ISBN: 978-1-118-94704-3
448 pages
May 2016
A one-of-a-kind guide to identifying and dealing with modern statistical developments in causality
Written by a group of well-known experts, Statistics and Causality: Methods for Applied Empirical Research focuses on the most up-to-date developments in statistical methods in respect to causality. Illustrating the properties of statistical methods to theories of causality, the book features a summary of the latest developments in methods for statistical analysis of causality hypotheses.
The book is divided into five accessible and independent parts. The first part introduces the foundations of causal structures and discusses issues associated with standard mechanistic and difference-making theories of causality. The second part features novel generalizations of methods designed to make statements concerning the direction of effects. The third part illustrates advances in Granger-causality testing and related issues. The fourth section focuses on counterfactual approaches and propensity score analysis. Finally, the fifth part presents designs for causal inference with an overview of the research designs commonly used in epidemiology. Statistics and Causality: Methods for Applied Empirical Research also includes:
New statistical methodologies and approaches to causal analysis in the context of the continuing development of philosophical theories
End-of-chapter bibliographies that provide references for further discussions and additional research topics
Discussions on the use and applicability of software when appropriate
Statistics and Causality: Methods for Applied Empirical Research is an ideal reference for practicing statisticians, applied mathematicians, psychologists, sociologists, logicians, medical professionals, epidemiologists, and educators who want to learn more about new methodologies in causal analysis. The book is also an excellent textbook for graduate-level courses in causality and qualitative logic.
List of Contributors ix
Preface xiii
Part I Base of Causality 1
1 Causation and the Aims of Inquiry 3
Edward J. Hall
See More
Covers an important topic at the interface of Physics and Mathematics
Didactical approach, suitable for students with minimal pre-requisites
Mathematically complete and precise
Many physical applications
This text explores how Clifford algebras and spinors have been sparking a collaboration and bridging a gap between Physics and Mathematics. This collaboration has been the consequence of a growing awareness of the importance of algebraic and geometric properties in many physical phenomena, and of the discovery of common ground through various touch points: relating Clifford algebras and the arising geometry to so-called spinors, and to their three definitions (both from the mathematical and physical viewpoint). The main point of contact are the representations of Clifford algebras and the periodicity theorems. Clifford algebras also constitute a highly intuitive formalism, having an intimate relationship to quantum field theory. The text strives to seamlessly combine these various viewpoints and is devoted to a wider audience of both physicists and mathematicians.
Among the existing approaches to Clifford algebras and spinors this book is unique in that it provides a didactical presentation of the topic and is accessible to both students and researchers. It emphasizes the formal character and the deep algebraic and geometric completeness, and merges them with the physical applications. The style is clear and precise, but not pedantic. The sole pre-requisites is a course in Linear Algebra which most students of Physics, Mathematics or Engineering will have covered as part of their undergraduate studies.
1: Preliminaries
2: Exterior Algebra and Grassmann Algebra
3: Geometric or Clifford Algebra
4: Classification and Representation of the Clifford Algebras
5: Clifford Algebras and Associated Groups
6: Spinors
Appendix: The Standard 2-Component Spinor Formalism
Hardback
Published: 19 May 2016 (Estimated)
256 Pages
246x171mm
ISBN: 9780198782926
Paperback | March 2016 | ISBN: 9780691161693
Hardcover | March 2016 | ISBN: 9780691161686
232 pp. | 7 x 10
Over the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights. In recent decades, model theory has joined this work through the theory of o-minimality, providing finiteness and uniformity statements and new structural tools.
For non-archimedean fields, such as the p-adics, the Berkovich analytification provides a connected topology with many thoroughgoing analogies to the real topology on the set of complex points, and it has become an important tool in algebraic dynamics and many other areas of geometry.
This book lays down model-theoretic foundations for non-archimedean geometry. The methods combine o-minimality and stability theory. Definable types play a central role, serving first to define the notion of a point and then properties such as definable compactness.
Beyond the foundations, the main theorem constructs a deformation retraction from the full non-archimedean space of an algebraic variety to a rational polytope. This generalizes previous results of V. Berkovich, who used resolution of singularities methods.
No previous knowledge of non-archimedean geometry is assumed. Model-theoretic prerequisites are reviewed in the first sections.
Ehud Hrushovski is professor of mathematics at the Hebrew University of Jerusalem. He is the coauthor of Finite Structures with Few Types (Princeton) and Stable Domination and Independence in Algebraically Closed Valued Fields. Francois Loeser is professor of mathematics at Pierre-and-Marie-Curie University in Paris.
Paperback | March 2016 | ISBN: 9780691144771
232 pp. | 6 x 9 | 2 line illus. 18 tables.
This book introduces the theory of complex surfaces through a comprehensive look at finite covers of the projective plane branched along line arrangements. Paula Tretkoff emphasizes those finite covers that are free quotients of the complex two-dimensional ball. Tretkoff also includes background on the classical Gauss hypergeometric function of one variable, and a chapter on the Appell two-variable F1 hypergeometric function.
The material in this book began as a set of lecture notes, taken by Tretkoff, of a course given by Friedrich Hirzebruch at ETH Zurich in 1996. The lecture notes were then considerably expanded by Hirzebruch and Tretkoff over a number of years. In this book, Tretkoff has expanded those notes even further, still stressing examples offered by finite covers of line arrangements. The book is largely self-contained and foundational material is introduced and explained as needed, but not treated in full detail. References to omitted material are provided for interested readers.
Aimed at graduate students and researchers, this is an accessible account of a highly informative area of complex geometry.
Paula Tretkoff is professor of mathematics at Texas A&M University and director of research in the National Center for Scientific Research (CNRS) at the Universite de Lille 1, France.
Hardcover | March 2016 | ISBN: 9780691162690
584 pp. | 7 x 10 | 3 halftones. 60 line illus.
Although group theory is a mathematical subject, it is indispensable to many areas of modern theoretical physics, from atomic physics to condensed matter physics, particle physics to string theory. In particular, it is essential for an understanding of the fundamental forces. Yet until now, what has been missing is a modern, accessible, and self-contained textbook on the subject written especially for physicists.
Group Theory in a Nutshell for Physicists fills this gap, providing a user-friendly and classroom-tested text that focuses on those aspects of group theory physicists most need to know. From the basic intuitive notion of a group, A. Zee takes readers all the way up to how theories based on gauge groups could unify three of the four fundamental forces. He also includes a concise review of the linear algebra needed for group theory, making the book ideal for self-study.
Provides physicists with a modern and accessible introduction to group theory
Covers applications to various areas of physics, including field theory, particle physics, relativity, and much more
Topics include finite group and character tables; real, pseudoreal, and complex representations; Weyl, Dirac, and Majorana equations; the expanding universe and group theory; grand unification; and much more
The essential textbook for students and an invaluable resource for researchers
Features a brief, self-contained treatment of linear algebra
An online illustration package is available to professors
A. Zee is professor of physics at the Kavli Institute for Theoretical Physics at the University of California, Santa Barbara. His books include Quantum Field Theory in a Nutshell, Einstein Gravity in a Nutshell, and Fearful Symmetry: The Search for Beauty in Modern Physics (all Princeton).