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Author: Javier Esparza
Publisher: Cambridge University Press
Published: 2011-03-10
Total Pages: 355
ISBN-13: 0521718201
DOWNLOAD EBOOKSurveys of current research in logical aspects of computer science that apply finite and infinite model-theoretic methods.
Author: Erich Grädel
Publisher: Springer Science & Business Media
Published: 2007-06-04
Total Pages: 447
ISBN-13: 3540688048
DOWNLOAD EBOOKFinite model theory,as understoodhere, is an areaof mathematicallogic that has developed in close connection with applications to computer science, in particular the theory of computational complexity and database theory. One of the fundamental insights of mathematical logic is that our understanding of mathematical phenomena is enriched by elevating the languages we use to describe mathematical structures to objects of explicit study. If mathematics is the science of patterns, then the media through which we discern patterns, as well as the structures in which we discern them, command our attention. It isthis aspect oflogicwhichis mostprominentin model theory,“thebranchof mathematical logic which deals with the relation between a formal language and its interpretations”. No wonder, then, that mathematical logic, and ?nite model theory in particular, should ?nd manifold applications in computer science: from specifying programs to querying databases, computer science is rife with phenomena whose understanding requires close attention to the interaction between language and structure. This volume gives a broadoverviewof some central themes of ?nite model theory: expressive power, descriptive complexity, and zero–one laws, together with selected applications to database theory and arti?cial intelligence, es- cially constraint databases and constraint satisfaction problems. The ?nal chapter provides a concise modern introduction to modal logic,which emp- sizes the continuity in spirit and technique with ?nite model theory.
Author: Igor Shparlinski
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 253
ISBN-13: 940111806X
DOWNLOAD EBOOKThis volume presents an exhaustive treatment of computation and algorithms for finite fields. Topics covered include polynomial factorization, finding irreducible and primitive polynomials, distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types, and new applications of finite fields to other araes of mathematics. For completeness, also included are two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number generators, modular arithmetic etc.), and computational number theory (primality testing, factoring integers, computing in algebraic number theory, etc.) The problems considered here have many applications in computer science, coding theory, cryptography, number theory and discrete mathematics. The level of discussion presuppose only a knowledge of the basic facts on finite fields, and the book can be recommended as supplementary graduate text. For researchers and students interested in computational and algorithmic problems in finite fields.
Author: Katrin Tent
Publisher: Cambridge University Press
Published: 2012-03-08
Total Pages: 259
ISBN-13: 052176324X
DOWNLOAD EBOOKConcise introduction to current topics in model theory, including simple and stable theories.
Author: Olle Häggström
Publisher: Cambridge University Press
Published: 2002-05-30
Total Pages: 132
ISBN-13: 9780521890014
DOWNLOAD EBOOKBased on a lecture course given at Chalmers University of Technology, this 2002 book is ideal for advanced undergraduate or beginning graduate students. The author first develops the necessary background in probability theory and Markov chains before applying it to study a range of randomized algorithms with important applications in optimization and other problems in computing. Amongst the algorithms covered are the Markov chain Monte Carlo method, simulated annealing, and the recent Propp-Wilson algorithm. This book will appeal not only to mathematicians, but also to students of statistics and computer science. The subject matter is introduced in a clear and concise fashion and the numerous exercises included will help students to deepen their understanding.
Author: Michael Aschbacher
Publisher: Cambridge University Press
Published: 2011-08-25
Total Pages: 329
ISBN-13: 1107601002
DOWNLOAD EBOOKA fusion system over a p-group S is a category whose objects form the set of all subgroups of S, whose morphisms are certain injective group homomorphisms, and which satisfies axioms first formulated by Puig that are modelled on conjugacy relations in finite groups. The definition was originally motivated by representation theory, but fusion systems also have applications to local group theory and to homotopy theory. The connection with homotopy theory arises through classifying spaces which can be associated to fusion systems and which have many of the nice properties of p-completed classifying spaces of finite groups. Beginning with a detailed exposition of the foundational material, the authors then proceed to discuss the role of fusion systems in local finite group theory, homotopy theory and modular representation theory. This book serves as a basic reference and as an introduction to the field, particularly for students and other young mathematicians.
Author: N. Broaddus
Publisher: Cambridge University Press
Published: 2018-09-06
Total Pages: 211
ISBN-13: 1108437621
DOWNLOAD EBOOKDetails some of the most recent developments at the interface of topology and geometric group theory. Ideal for graduate students.
Author: Allen L. Mann
Publisher: Cambridge University Press
Published: 2011-05-05
Total Pages: 215
ISBN-13: 1139495917
DOWNLOAD EBOOKBringing together over twenty years of research, this book gives a complete overview of independence-friendly logic, an exciting logical formalism at the interface of logic and game theory. It is suitable for graduate students and advanced undergraduates who have taken a course on first-order logic.
Author: Grant Walker
Publisher: Cambridge University Press
Published: 2017-11-09
Total Pages: 382
ISBN-13: 1108359280
DOWNLOAD EBOOKThis is the first book to link the mod 2 Steenrod algebra, a classical object of study in algebraic topology, with modular representations of matrix groups over the field F of two elements. The link is provided through a detailed study of Peterson's `hit problem' concerning the action of the Steenrod algebra on polynomials, which remains unsolved except in special cases. The topics range from decompositions of integers as sums of 'powers of 2 minus 1', to Hopf algebras and the Steinberg representation of GL(n, F). Volume 1 develops the structure of the Steenrod algebra from an algebraic viewpoint and can be used as a graduate-level textbook. Volume 2 broadens the discussion to include modular representations of matrix groups.
Author: Grant Walker
Publisher: Cambridge University Press
Published: 2017-11-09
Total Pages: 372
ISBN-13: 1108359299
DOWNLOAD EBOOKThis is the first book to link the mod 2 Steenrod algebra, a classical object of study in algebraic topology, with modular representations of matrix groups over the field F of two elements. The link is provided through a detailed study of Peterson's 'hit problem' concerning the action of the Steenrod algebra on polynomials, which remains unsolved except in special cases. The topics range from decompositions of integers as sums of 'powers of 2 minus 1', to Hopf algebras and the Steinberg representation of GL(n,F). Volume 1 develops the structure of the Steenrod algebra from an algebraic viewpoint and can be used as a graduate-level textbook. Volume 2 broadens the discussion to include modular representations of matrix groups.
