. Weibel and published by American Mathematical Soc.. This book was released on 2013-06-13 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Informally, $K$-theory is a tool for probing the structure of a mathematical object such as a ring or a topological space in terms of suitably parameterized vector spaces and producing important intrinsic invariants which are useful in the study of algebr
Download or read book Algebraic Theories formulary Titled Modern Algebraic Theories written by Leonard E. Dickson and published by . This book was released on 1959 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic Theories written by J. Adámek and published by Cambridge University Press. This book was released on 2010-11-18 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic theories, introduced as a concept in the 1960s, have been a fundamental step towards a categorical view of general algebra. Moreover, they have proved very useful in various areas of mathematics and computer science. This carefully developed book gives a systematic introduction to algebra based on algebraic theories that is accessible to both graduate students and researchers. It will facilitate interactions of general algebra, category theory and computer science. A central concept is that of sifted colimits - that is, those commuting with finite products in sets. The authors prove the duality between algebraic categories and algebraic theories and discuss Morita equivalence between algebraic theories. They also pay special attention to one-sorted algebraic theories and the corresponding concrete algebraic categories over sets, and to S-sorted algebraic theories, which are important in program semantics. The final chapter is devoted to finitary localizations of algebraic categories, a recent research area.
Download or read book Modern Algebra and the Rise of Mathematical Structures written by Leo Corry and published by Birkhäuser. This book was released on 2012-12-06 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes two stages in the historical development of the notion of mathematical structures: first, it traces its rise in the context of algebra from the mid-1800s to 1930, and then considers attempts to formulate elaborate theories after 1930 aimed at elucidating, from a purely mathematical perspective, the precise meaning of this idea.
Download or read book Algebraic theories written by Leonard Eugene Dickson and published by . This book was released on 1959 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic Theories written by Leonard Eugene Dickson and published by . This book was released on 1959 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theory of Algebraic Integers written by Richard Dedekind and published by Cambridge University Press. This book was released on 1996-09-28 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: A translation of a classic work by one of the truly great figures of mathematics.
Download or read book Labyrinth of Thought written by Jose Ferreiros and published by Springer Science & Business Media. This book was released on 2001-11-01 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: "José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)
Download or read book Abstract Algebra written by Thomas Judson and published by Orthogonal Publishing L3c. This book was released on 2023-08-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract Algebra: Theory and Applications is an open-source textbook that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many non-trivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.
Download or read book Elements of Modern Mathematics written by Kenneth O, May and published by Dover Publications. This book was released on 2019-11-13 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: An unusually thoughtful and well-constructed introduction to the serious study of mathematics, this book requires no background beyond high school courses in plane geometry and elementary algebra. From that starting point, it is designed to lead readers willing to work through its exercises and problems to the achievement of basic mathematical literacy. The text provides a fundamental orientation in modern mathematics, an essential vocabulary of mathematical terms, and some facility in the use of mathematical concepts and symbols. From there, readers will be equipped to move on to more serious work, and they'll be well on the way to having the tools essential for work in the physical sciences, engineering, and the biological and social sciences. Starting with elementary treatments of algebra, logic, and set theory, the book advances to explorations of plane analytic geometry, relations and functions, numbers, and calculus. Subsequent chapters discuss probability, statistical inference, and abstract mathematical theories. Each section is enhanced with exercises in the text and problems at the end. Answers to the exercises and some of the problems are included at the end of each section.
Download or read book Algebraic Theories written by Leonard Eugene Dickson (Mathematiker, USA) and published by . This book was released on 1959 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Local Structure of Algebraic K Theory written by Bjørn Ian Dundas and published by Springer Science & Business Media. This book was released on 2012-09-06 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homological invariants offered by motivic cohomology and topological cyclic homology. This book covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference between the theories are ‘locally constant’. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain a host of ‘nearby’ calculations in K-theory. For instance, Quillen's calculation of the K-theory of finite fields gives rise to Hesselholt and Madsen's calculations for local fields, and Voevodsky's calculations for the integers give insight into the diffeomorphisms of manifolds. In addition to the proof of the full integral version of the local correspondence between K-theory and topological cyclic homology, the book provides an introduction to the necessary background in algebraic K-theory and highly structured homotopy theory; collecting all necessary tools into one common framework. It relies on simplicial techniques, and contains an appendix summarizing the methods widely used in the field. The book is intended for graduate students and scientists interested in algebraic K-theory, and presupposes a basic knowledge of algebraic topology.
