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Numerical Mathematics
Numerical Mathematics presents the innovative approach of using numerical methods as a practical laboratory for all undergraduate mathematics courses in science and engineering streams. The authors bridge the gap between numerical methods and undergraduate mathematics and emphasize the graphical visualization of mathematical properties, numerical verification of formal statements, and illustrations of the mathematical ideas. Students using Numerical Mathematics as a supplementary reference for basic mathematical courses will be encouraged to deveolp their mathematical intuition with an effective component of technology, while students using it as the primary text for numerical courses will have a broader, reinforced understanding of the subject.
Handbook on Systemic Risk
The Handbook on Systemic Risk, written by experts in the field, provides researchers with an introduction to the multifaceted aspects of systemic risks facing the global financial markets. The Handbook explores the multidisciplinary approaches to analyzing this risk, the data requirements for further research, and the recommendations being made to avert financial crisis. The Handbook is designed to encourage new researchers to investigate a topic with immense societal implications as well as to provide, for those already actively involved within their own academic discipline, an introduction to the research being undertaken in other disciplines. Each chapter in the Handbook will provide researchers with a superior introduction to the field and with references to more advanced research articles. It is the hope of the editors that this Handbook will stimulate greater interdisciplinary academic research on the critically important topic of systemic risk in the global financial markets.
Introduction to Central Banking
This open access book gives a concise introduction to the practical implementation of monetary policy by modern central banks. It describes the conventional instruments used in advanced economies and the unconventional instruments that have been widely adopted since the financial crisis of 2007–2008. Illuminating the role of central banks in ensuring financial stability and as last resort lenders, it also offers an overview of the international monetary framework. A flow-of-funds framework is used throughout to capture this essential dimension in a consistent and unifying manner, providing a unique and accessible resource on central banking and monetary policy, and its integration with financial stability. Addressed to professionals as well as bachelors and masters students of economics, this book is suitable for a course on economic policy. Useful prerequisites include at least a general idea of the economic institutions of an economy, and knowledge of macroeconomics and monetary economics, but readers need not be familiar with any specific macroeconomic models.
Lecture Notes on O-Minimal Structures and Real Analytic Geometry
This volume was produced in conjunction with the Thematic Program in o-Minimal Structures and Real Analytic Geometry, held from January to June of 2009 at the Fields Institute. Five of the six contributions consist of notes from graduate courses associated with the program: Felipe Cano on a new proof of resolution of singularities for planar analytic vector fields; Chris Miller on o-minimality and Hardy fields; Jean-Philippe Rolin on the construction of o-minimal structures from quasianalytic classes; Fernando Sanz on non-oscillatory trajectories of vector fields; and Patrick Speissegger on pfaffian sets. The sixth contribution, by Antongiulio Fornasiero and Tamara Servi, is an adaptation...
k-Schur Functions and Affine Schubert Calculus
This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and states the current open problems. Affine Schubert calculus lies at the crossroads of combinatorics, geometry, and representation theory. Its modern development is motivated by two seemingly unrelated directions. One is the introduction of k-Schur functions in the study of Macdonald polynomial positivity, a mostly combinatorial branch of symmetric function theory. The other direction is the study of the Schubert bases of the (co)homology of the affine Grassmannian, an algebro-topological formulation of a problem in enumerative geometry. This is the first introductory text on this subject. It contains many examples in Sage, a free open source general purpose mathematical software system, to entice the reader to investigate the open problems. This book is written for advanced undergraduate and graduate students, as well as researchers, who want to become familiar with this fascinating new field.
Infinite Dimensional Dynamical Systems
This collection covers a wide range of topics of infinite dimensional dynamical systems generated by parabolic partial differential equations, hyperbolic partial differential equations, solitary equations, lattice differential equations, delay differential equations, and stochastic differential equations. Infinite dimensional dynamical systems are generated by evolutionary equations describing the evolutions in time of systems whose status must be depicted in infinite dimensional phase spaces. Studying the long-term behaviors of such systems is important in our understanding of their spatiotemporal pattern formation and global continuation, and has been among major sources of motivation a...
New Approaches to Economic Challenges The Financial System
The New Approaches to Economic Challenges (NAEC) initiative was established to distil lessons from the Global Financial Crisis and now the systemic crises sparked by the COVID-19 pandemic. This book publishes short summaries of a diverse range of thinking and proposals from a prestigious series of experts.
Constructing the Family
In nineteenth-century England, legal conceptions of work and family changed in fundamental ways. Notably, significant legal moves came into play that changed the legal understanding of the family. Constructing the Family examines the evolution of the legal-discursive framework governing work and family relations. Luke Taylor considers the intersecting intellectual and institutional forces that contributed to the dissolution of the household, the establishment of separate spheres of work and family, and the emergence of modern legal and social ideas concerning work and family. He shows how specific legal-institutional moves contributed to the creation of the family’s categorical status in the social and legal order and a distinct and exceptional body of rules – Family Law – for its governance. Shedding light on the historical processes that contributed to the emergence of English Family Law, Constructing the Family shows how work and family became separate regulatory domains, and in so doing reveals the contingent nature of the modern legal family.
Optimization and Data Analysis in Biomedical Informatics
This volume covers some of the topics that are related to the rapidly growing field of biomedical informatics. In June 11-12, 2010 a workshop entitled ‘Optimization and Data Analysis in Biomedical Informatics’ was organized at The Fields Institute. Following this event invited contributions were gathered based on the talks presented at the workshop, and additional invited chapters were chosen from world’s leading experts. In this publication, the authors share their expertise in the form of state-of-the-art research and review chapters, bringing together researchers from different disciplines and emphasizing the value of mathematical methods in the areas of clinical sciences. This work is targeted to applied mathematicians, computer scientists, industrial engineers, and clinical scientists who are interested in exploring emerging and fascinating interdisciplinary topics of research. It is designed to further stimulate and enhance fruitful collaborations between scientists from different disciplines.
Blaschke Products and Their Applications
Blaschke Products and Their Applications presents a collection of survey articles that examine Blaschke products and several of its applications to fields such as approximation theory, differential equations, dynamical systems, harmonic analysis, to name a few. Additionally, this volume illustrates the historical roots of Blaschke products and highlights key research on this topic. For nearly a century, Blaschke products have been researched. Their boundary behaviour, the asymptomatic growth of various integral means and their derivatives, their applications within several branches of mathematics, and their membership in different function spaces and their dynamics, are a few examples of where Blaschke products have shown to be important. The contributions written by experts from various fields of mathematical research will engage graduate students and researches alike, bringing the reader to the forefront of research in the topic. The readers will also discover the various open problems, enabling them to better pursue their own research.
