Author : J. Lambek
Publisher : Cambridge University Press
Page : 308 pages
File Size : 34,73 MB
Release : 1988-03-25
Category : Mathematics
ISBN : 9780521356534
Part I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.
Author : Joachim Lambek
Publisher :
Page : 293 pages
File Size : 11,33 MB
Release : 1988
Category : Categories (Mathematics)
ISBN :
Author : B. Jacobs
Publisher : Gulf Professional Publishing
Page : 784 pages
File Size : 33,34 MB
Release : 2001-05-10
Category : Computers
ISBN : 9780444508539
This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.
Author : M. Makkai
Publisher : Springer
Page : 317 pages
File Size : 15,80 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540371001
Author : Jouko Väänänen
Publisher : Cambridge University Press
Page : 381 pages
File Size : 21,17 MB
Release : 2011-05-05
Category : Mathematics
ISBN : 1139496336
This gentle introduction to logic and model theory is based on a systematic use of three important games in logic: the semantic game; the Ehrenfeucht–Fraïssé game; and the model existence game. The third game has not been isolated in the literature before but it underlies the concepts of Beth tableaux and consistency properties. Jouko Väänänen shows that these games are closely related and in turn govern the three interrelated concepts of logic: truth, elementary equivalence and proof. All three methods are developed not only for first order logic but also for infinitary logic and generalized quantifiers. Along the way, the author also proves completeness theorems for many logics, including the cofinality quantifier logic of Shelah, a fully compact extension of first order logic. With over 500 exercises this book is ideal for graduate courses, covering the basic material as well as more advanced applications.
Author : Tom Leinster
Publisher : Cambridge University Press
Page : 193 pages
File Size : 20,23 MB
Release : 2014-07-24
Category : Mathematics
ISBN : 1107044243
A short introduction ideal for students learning category theory for the first time.
Author : Dorian Goldfeld
Publisher : Cambridge University Press
Page : 65 pages
File Size : 13,29 MB
Release : 2006-08-03
Category : Mathematics
ISBN : 1139456202
L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with a basic knowledge of classical analysis, complex variable theory, and algebra. Also within the volume are many new results not yet found in the literature. The exposition provides complete detailed proofs of results in an easy-to-read format using many examples and without the need to know and remember many complex definitions. The main themes of the book are first worked out for GL(2,R) and GL(3,R), and then for the general case of GL(n,R). In an appendix to the book, a set of Mathematica functions is presented, designed to allow the reader to explore the theory from a computational point of view.
Author : A. J. Berrick
Publisher : Cambridge University Press
Page : 384 pages
File Size : 17,17 MB
Release : 2000-05-25
Category : Mathematics
ISBN : 9780521632768
This book, first published in 2000, is a concise introduction at graduate level to ring theory, module theory and number theory.
Author : M. Makkai
Publisher :
Page : 320 pages
File Size : 44,6 MB
Release : 2014-09-01
Category :
ISBN : 9783662197813
Author : Velimir Jurdjevic
Publisher : Cambridge University Press
Page : 516 pages
File Size : 26,47 MB
Release : 1997
Category : Mathematics
ISBN : 0521495024
Geometric control theory is concerned with the evolution of systems subject to physical laws but having some degree of freedom through which motion is to be controlled. This book describes the mathematical theory inspired by the irreversible nature of time evolving events. The first part of the book deals with the issue of being able to steer the system from any point of departure to any desired destination. The second part deals with optimal control, the question of finding the best possible course. An overlap with mathematical physics is demonstrated by the Maximum principle, a fundamental principle of optimality arising from geometric control, which is applied to time-evolving systems governed by physics as well as to man-made systems governed by controls. Applications are drawn from geometry, mechanics, and control of dynamical systems. The geometric language in which the results are expressed allows clear visual interpretations and makes the book accessible to physicists and engineers as well as to mathematicians.
