This textbook introduces geometric measure theory through the notion of currents. Currents, continuous linear functionals on spaces of differential forms, are a natural language in which to formulate
The development of hierarchical models and Markov chain Monte Carlo (MCMC) techniques forms one of the most profound advances in Bayesian analysis since the 1970s and provides the basis for advances i
The development of hierarchical models and Markov chain Monte Carlo (MCMC) techniques forms one of the most profound advances in Bayesian analysis since the 1970s and provides the basis for advances i
This volume presents an authoritative, up-to-date review of analytic number theory. It contains outstanding contributions from leading international figures in this field. Core topics discussed include the theory of zeta functions, spectral theory of automorphic forms, classical problems in additive number theory such as the Goldbach conjecture, and Diophantine approximations and equations. This will be a valuable book for graduates and researchers working in number theory.
This book originates from graduate courses given in Cambridge and London. It provides a brisk, thorough treatment of the foundations of algebraic number theory, and builds on that to introduce more advanced ideas. Throughout, the authors emphasise the systematic development of techniques for the explicit calculation of the basic invariants, such as rings of integers, class groups, and units. Moreover they combine, at each stage of development, theory with explicit computations and applications, and provide motivation in terms of classical number-theoretic problems. A number of special topics are included that can be treated at this level but can usually only be found in research monographs or original papers, for instance: module theory of Dedekind domains; tame and wild ramifications; Gauss series and Gauss periods; binary quadratic forms; and Brauer relations. This is the only textbook at this level which combines clean, modern algebraic techniques together with a substantial arithme
First published in 1967, this volume posits that the science of international relations is concerned with observation, analysis and theorizing on the relations between states. An analysis of a particular problem such as the disarmament or the Cuban dispute forms a proper part of the study, but Dr Burton insists that such an analysis should be made within the framework of a general theory concerning the patterns of interaction between states. The author examines the nature of international relations as a discipline, and points to the inadequacies of much orthodox theory and practice, with particular reference to orthodox power theories. He draws attention to certain features in the altering world environment which accentuate these inadequacies. Dr Burton's concern is the establishment of non-power models and concepts required to describe international relations in the nuclear age.
In this book, T. L. Short corrects widespread misconceptions of Peirce's theory of signs and demonstrates its relevance to contemporary analytic philosophy of language, mind and science. Peirce's theory of mind, naturalistic but nonreductive, bears on debates of Fodor and Millikan, among others. His theory of inquiry avoids foundationalism and subjectivism, while his account of reference anticipated views of Kripke and Putnam. Peirce's realism falls between 'internal' and 'metaphysical' realism and is more satisfactory than either. His pragmatism is not verificationism; rather, it identifies meaning with potential growth of knowledge. Short distinguishes Peirce's mature theory of signs from his better-known but paradoxical early theory. He develops the mature theory systematically on the basis of Peirce's phenomenological categories and concept of final causation. The latter is distinguished from recent and similar views, such as Brandon's, and is shown to be grounded in forms of expla
The emergence of a new theory of literature in the German Romantic period constituted a decisive turning point in the history of criticism. Prepared by new trends in critical thought during the latter half of the eighteenth century, a view of the literary work and the artistic process developed which diverged sharply from the dominant classicist understanding of aesthetics and poetics. It recognised the infinite changeability of genres, their constant mingling, and the frequent emergence of new literary forms, and asserted the rights of genius and creative imagination. It was also characterised by its intimate connection with the prevailing philosophy of its time, transcendental idealism. Professor Behler provides a new account of this crucial movement, illustrating each theoretical topic with close reference to a characteristic work by a major writer of the period.
There has been a resurgence of interest in classical invariant theory driven by several factors: new theoretical developments; a revival of computational methods coupled with powerful new computer algebra packages; and a wealth of new applications, ranging from number theory to geometry, physics to computer vision. This book provides readers with a self-contained introduction to the classical theory as well as modern developments and applications. The text concentrates on the study of binary forms (polynomials) in characteristic zero, and uses analytical as well as algebraic tools to study and classify invariants, symmetry, equivalence and canonical forms. It also includes a variety of innovations that make this text of interest even to veterans of the subject. Aimed at advanced undergraduate and graduate students the book includes many exercises and historical details, complete proofs of the fundamental theorems, and a lively and provocative exposition.
