ISBN13: 9780195137316
hardback, 1008 pages May 2009,
This edited volume presents a comprehensive history of modern logic from the Middle Ages through the end of the twentieth century. In addition to a history of symbolic logic, the contributors also examine developments in the philosophy of logic and philosophical logic in modern times. The book begins with chapters on late medieval developments and logic and philosophy of logic from Humanism to Kant. The following chapters focus on the emergence of symbolic logic with special emphasis on the relations between logic and mathematics, on the one hand, and on logic and philosophy, on the other. This discussion is completed by a chapter on the themes of judgment and inference from 1837-1936. The volume contains a section on the development of mathematical logic from 1900-1935, followed by a section on main trends in mathematical logic after the 1930s. The volume goes on to discuss modal logic from Kant till the late twentieth century, and logic and semantics in the twentieth century; the philosophy of alternative logics; the philosophical aspects of inductive logic; the relations between logic and linguistics in the twentieth century; the relationship between logic and artificial intelligence; and ends with a presentation of the main schools of Indian logic.
The Development of Modern Logic includes many prominent philosophers from around the world who work in the philosophy and history of mathematics and logic, who not only survey developments in a given period or area but also seek to make new contributions to contemporary research in the field. It is the first volume to discuss the field with this breadth of coverage and depth, and will appeal to scholars and students of logic and its philosophy. Product Details
1. Introduction , Leila Haaparanta 2. Late Medieval Logic , Tuomo Aho and Mikko Yrjonsuuri 3. Logic and Philosophy of Logic from Humanism to Kant , Mirella Capozzi and Gino Roncaglia 4. The Emergence of Symbolic Logic: the Interplay between Logic and Mathematics The Mathematical Origins of Nineteenth Century Algebra of Logic, Volker Peckhaus; Gottlob Frege, Christian Thiel 5. The Emergence of Symbolic Logic: the Interplay between Logic and Philosophy The Logic Question , Risto Vilkko The Relations between Logic and Philosophy 1874-1931 , Leila Haaparanta 6. A Century of Judgement and Inference: 1837-1936 Some Strands in the Development of Logic , G^"oran Sundholm 7. The Development of Mathematical Logic from Russell to Tarski 1900-1935 , Paolo Mancosu, Richard Zach, and Calixto Badesa 8. Main Trends in Mathematical Logic after the 1930s Set Theory, Model Theory, and Computability Theory , Wilfrid Hodges Proof Theory of Classical and Intuitionistic Logic , Jan von Plato; 9. Modal Logic from Kant to Possible Worlds Semantics, Tapio Korte, Ari Maunu, and Tuomo Aho Appendix: Conditionals and Possible Worlds: On C. S. Peirce's Conception of Conditionals and Modalities , Risto Hilpinen 10. Logic and Semantics in the Twentieth Century , Gabriel Sandu and Tuomo Aho 11. The Philosophy of Alternative Logics , Andrew Aberdein and Stephen Read 12. Philosophy of Inductive Logic , Sandy Zabell 13. Logic and Linguistics in the Twentieth Century , Alessandro Lenci and Gabriel Sandu 14. Logic and Artificial Intelligence , Richmond Thomason 15. Indian Logic , J. N. Mohanty, S.
ISBN: 978-0-19-956482-8
Estimated publication date: April 2009
464 pages, 46 line drawings, 234x156 mm
Provides concise introduction to several branches of mathematical physics.
Focuses on fundamental concepts, but avoids excessive technical details.
Bridges gap between basic and highly specialised courses.
Written in an informal style.
Assumes minimal technical background.
Enables early appreciation of modern mathematics and its application in modern physics.
Four new chapters on Lie groups and fibre bundles leading to an exposition of guage theory and the standard model of elementary particle physics.
This second edition of Tensors and Manifolds is based on courses taken by advanced undergraduate and beginning graduate students in mathematics and physics, giving an introduction to the expanse of modern mathematics and its application in modern physics. It aims to fill the gap between the basic courses and the highly technical and specialised courses which both mathematics and physics students require in ther advanced training, while simultaneously trying to promote, at an early stage, a better appreciation and understanding of each other's discipline. The book sets forth the basic principles of tensors and manifolds, describing how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics. The existing material from the first edition has been reworked and extended in some sections to provide extra clarity, with additional problems. Four new chapters on Lie groups and fibre bundles have been included, leading to an exposition of gauge theory and the standard model of elementary particle physics. Mathematical rigour combined with an informal style makes this a very accessible book and will provide the reader with an enjoyable panorama of interesting mathematics and physics.
ISBN: 978-0-19-956308-1 (Paperback)
ISBN: 978-0-19-956307-4 (Hardback)
Estimated publication date: June 2009
224 pages, 56 line illustrations, 234x156 mm
Clear, concise layout and exposition of ideas
Extensive cross-referencing
Numerous exercises, with hints for the more challenging ones
A companion website provides supplementary materials with extra explanations and examples
Contains new material on standard surfaces, which introduces the more geometric aspects of topology as well as amplifying the section on quotient spaces.
More examples and explanations to help the reader, and many more diagrams.
One of the ways in which topology has influenced other branches of mathematics in the past few decades is by putting the study of continuity and convergence into a general setting. This new edition of Wilson Sutherland's classic text introduces metric and topological spaces by describing some of that influence. The aim is to move gradually from familiar real analysis to abstract topological spaces, using metric spaces as a bridge between the two. The language of metric and topological spaces is established with continuity as the motivating concept. Several concepts are introduced, first in metric spaces and then repeated for topological spaces, to help convey familiarity. The discussion develops to cover connectedness, compactness and completeness, a trio widely used in the rest of mathematics.
