May 20, 2002 · The goal of K-theory is to generalize linear algebra, the latter of which deals with linear transformations on vector spaces over fields. K-theory tries to find out, and make rigorous, what constructions in linear algebra carry over when the field is replaced by a ring R and the vector space is replaced by a module over this ring. Algebraic K-theory is a discipline which is internally coherent, but has strong connections to diverse mathematical disciplines, and has contributed solutions to problems in algebra, number theory, analysis, geometry and functional analysis. It even has links to particle physics. Overview. This book is both an introduction to K-theory and a text in algebra. These two roles are entirely compatible. On the one hand, nothing more than the basic algebra of groups, rings, and modules is needed to explain the clasical algebraic K-theory. On the other hand, K-theory is a natural organizing principle for the standard topics of a second course in algebra, and these topics are.

An Algebraic Introduction to K-Theory. This book is an introduction to K-theory and a text in algebra. These two roles are entirely compatible. On the one hand, nothing more than the basic algebra of groups, rings, and modules is needed to explain the classical algebraic K-theory. On the other hand,K-theory is a natural organizing principle for the standard topics of a second course in algebra,. Jan 01, 2002 · An Algebraic Introduction to K-Theory. This book is both an introduction to K-theory and a text in algebra. These two roles are entirely compatible. On the one hand, nothing more than the basic algebra of groups, rings, and modules is needed to explain the clasical algebraic K-theory.

Book Description. This is an introduction to algebraic K-theory with no prerequisite beyond a first semester of algebra including Galois theory and modules over a principal ideal domain. The presentation is almost entirely self-contained, and is divided into short sections with exercises to reinforce the ideas and suggest further lines of inquiry. Algebraic K-Theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory. The broad range of these topics has tended to give the subject an aura of inapproachability. This book, based. classical aspects of algebraic K-theory, with some of its applications to geometry and topology. Introduction Classically, algebraic K-theory of rings is the study of the family of K-theory functors K n: Rings−→ AbelianGroups n= 0,1,2. For a given ring R, the groups K 0R, K. ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS FOUNDED EDITOR G.-C. ROTA Editorial Board P. Flajolet, M. Ismail, E. Lutwak 40 N. White ed. Matroid Applications 41 S. Sakai Operator Algebras in Dynamical Systems 42 W. Hodges Basic Model Theory 43 H. Stahl and V. Totik General Orthogonal Polynomials 45 G. Da Prato and J. Zabczyk Stochastic Equations in Inﬁnite.

87 Bruce A. Magurn An algebraic introduction to K-theory 88 Teo Mora Solving polynomial equation systems I 89 Klaus Bichtelor Stochastic integration with jumps 90 M. Lothaire Algebraic combinatorics on words 91 A. A. Ivanov & S. V. Shpectorov Geometry of sporadic groups 2 92 Peter McMullen & Egon Schulte Abstract regular polytopes 93 G. Gierz. 87. Bruce A. Magurn An Algebraic Introduction to K-Theory 88. Teo Mora Solving Polynomial Equation Systems I 89. Klaus Bichteler Stochastic Integration with Jumps 90. M. Lothaire Algebraic Combinatorics on Words 91. A. A. Ivanov and S. V. Shpectorov Geometry of Sporadic Groups, 2 92. Peter McMullen and Egon Schulte Abstract Regular Polytopes 93. G. Encyclopedia of Mathematics and Its Applications. 87 B.A. Magurn An Algebraic Introduction to K-Theory. 2.4 Further applications of conjugacy 64 2.5 Differentiability in measure and category 77 2.6 Second-order differentiability 83 2.7 Support and extremal structure 91. This is an introduction to algebraic K-theory with no prerequisite beyond a first semester of algebra including Galois theory and modules over a principal ideal domain. The presentation is almost entirely self-contained, and is divided into short sections with exercises to.