This account is a study of twofold symmetry in algebraic topology. The author discusses specifically the antipodal involution of a real vector bundle - multiplication by - I in each fibre; doubling and squaring operations; the symmetry of bilinear forms and Hermitian K-theory. In spite of its title, this is not a treatise on equivariant topology; rather it is the language in which to describe the symmetry. Familiarity with the basic concepts of algebraic topology (homotopy, stable homotopy, homology, K-theory, the Pontrjagin―Thom transfer construction) is assumed. Detailed proofs are not given (the expert reader will be able to supply them when necessary) yet nowhere is credibility lost. Thus the approach is elementary enough to provide an introduction to the subject suitable for graduate students although research workers will find here much of interest.
In this book, T. L. Short corrects widespread misconceptions of Peirce's theory of signs and demonstrates its relevance to contemporary analytic philosophy of language, mind and science. Peirce's theory of mind, naturalistic but nonreductive, bears on debates of Fodor and Millikan, among others. His theory of inquiry avoids foundationalism and subjectivism, while his account of reference anticipated views of Kripke and Putnam. Peirce's realism falls between 'internal' and 'metaphysical' realism and is more satisfactory than either. His pragmatism is not verificationism; rather, it identifies meaning with potential growth of knowledge. Short distinguishes Peirce's mature theory of signs from his better-known but paradoxical early theory. He develops the mature theory systematically on the basis of Peirce's phenomenological categories and concept of final causation. The latter is distinguished from recent and similar views, such as Brandon's, and is shown to be grounded in forms of expla
The primary goal of this 2003 book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of finite-generatedness of the algebra of invariants, the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples which originate in classical algebraic geometry. Based on lectures given at University of Michigan, Harvard University and Seoul National University, the book is written in an accessible style and contains many examples and exercises. A novel feature of the book is a discussion of possible linearizations of actions and the variation of quotients under the change of linearization. Also includes the construction of toric varieties as torus quotients of affine spaces.
There has been a resurgence of interest in classical invariant theory driven by several factors: new theoretical developments; a revival of computational methods coupled with powerful new computer algebra packages; and a wealth of new applications, ranging from number theory to geometry, physics to computer vision. This book provides readers with a self-contained introduction to the classical theory as well as modern developments and applications. The text concentrates on the study of binary forms (polynomials) in characteristic zero, and uses analytical as well as algebraic tools to study and classify invariants, symmetry, equivalence and canonical forms. It also includes a variety of innovations that make this text of interest even to veterans of the subject. Aimed at advanced undergraduate and graduate students the book includes many exercises and historical details, complete proofs of the fundamental theorems, and a lively and provocative exposition.
The term “subalternity” refers to a condition of subordination brought about by colonization or other forms of economic, social, racial, linguistic, and/or cultural dominance. Subaltern s
The term “subalternity” refers to a condition of subordination brought about by colonization or other forms of economic, social, racial, linguistic, and/or cultural dominance. Subaltern st
The concept of Floer homology was one of the most striking developments in differential geometry. It yields rigorously defined invariants which can be viewed as homology groups of infinite-dimensional cycles. The ideas led to great advances in the areas of low-dimensional topology and symplectic geometry and are intimately related to developments in Quantum Field Theory. The first half of this book gives a thorough account of Floer's construction in the context of gauge theory over 3 and 4-dimensional manifolds. The second half works out some further technical developments of the theory, and the final chapter outlines some research developments for the future - including a discussion of the appearance of modular forms in the theory. The scope of the material in this book means that it will appeal to graduate students as well as those on the frontiers of the subject.
The new theory of Jacobi forms over totally real number fields introduced in this monograph is expected to give further insight into the arithmetic theory of Hilbert modular forms, its L-series, and i
Hidden in the depths of Marx's epistemology is his theory of the phenomenal forms, whose implications have not been sufficiently explored from an educational perspective. This book argues that phenome
L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with a basic knowledge of classical analysis, complex variable theory, and algebra. Also within the volume are many new results not yet found in the literature. The exposition provides complete detailed proofs of results in an easy-to-read format using many examples and without the need to know and remember many complex definitions. The main themes of the book are first worked out for GL(2,R) and GL(3,R), and then for the general case of GL(n,R). In an appendix to the book, a set of Mathematica functions is presented, designed to allow the reader to explore the theory from a computational point of view.
