Edited by S. Barry Cooper / University of Leeds ・Herman Geuvers / Radboud Universiteit Nijmegen
Anand Pillay / University of Leeds ・ Jouko Vaananen / University of Amsterdam and University of Helsinki

Logic Colloquium 2006

Series: Lecture Notes in Logic
Hardback (ISBN-13: 9780521110815)

The Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium, is among the most prestigious annual meetings in the field. The current volume with contributions from plenary speakers and selected special session speakers, contains both expository and research papers by some of the best logicians in the world. The most topical areas of current research are covered: valued fields, Hrushovski constructions (from model theory), algorithmic randomness, relative computability (from computability theory), strong forcing axioms and cardinal arithmetic, large cardinals and determinacy (from set theory), as well as foundational topics such as algebraic set theory, reverse mathematics, and unprovability. This volume will be invaluable for experts as well as those interested in an overview of central contemporary themes in mathematical logic.

* Describes a new methodology for the analysis of data and planing of experiments * Combines solid, well-known, results in algebra and statistics into a systematic, step-by-step method * Leads to descriptive, inferential, and broadly qualitative analysis of the experimental results

Contents

1. Definability and elementary equivalence in the Ershov difference hierarchy Marat M. Arslanov; 2. A unified approach to algebraic set theory Benno van den Berg and Leke Moerdijk; 3. Brief introduction to unprovability Andrey Bovykin; 4. Higher-order abstract syntax in type theory Venanzio Capretta and Amy P. Felty; 5. An introduction to b-minimality Raf Cluckers; 6. The sixth lecture on algorithmic randomness Rod Downey; 7. The inevitability of logical strength: strict reverse mathematics Harvey M. Friedman; 8. Applications of logic in algebra: examples from clone theory; 9. On infinite imaginaries Ehud Hrushovski; 10. Strong minimal covers and a question of Yates: the story so far Andrew E. M. Lewis; 10. Embeddings into the Turing degrees Antonio Montalban; 11. Randomness - beyond Lebesgue measure Jan Reimann; 12. The derived model theorem J. R. Steel; 13. Forcing axioms and cardinal arithmetic Boban Velivckovic; 14. Hrushovski's amalgamation construction Frank O. Wagner.

Leslie Ann Goldberg / Sandia National Laboratories, Peru

Efficient Algorithms for Listing Combinatorial Structures

Series: Distinguished Dissertations in Computer Science (No. 5)
Paperback (ISBN-13: 9780521117883)

First published in 1993, this thesis is concerned with the design of efficient algorithms for listing combinatorial structures. The research described here gives some answers to the following questions: which families of combinatorial structures have fast computer algorithms for listing their members* What general methods are useful for listing combinatorial structures* How can these be applied to those families which are of interest to theoretical computer scientists and combinatorialists* Amongst those families considered are unlabelled graphs, first order one properties, Hamiltonian graphs, graphs with cliques of specified order, and k-colourable graphs. Some related work is also included, which compares the listing problem with the difficulty of solving the existence problem, the construction problem, the random sampling problem, and the counting problem. In particular, the difficulty of evaluating Polya’s cycle polynomial is demonstrated.

* Winner of distinguished dissertation award * Contains material of interest to combinatorialists as well as computer scientists

Contents

1. Introduction; 2. Techniques for listing combinatorial structures; 3. Applications to particular families of structures; 4. Directions for future work on listing; 5. Related results; 6. Bibliography.

T. H. Tse / The University of Hong Kong

A Unifying Framework for Structured Analysis and Design Models
An Approach Using Initial Algebra Semantics and Category Theory

Series: Cambridge Tracts in Theoretical Computer Science (No. 11)
Paperback (ISBN-13: 9780521117876)

Structured methodologies are a popular and powerful tool in information systems development. Many different ones exist, each employing a number of models and so a specification must be converted from one form to another during the development process. To solve this problem, Dr Tse here proposes a unifying framework behind popular structured models. He approaches the problem from the viewpoints of algebra and category theory. He not only develops the frameworks but also illustrates their practical and theoretical usefulness. Thus this book will provide insight for software engineers into how methodologies can be formalised and will open up a range of applications and problems for theoretical computer scientists.