Topology also has a more geometric aspect which is familiar in popular expositions of the subject as `rubber-sheet geometry', with pictures of Mobius bands, doughnuts, Klein bottles and the like; this geometric aspect is illustrated by describing some standard surfaces, and it is shown how all this fits into the same story as the more analytic developments.
The book is primarily aimed at second- or third-year mathematics students. There are numerous exercises, many of the more challenging ones accompanied by hints, as well as a companion website, with further explanations and examples as well as material supplementary to that in the book.
Readership: Second year and above undergraduates in Mathematics.
Preface
1. Introduction
2. Notation and terminology
3. More on sets and functions
4. Review of some real analysis
5. Metric spaces
6. More concepts in metric spaces
7. Topological spaces
8. Continuity in topological spaces; bases
9. Some concepts in topological spaces
10. Subspaces and product spaces
11. The Hausdorff condition
12. Connected spaces
13. Compact spaces
14. Sequential compactness
15. Quotient spaces and surfaces
16. Uniform convergence
17. Complete metric spaces
References
Index
ISBN: 978-0-19-852762-6 (hardback)
ISBN: 978-0-19-852763-3 (Paperback)
Estimated publication date: June 2009
304 pages, 65 line figs., 246x189 mm
Series: Oxford Master Series in Physics number 16
Accessible introduction to quantum information, computing and communications.
Class-tested, based on lectures at advanced undergraduate and beginning graduate level.
Includes ample tutorial material and numerous exercises at chapter ends.
Includes technical appendices at the end of the book.
Quantum information- the subject- is a new and exciting area of science, which brings together physics, information theory, computer science and mathematics. "Quantum Information"- the book- is based on two successful lecture courses given to advanced undergraduate and beginning postgraduate students in physics. The intention is to introduce readers at this level to the fundamental, but offer rather simple, ideas behind ground-breaking developments including quantum cryptography, teleportation and quantum computing. The text is necessarily rather mathematical in style, but the mathematics nowhere allowed priority over the key physical ideas. My aim throughout was to be as complete and self- contained but to avoid, as far as possible, lengthy and formal mathematical proofs. Each of the eight chapters is followed by about forty exercise problems with which the reader can test their understanding and hone their skills. These will also provide a valuable resource to tutors and lectures.
Readership: Students of physics and of computer science and researchers interested in quantum information, quantum computing and the foundations of quantum theory.
1. Probability and Information
2. Elements of Quantum Theory
3. Quantum Cryptography
4. Generalized Measurements
5. Entaglement
6. Quantum Information processing
7. Quantum Computation
8. Quantum Information theory
ISBN: 978-0-19-954758-6 (Hardback)
Estimated publication date: August 2009
672 pages, 150 line and halftone figures, 246x171 mm
Series: Oxford Graduate Texts
Comprehensive updated synthesis of statistical physics and quantum field theory
Introduction to new and powerful methods of analysis
Ideal combination of physical ideas and mathematical tools
Self-contained introduction to many important areas of physics
High-quality discussion and thorough analysis of many physical phenomena
This book provides a thorough introduction to the fascinating world of phase transitions as well as many related topics, including random walks, combinatorial problems, quantum field theory and S-matrix. Fundamental concepts of phase transitions, such as order parameters, spontaneous symmetry breaking, scaling transformations, conformal symmetry, and anomalous dimensions, have deeply changed the modern vision of many areas of physics, leading to remarkable developments in statistical mechanics, elementary particle theory, condensed matter physics and string theory. This self-contained book provides an excellent introduction to frontier topics of exactly solved models in statistical mechanics and quantum field theory, renormalization group, conformal models, quantum integrable systems, duality, elastic S-matrix, thermodynamics Bethe ansatz and form factor theory. The clear discussion of physical principles is accompanied by a detailed analysis of several branches of mathematics, distinguished for their elegance and beauty, such as infinite dimensional algebras, conformal mappings, integral equations or modular functions.
Besides advanced research themes, the book also covers many basic topics in statistical mechanics, quantum field theory and theoretical physics. Each argument is discussed in great detail, paying attention to an overall coherent understanding of physical phenomena. Mathematical background is provided in supplements at the end of each chapter, when appropriate. The chapters are also followed by problems of different levels of difficulty. Advanced undergraduate and graduate students will find a rich and challenging source for improving their skills and for accomplishing a comprehensive learning of the many facets of the subject.
Readership: Graduate students in physics and mathematics, advanced undergraduate students in physics and mathematics. Also researchers in statistical mechanics, field theory, condensed matter physics and mathematical physics.
I: Introductory Notions
1. Introduction
2. One-dimensional systems
3. Approximate solutions
II: Bidimensional lattice models
4. Duality of two-dimensional Ising model
5. Combinatorial solutions of the Ising model
6. Transfer matrix of the two-dimensional Ising model
III: Quantum field theory and conformal variance
7. Quantum field theory
8. Renormalization group
9. Fermionic formulation of the Ising model
10. Conformal field theory
11. Minimal conformal models
12. Conformal field theory of free Bosonic and Fermionic fields
13. Conformal field theories with extended symmetries
14. The arena of conformal models
IV: Away from criticality
15. In the vicinity of the critical points
16. Integrable quantum field theories
17. S-matrix theory
18. Exact S-matrices
19. Thermodynamics Bethe Ansatz
20. Form factors and correlation functions
21. Non-integrable aspects