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Beginning with art and architecture and culminating with science and mathematics itself, this book discusses geometric ideas and their many applications throughout history. These range from ancient to modern, concrete to abstract, and familiar to cutting edge. Each chapter is written by a leading expert or pioneer in their own field, and the book should be a valuable resource for students and teachers of geometry alike.
Symbolic dynamics originated as a tool for analyzing dynamical systems and flows by discretizing space as well as time. The development of information theory gave impetus to the study of symbol sequences as objects in their own right. Today, symbolic dynamics has expanded to encompass multi-dimensional arrays of symbols and has found diverse applications both within and beyond mathematics. This volume is based on the AMS Short Course on Symbolic Dynamics and its Applications. It contains introductory articles on the fundamental ideas of the field and on some of its applications. Topics include the use of symbolic dynamics techniques in coding theory and in complex dynamics, the relation between the theory of multi-dimensional systems and the dynamics of tilings, and strong shift equivalence theory. Contributors to the volume are experts in the field and are clear expositors. The book is suitable for graduate students and research mathematicians interested in symbolic dynamics and its applications.
This volume contains the proceedings of the conference, Symbolic Dynamics and its Applications, held at Yale University in the summer of 1991 in honour of Roy L. Adler on his sixtieth birthday. The conference focused on symbolic dynamics and its applications to other fields, including: ergodic theory, smooth dynamical systems, information theory, automata theory, and statistical mechanics. Featuring a range of contributions from some of the leaders in the field, this volume presents an excellent overview of the subject.
This book chronicles how America's most glorious and historically significant harbor was rescued from decades of pollution and neglect by a community of caring citizens who were linked to an environmentally committed judge and his special harbor master. This dynamic public-private team shaped novel legal and political procedures for governing and restoring the harbor.
What does style mean in mathematics? Style is both how one does something and how one communicates what was done. In this book, the author investigates the worlds of the well-known numbers, the binomial coefficients. He follows the example of Raymond Queneau's Exercises in Style.
Naomi Schaefer Riley offers a compelling look at the struggles of interfaith marriages in the United States.
For International Relations scholars, discussions of globalization inevitably turn to questions of sovereignty. How much control does a country have over its borders, people and economy? Where does that authority come from? Sovereign Lives explores these changes through reading of humanitarian intervention, human rights discourses, securitization, refugees, the fragmentation of identities and the practices of development.
Based on a capstone course that the author taught to upper division undergraduate students with the goal to explain and visualize the connections between different areas of mathematics and the way different subject matters flow from one another, this book is suitable for those with a basic knowledge of high school mathematics.
This volume contains lectures from the Graduate Summer School “Quantum Field Theory and Manifold Invariants” held at Park City Mathematics Institute 2019. The lectures span topics in topology, global analysis, and physics, and they range from introductory to cutting edge. Topics treated include mathematical gauge theory (anti-self-dual equations, Seiberg-Witten equations, Higgs bundles), classical and categorified knot invariants (Khovanov homology, Heegaard Floer homology), instanton Floer homology, invertible topological field theory, BPS states and spectral networks. This collection presents a rich blend of geometry and topology, with some theoretical physics thrown in as well, and so provides a snapshot of a vibrant and fast-moving field. Graduate students with basic preparation in topology and geometry can use this volume to learn advanced background material before being brought to the frontiers of current developments. Seasoned researchers will also benefit from the systematic presentation of exciting new advances by leaders in their fields.
Terrorism motivated by Islamist religious ideology has been on the rise for the last forty years. Why? The three prior waves of terrorism—anarchist, nationalist, and Marxist—arose generally from a combination of geopolitical events and local grievances. This “fourth wave” of terrorism, however, has risen out of a different set of conditions. Existing analyses of terrorism often consider how terrorist ideologies have evolved or how grievances have changed over time. But these approaches miss what could be called the “supply” side of ideology—how state and nonstate actors have exported an ideology of Islamism and how this ideology has taken root beyond what grievances or ideologi...