Monoidal Categories and Topological Field Theory


Book Description

This monograph is devoted to monoidal categories and their connections with 3-dimensional topological field theories. Starting with basic definitions, it proceeds to the forefront of current research. Part 1 introduces monoidal categories and several of their classes, including rigid, pivotal, spherical, fusion, braided, and modular categories. It then presents deep theorems of Müger on the center of a pivotal fusion category. These theorems are proved in Part 2 using the theory of Hopf monads. In Part 3 the authors define the notion of a topological quantum field theory (TQFT) and construct a Turaev-Viro-type 3-dimensional state sum TQFT from a spherical fusion category. Lastly, in Part 4 this construction is extended to 3-manifolds with colored ribbon graphs, yielding a so-called graph TQFT (and, consequently, a 3-2-1 extended TQFT). The authors then prove the main result of the monograph: the state sum graph TQFT derived from any spherical fusion category is isomorphic to the Reshetikhin-Turaev surgery graph TQFT derived from the center of that category. The book is of interest to researchers and students studying topological field theory, monoidal categories, Hopf algebras and Hopf monads.




BIG Jobs Guide


Book Description

Jobs using mathematics, statistics, and operations research are projected to grow by almost 30% over the next decade. BIG Jobs Guide helps job seekers at every stage of their careers in these fields explore opportunities in business, industry, and government (BIG). Written in a conversational and practical tone, BIG Jobs Guide offers insight on topics such as: - What skills can I offer employers? - How do I write a high-impact r?esume? - Where can I find a rewarding internship? - What kinds of jobs are out there for me? The Guide also offers insights to advisors and mentors on topics such as how departments can help students get BIG jobs and how faculty members and internship mentors can build institutional relationships. Whether you're an undergraduate or graduate student or a job seeker in mathematics, statistics, or operations research, this hands-on book will help you reach your goal?landing an internship, getting your first job or transitioning to a new one.




Practical Analysis of Algorithms


Book Description

This book introduces the essential concepts of algorithm analysis required by core undergraduate and graduate computer science courses, in addition to providing a review of the fundamental mathematical notions necessary to understand these concepts. Features: includes numerous fully-worked examples and step-by-step proofs, assuming no strong mathematical background; describes the foundation of the analysis of algorithms theory in terms of the big-Oh, Omega, and Theta notations; examines recurrence relations; discusses the concepts of basic operation, traditional loop counting, and best case and worst case complexities; reviews various algorithms of a probabilistic nature, and uses elements of probability theory to compute the average complexity of algorithms such as Quicksort; introduces a variety of classical finite graph algorithms, together with an analysis of their complexity; provides an appendix on probability theory, reviewing the major definitions and theorems used in the book.




Elements of Phase Transitions and Critical Phenomena


Book Description

As an introductory account of the theory of phase transitions and critical phenomena, this book reflects lectures given by the authors to graduate students at their departments and is thus classroom-tested to help beginners enter the field. Most parts are written as self-contained units and every new concept or calculation is explained in detail without assuming prior knowledge of the subject. The book significantly enhances and revises a Japanese version which is a bestseller in the Japanese market and is considered a standard textbook in the field. It contains new pedagogical presentations of field theory methods, including a chapter on conformal field theory, and various modern developments hard to find in a single textbook on phase transitions. Exercises are presented as the topics develop, with solutions found at the end of the book, making the text useful for self-teaching, as well as for classroom learning.




Red Dynamite


Book Description

In Red Dynamite, Carl R. Weinberg argues that creationism's tenacious hold on American public life depended on culture-war politics inextricably embedded in religion. Many Christian conservatives were convinced that evolutionary thought promoted immoral and even bestial social, sexual, and political behavior. The "fruits" of subscribing to Darwinism were, in their minds, a dangerous rearrangement of God-given standards and the unsettling of traditional hierarchies of power. Despite claiming to focus exclusively on science and religion, creationists were practicing politics. Their anticommunist campaign, often infused with conspiracy theory, gained power from the fact that the Marxist founders, the early Bolshevik leaders, and their American allies were staunch evolutionists. Using the Scopes "Monkey" Trial as a starting point, Red Dynamite traces the politically explosive union of Darwinism and communism over the next century. Across those years, social evolution was the primary target of creationists, and their "ideas have consequences" strategy instilled fear that shaped the contours of America's culture wars. By taking the anticommunist arguments of creationists seriously, Weinberg reveals a neglected dimension of antievolutionism and illuminates a source of the creationist movement's continuing strength. Thanks to generous funding from Indiana University and its participation in TOME (Toward an Open Monograph Ecosystem), the ebook editions of this book are available as Open Access volumes from Cornell Open (cornellpress.cornell.edu/cornell-open) and other repositories.




Police Mission


Book Description

What is the best management style for the police? Police Mission discusses the values and norms inherent in the American police mission, and examines how police respond to challenges that arise while attempting to uphold this mission. It reveals that the way officers are being trained in ethics and human relations are not effective as they could be, and argues that policing has to move towards a greater emphasis on human values, moral sensitivity, and discerning judgment. A large number of themes ranging from personnel management, occupational culture, and innovative experiments in US policing techniques are examined. Several organizational theories as well as examples of international policing efforts from England to Japan are also analyzed. An important contribution to police literature, this book will be a valuable aid to students of criminology as well as practitioners and researchers of police science.




Infinite Dimensional Analysis


Book Description

This text was born out of an advanced mathematical economics seminar at Caltech in 1989-90. We realized that the typical graduate student in mathematical economics has to be familiar with a vast amount of material that spans several traditional fields in mathematics. Much of the mate rial appears only in esoteric research monographs that are designed for specialists, not for the sort of generalist that our students need be. We hope that in a small way this text will make the material here accessible to a much broader audience. While our motivation is to present and orga nize the analytical foundations underlying modern economics and finance, this is a book of mathematics, not of economics. We mention applications to economics but present very few of them. They are there to convince economists that the material has so me relevance and to let mathematicians know that there are areas of application for these results. We feel that this text could be used for a course in analysis that would benefit math ematicians, engineers, and scientists. Most of the material we present is available elsewhere, but is scattered throughout a variety of sources and occasionally buried in obscurity. Some of our results are original (or more likely, independent rediscoveries). We have included some material that we cannot honestly say is neces sary to understand modern economic theory, but may yet prove useful in future research.




Braid Groups


Book Description

In this well-written presentation, motivated by numerous examples and problems, the authors introduce the basic theory of braid groups, highlighting several definitions that show their equivalence; this is followed by a treatment of the relationship between braids, knots and links. Important results then treat the linearity and orderability of the subject. Relevant additional material is included in five large appendices. Braid Groups will serve graduate students and a number of mathematicians coming from diverse disciplines.




Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations


Book Description

This work was initiated in the summer of 1985 while all of the authors were at the Center of Nonlinear Studies of the Los Alamos National Laboratory; it was then continued and polished while the authors were at Indiana Univer sity, at the University of Paris-Sud (Orsay), and again at Los Alamos in 1986 and 1987. Our aim was to present a direct geometric approach in the theory of inertial manifolds (global analogs of the unstable-center manifolds) for dissipative partial differential equations. This approach, based on Cauchy integral mani folds for which the solutions of the partial differential equations are the generating characteristic curves, has the advantage that it provides a sound basis for numerical Galerkin schemes obtained by approximating the inertial manifold. The work is self-contained and the prerequisites are at the level of a graduate student. The theoretical part of the work is developed in Chapters 2-14, while in Chapters 15-19 we apply the theory to several remarkable partial differ ential equations.




Helaman Ferguson


Book Description