Synopsis This is an introduction to algebraic K-theory with no prerequisite beyond a first semester of algebra including Galois theory and modules over a principal ideal domain. The presentation is almost entirely self-contained, and is divided into short sections with exercises to reinforce the ideas and suggest further lines of inquiry. K-Theory has an interdisciplinary flavour within modern mathematics, being present in diverse subjects such as algebraic topology, number theory, operator theory and dynamical systems, to mention but a few. In this course we will present the basic tools of the subject, with a stress on applications in various areas by means of examples. The resulting interplay of algebra, geometry, and topology in \K\-theory provides a fascinating glimpse of the unity of mathematics. This book is a comprehensive introduction to the subject of algebraic \K\-theory.

K -theory was invented in the late 1950s by Alexander Grothendieck in his study of intersection theory on algebraic varieties. In the modern language, Grothendieck defined only K0, the zeroth K -group, but even this single group has plenty of applications, such as the Grothendieck–Riemann–Roch theorem. Algebraic K-Theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory. The broad range of these topics has tended to give the subject an aura of inapproachability. This book, based on a course at the University of Maryland in the fall of 1990, is intended to enable graduate. Topics in Algebraic Graph Theory Encyclopedia of Mathematics and its Applications Lowell W. Beineke, Robin J. Wilson, Peter J. Cameron The rapidly expanding area of algebraic graph theory uses two different branches of algebra to explore various aspects of graph theory: linear algebra for spectral theory and group theory for studying.

Jun 24, 1994 · Algebraic K-Theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory. The broad range of these topics has tended to give the subject an aura of inapproachability. Magurn, Bruce A. 2009, An algebraic introduction to K-theory, Encyclopedia of Mathematics and its Applications, 87 corrected paperback ed., Cambridge University Press, ISBN 978-0-521-10658-0 Srinivas, V. 2008, Algebraic K -theory, Modern Birkhäuser Classics Paperback reprint of the 1996 2nd ed., Boston, MA: Birkhäuser, ISBN 978-0-8176-4736-0, Zbl 1125.19300. Find helpful customer reviews and review ratings for An Algebraic Introduction to K-Theory Encyclopedia of Mathematics and its Applications at. Read honest and unbiased product reviews from our users. An Algebraic Introduction to K-Theory Encyclopedia of Mathematics and its Applications Book 87 May 20, 2002 by Bruce A. Magurn 1.

Nov 26, 2015 · B. Magurn, An Algebraic Introduction to K-Theory, Encyclopedia of Mathematics and its Applications, Vol. 87, Cambridge University Press, Cambridge, 2002. Google Scholar [11]. Introduction. Algebraic K-Theory has become an increasingly active area of research. With its connections to algebra, algebraic geometry, topology, and number theory, it has implications for a wide variety of researchers and graduate students in mathematics. The book is based on lectures given at the author's home institution, the Tata. Algebra, branch of mathematics in which arithmetical operations and formal manipulations are applied to abstract symbols rather than specific numbers. This article presents algebra’s history, tracing the evolution of the equation, number systems, symbols, and the modern abstract structural view of algebra.

An Algebraic Introduction to K-Theory, Encyclopedia of Mathematics and its Applications,87, Cambridge University Press, Cambridge, 2002. Conf. on “Topological Algebras and Applications,” Oulu Finland, 2001. Acta Univ. Oul.A408 2004, 145–160. MathSciNet; Google Scholar. ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS FOUNDING EDITOR GIAN-CARLO ROTA Editorial Board R. Doran, P. Flajolet, M. Ismail, T. Y. Lam, E. Lutwak Volume 102 The titles below, and earlier volumes in the series, are available from booksellers or from Cambridge University Press at50 F. Borceux Handbook of Categorical Algebra I. The K-Book: An Introduction to Algebraic K-Theory, by Charles A. Weibel, Graduate Studies in Mathematics, 145. American Mathematical Society, Providence, RI, 2013. 642 pp. A version of this book is available online for free. An Algebraic Introduction to K-theory, by Bruce Magurn, Encyclopedia of Mathematics and its Applications, 87.

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