Contents

1. Introduction; 2. Desirable features of systems development environments; 3. A comparison with related projects; 4. Initial algebra as a unifying framework for structured models; 5. Category theory as a unifying framework for structured models; 6. The identification of unstructuredness; 7. A prototype system to implement the unifying framework; 8. Future directions; 9. Conclusions; References; Appendices.

Edited by Felipe Cucker / City University of Hong Kong
Allan Pinkus / Technion - Israel Institute of Technology, Haifa
Michael J. Todd / Cornell University, New York

Foundations of Computational Mathematics, Hong Kong 2008

Series: London Mathematical Society Lecture Note Series (No. 363)
Paperback (ISBN-13: 9780521739702)

This volume is a collection of articles based on the plenary talks presented at the 2008 meeting in Hong Kong of the Society for the Foundations of Computational Mathematics. The talks were given by some of the foremost world authorities in computational mathematics. The topics covered reflect the breadth of research within the area as well as the richness and fertility of interactions between seemingly unrelated branches of pure and applied mathematics. As a result this volume will be of interest to researchers in the field of computational mathematics and also to non-experts who wish to gain some insight into the state of the art in this active and significant field.

* Chapters based on plenary talks given by world authorities * Reflects the richness and diversity of the area of computational mathematics * Written to appeal to non-experts and to specialists

Contents

Preface; Contributors; 1. Smoothed analysis of condition numbers Peter Burgisser; 2. A world of binomials Alicia Dickenstein; 3. Linear and nonlinear subdivision schemes in geometric modeling Nira Dyn; 4. Energy preserving and energy stable schemes for the shallow water equations Ulrik Fjordholm, Siddhartha Mishra and Eitan Tadmor; 5. Pathwise convergence of numerical schemes for random and stochastic differential equations A. Jentzen, P. E. Kloeden and A. Neuenkirch; 6. Some properties of the global behaviour of conservative low-dimensional systems Carles Simo; 7. A panoramic view of asymptotics R. Wong; 8. Tractability of multivariate problems H. Wo*niakowski.

Edited by Sophie Huczynska / University of St Andrews, Scotland
James D. Mitchell / University of St Andrews, Scotland
Colva M. Roney-Dougal / University of St Andrews, Scotland

Surveys in Combinatorics 2009

Series: London Mathematical Society Lecture Note Series (No. 365)
Paperback (ISBN-13: 9780521741736)

This volume contains survey articles based on the invited lectures given at the Twenty-second British Combinatorial Conference, held in July 2009 at the University of St Andrews. This biennial conference is a well-established international event, with speakers from all over the world. By its nature this volume provides an up-to-date overview of current research activity in several areas of combinatorics, including graph theory, design theory and packing problems. Each article is clearly written and assumes little prior knowledge on the part of the reader. The authors are some of the world’s foremost researchers in their fields, and here they summarise existing results, and give a unique preview of the most recent developments. The book provides a valuable survey of the present state of knowledge in combinatorics. It will be useful to research workers and advanced graduate students, primarily in mathematics but also in computer science, statistics and engineering.

* Contains high quality survey articles based on the invited lectures given at the British Combinatorial Conference in July 2009 * Authored by some of the world’s leading researchers in their respective fields, ranging from theory to applications * A valuable summary of the current state of the field, including the very latest research

Contents

Preface; 1. Graph decompositions and symmetry Arrigo Bonisoli; 2. Combinatorics of optimal designs R. A. Bailey and Peter J. Cameron; 3. Regularity and the spectra of graphs W. H. Haemers; 4. Trades and t-designs G. B. Khosrovshahi and B. Tayfeh-Rezaie; 5. Extremal graph packing problems: Ore-type versus Dirac-type H. A. Kierstead, A. V. Kostochka, and G. Yu; 6. Embedding large subgraphs into dense graphs Daniela Kuhn and Deryk Osthus; 7. Counting planar graphs and related families of graphs Omer Gimenez and Marc Noy; 8. Metrics for sparse graphs B. Bollobas and O. Riordan; 9. Recent results on chromatic and flow roots of graphs and matroids G. F. Royle.