Forcing with Random Variables and Proof Complexity

Author: Jan Krajíček
Publisher: Cambridge University Press
ISBN: 9781139493925
Release Date: 2010-12-23
Genre: Mathematics

This book introduces a new approach to building models of bounded arithmetic, with techniques drawn from recent results in computational complexity. Propositional proof systems and bounded arithmetics are closely related. In particular, proving lower bounds on the lengths of proofs in propositional proof systems is equivalent to constructing certain extensions of models of bounded arithmetic. This offers a clean and coherent framework for thinking about lower bounds for proof lengths, and it has proved quite successful in the past. This book outlines a brand new method for constructing models of bounded arithmetic, thus for proving independence results and establishing lower bounds for proof lengths. The models are built from random variables defined on a sample space which is a non-standard finite set and sampled by functions of some restricted computational complexity. It will appeal to anyone interested in logical approaches to fundamental problems in complexity theory.

Logical Approaches to Computational Barriers

Author: Arnold Beckmann
Publisher: Springer Science & Business Media
ISBN: 9783540354666
Release Date: 2006-06-26
Genre: Computers

This book constitutes the refereed proceedings of the Second International Conference on Computability in Europe, CiE 2006, held in Swansea, UK, in June/July 2006. The 31 revised full papers presented together with 30 invited papers were carefully reviewed and selected from about 80 submissions. Among them are papers corresponding to 8 plenary talks and papers of 6 special sessions entitled proofs and computation, computable analysis, challenges in complexity, foundations of programming, mathematical models of computers and hypercomputers, and G??del centenary: G??del's legacy for computability.

Complexity Science

Author: Robin Ball
Publisher: Cambridge University Press
ISBN: 9781107640566
Release Date: 2013-11-21
Genre: Mathematics

This book presents introductions to the essential mathematical aspects of complexity science, suitable for advanced undergraduate/masters-level students and researchers.

Evolution Equations

Author: Kaïs Ammari
Publisher: Cambridge University Press
ISBN: 9781108331036
Release Date: 2017-10-05
Genre: Mathematics

The proceedings of the summer school held at the Université Savoie Mont Blanc, France, 'Mathematics in Savoie 2015', whose theme was long time behavior and control of evolution equations. The event was attended by world-leading researchers from the community of control theory, as well as young researchers from around the globe. This volume contains surveys of active research topics, along with original research papers containing exciting new results on the behavior of evolution equations. It will therefore benefit both graduate students and researchers. Key topics include the recent view on the controllability of parabolic systems that permits the reader to overview the moment method for parabolic equations, as well as numerical stabilization and control of partial differential equations.

Economics for Mathematicians

Author: John William Scott Cassels
Publisher: Cambridge University Press
ISBN: 9780521286145
Release Date: 1981-12-10
Genre: Business & Economics

This is the expanded notes of a course intended to introduce students specializing in mathematics to some of the central ideas of traditional economics. The book should be readily accessible to anyone with some training in university mathematics; more advanced mathematical tools are explained in the appendices. Thus this text could be used for undergraduate mathematics courses or as supplementary reading for students of mathematical economics.

Geometric Analysis of Hyperbolic Differential Equations An Introduction

Author: S. Alinhac
Publisher: Cambridge University Press
ISBN: 9781139485814
Release Date: 2010-05-20
Genre: Mathematics

Its self-contained presentation and 'do-it-yourself' approach make this the perfect guide for graduate students and researchers wishing to access recent literature in the field of nonlinear wave equations and general relativity. It introduces all of the key tools and concepts from Lorentzian geometry (metrics, null frames, deformation tensors, etc.) and provides complete elementary proofs. The author also discusses applications to topics in nonlinear equations, including null conditions and stability of Minkowski space. No previous knowledge of geometry or relativity is required.

Advances in Elliptic Curve Cryptography

Author: Ian F. Blake
Publisher: Cambridge University Press
ISBN: 1139441221
Release Date: 2005-04-25
Genre: Mathematics

Since the appearance of the authors' first volume on elliptic curve cryptography in 1999 there has been tremendous progress in the field. In some topics, particularly point counting, the progress has been spectacular. Other topics such as the Weil and Tate pairings have been applied in new and important ways to cryptographic protocols that hold great promise. Notions such as provable security, side channel analysis and the Weil descent technique have also grown in importance. This second volume addresses these advances and brings the reader up to date. Prominent contributors to the research literature in these areas have provided articles that reflect the current state of these important topics. They are divided into the areas of protocols, implementation techniques, mathematical foundations and pairing based cryptography. Each of the topics is presented in an accessible, coherent and consistent manner for a wide audience that will include mathematicians, computer scientists and engineers.

1089 and All that a Journey Into Mathematics

Author: D. J. Acheson
Publisher: Oxford University Press, USA
ISBN: 0198516231
Release Date: 2002
Genre: Mathematics

This excellent book, written by the established author David Acheson, makes mathematics accessible to everyone. Providing an entertaining and witty overview of the subject, the text includes several fascinating puzzles, and is accompanied by numerous illustrations and sketches by world famous cartoonists. This unusual book is one of the most readable explanations of mathematics available.

Lectures on the Coupling Method

Author: Torgny Lindvall
Publisher: Courier Corporation
ISBN: 9780486153247
Release Date: 2012-08-15
Genre: Mathematics

Practical and easy-to-use reference progresses from simple to advanced topics, covering, among other topics, renewal theory, Markov chains, Poisson approximation, ergodicity, and Strassen's theorem. 1992 edition.

Recurrence Sequences

Author: Graham Everest
Publisher: American Mathematical Soc.
ISBN: 9781470423155
Release Date: 2015-09-03

Recurrence sequences are of great intrinsic interest and have been a central part of number theory for many years. Moreover, these sequences appear almost everywhere in mathematics and computer science. This book surveys the modern theory of linear recurrence sequences and their generalizations. Particular emphasis is placed on the dramatic impact that sophisticated methods from Diophantine analysis and transcendence theory have had on the subject. Related work on bilinear recurrences and an emerging connection between recurrences and graph theory are covered. Applications and links to other areas of mathematics are described, including combinatorics, dynamical systems and cryptography, and computer science. The book is suitable for researchers interested in number theory, combinatorics, and graph theory.

Women in Ancient Greece and Rome

Author: Michael Massey
Publisher: Cambridge University Press
ISBN: 0521318076
Release Date: 1988-09-29
Genre: Juvenile Nonfiction

Michael Massey's thorough and provocative account is an ideal resource book for students following courses in classical studies and classical civilization. It draws on a wide range of contemporary quotations and is well illustrated with examples of original painting and sculpture. The book is divided into two sections--on Greece and on Rome--with material organized under thematic headings, ranging from religion to exploitation, entertainment to employment.