Part of Lecture Notes in Logic
Publication planned for: February 2016
format: Hardback
isbn: 9781107033399
Arising from a special session held at the 2010 North American Annual Meeting of the Association for Symbolic Logic, this volume is an international cross-disciplinary collaboration with contributions from leading experts exploring connections across their respective fields. Themes range from philosophical examination of the foundations of physics and quantum logic, to exploitations of the methods and structures of operator theory, category theory, and knot theory in an effort to gain insight into the fundamental questions in quantum theory and logic. The book will appeal to researchers and students working in related fields, including logicians, mathematicians, computer scientists, and physicists. A brief introduction provides essential background on quantum mechanics and category theory, which, together with a thematic selection of articles, may also serve as the basic material for a graduate course or seminar.
Preface Jennifer Chubb, Ali Eskandarian and Valentina Harizanov
Introduction Jennifer Chubb, Ali Eskandarian and Valentina Harizanov
1. A (very) brief tour of quantum mechanics, computation, and category theory Jennifer Chubb and Valentina Harizanov
2. Could logic be empirical? The Putnam?Kripke debate Allen Stairs
3. The essence of quantum theory for computers William C. Parke
4. Fiber products of measures and quantum foundations Adam Brandenburger and H. Jerome Keisler
5. Operational theories and categorical quantum mechanics Samson Abramsky and Chris Heunen
6. Relating operator spaces via adjunctions Bart Jacobs and Jorik Mandemaker
7. Topos-based logic for quantum systems and bi-Heyting algebras Andreas Doring
8. The logic of quantum mechanics ? take II Bob Coecke
9. Reasoning about meaning in natural language with compact closed categories and Frobenius algebras Dimitri Kartsaklis, Mehrnoosh Sadrzadeh, Stephen Pulman and Bob Coecke
10. Knot logic and topological quantum computing with Majorana fermions Louis H. Kauffman
Index.
Publication planned for: March 2016
format: Paperback
isbn: 9781316603840
Originally published in 1927, as the first of a two-part set, this informative and systematically organised textbook, primarily aimed at university students, contains a vectorial treatment of geometry, reasoning that by the use of such vector methods, geometry is able to be 'both simplified and condensed'. Chapters I-XI discuss the more elementary parts of the subject, whilst the remainder is devoted to an exploration of the more complex differential invariants for a surface and their applications. Chapter titles include, 'Curves with torsion', 'Geodesics and geodesic parallels' and 'Triply orthogonal systems of surfaces'. Diagrams are included to supplement the text. Providing a detailed overview of the subject and forming a solid foundation for study of multidimensional differential geometry and the tensor calculus, this book will prove an invaluable reference work to scholars of mathematics as well as to anyone with an interest in the history of education.
Preface
Introduction. Vector notation and formulae
1. Curves with torsion
2. Envelopes, developable surfaces
3. Curvilinear coordinates on a surface. Fundamental magnitudes
4. Curves on a surface
5. The equations of Gauss and of Codazzi
6. Geodesics and geodesic parallels
7. Quadric surfaces, ruled surfaces
8. Evolute or surface of centres. Parallel surfaces
9. Conformal and spherical representations. Minimal surfaces
10. Congruences of lines
11. Triply orthogonal systems of surfaces
12. Differential invariants for a surface
Conclusion. Further recent advances
Note 1. Directions on a surface
Note 2. On the curvatures of a surface
Index.
By discussing topics such as shape representations, relaxation theory and
optimal transport, trends and synergies of mathematical tools required for
optimization of geometry and topology of shapes are explored. Furthermore,
applications in science and engineering, including economics, social sciences,
biology, physics and image processing are covered.
Maitine Bergounioux, Universite d'Orleans, France.
Radon Series on Computational and Applied Mathematics 17
xvi, 300 pages, 20 Fig.
Hardcover:
ISBN 978-3-11-043926-7
With a focus on the interplay between mathematics and applications of imaging,
the first part covers topics from optimization, inverse problems and shape spaces
to computer vision and computational anatomy. The second part is geared
towards geometric control and related topics, including Riemannian geometry,
celestial mechanics and quantum control.
Maitine Bergounioux, Universite d'Orleans, France.
Radon Series on Computational and Applied Mathematics 18
xvi, 300 pages, 40 Fig.
Hardcover:
ISBN 978-3-11-043923-6
From basic algebraic structures to cryptography, arithmetic with elliptic curves,
and automata ? this textbook contains a modern introduction to discrete
algebraic methods as required by mathematicians and computer scientists in the
age of the internet. It lays foundations for theoretical computer science and is
suitable for master students with a basic background in mathematics.
* Contains brief chapter summaries as well as examples, problems and
solutions.
*References for further reading in every chapter.
* Mathematical derivations are illustrated by a plethora of illustrations.
Volker Diekert, Manfred Kufleitner and Ulrich Hertrampf, Stuttgart,
Germany; Gerhard Rosenberger, Hamburg, Germany.
De Gruyter Textbook
xii, 340 pages, 90 Fig.
Paperback:
ISBN 978-3-11-041332-8
Date of Publication: May 2016
Language of Publication: English
Subjects:
Algebra and Number Theory
Algorithms
Combinatorics and Graph Theory
Theoretical Informatics
By connecting dynamical systems and number theory this graduate textbook on
ergodic theory covers a highly active area of mathematics, where a variety of
strands of research open up. After introducing number-theoretical dynamical
systems, the text touches on foundations and renewal theory before covering
infinite ergodic theory. Applications such as continued fraction expansion and
sum-level sets are discussed as well.
* A unique coverage of the relation between infinite ergodic theory and
number
theory.
* Example solutions to select exercises included in the appendix.
*u Useful for a course serving master (and advanced bachelor) and PhD students.
Sara Munday, University of York, United Kingdom;
Marc Kessebohmer and Bernd Stratmann, University of Bremen, Germany.
De Gruyter Textbook
xvi, 200 pages, 15 Fig.
Paperback:
ISBN 978-3-11-043941-0
Date of Publication: May 2016
Language of Publication: English
Subjects:
Algebra and Number Theory
Differential Equations and Dynamical Systems
This accessible and easy-to-read book provides many examples to illustrate
diverse topics in probability and statistics, from initial concepts up to advanced
calculations. Special attention is devoted to inequalities in probabilities and
moments and transforms in random variables. For students of mathematics,
statistics, engineering, and other quantitative sciences.
* Many examples and illustrations
* Exercises at the end of each section
* Mathematically rigorous, but exaggerate formalism is avoided
* For students of Mathematics, Statistics, Engineering and other quantitative
Sciences
Peter Zornig, University of Brasilia, Asa Norte, Brazil.
De Gruyter Textbook
Approx. x, 390 pages
Paperback:
ISBN 978-3-11-036319-7
Date of Publication: May 2016
Language of Publication: English
Subjects: Probability and Statistics
This graduate textbook on functional analysis offers a concise introduction into
the field. The authors established a modern and modular structure which allows
easy assimilation of content often displayed in much more elaborate ways. It is
thus not only suitable for graduate students but also for advanced
undergraduates.
* Modularly structured into teaching units.
* Bridges the gap between elementary and advanced topics in analysis for
advanced undergraduate and graduate students in mathematics and physics.
Gerardo Chacon, Gallaudet University, DC, USA.
Humberto Rafeiro, Juan Vallejo, Pontificia Universidad Javeriana, Bogota,Colombia.
De Gruyter Textbook
xx, 250 pages, 30 Fig.
Paperback:
ISBN 978-3-11-044191-8
Date of Publication: September 2016
Language of Publication: English
Subjects: Analysis