Search results for ""mp-amm american mathematical""

This book has a dual objective: firstly to introduce some of the most important and widespread environmental issues; secondly to illustrate the vital role played by mathematical models in investigating these issues. The emphasis throughout is on fundamental principles and concepts, not on technical mastery of state-of-the-art models.

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Dirichlet (1805-1859) is well known for his significant contributions to several branches of mathematics. In analysis, he is remembered for his work in potential theory, especially his study of harmonic functions with prescribed boundary values, now known as the Dirichlet problem. This work features two volumes of ""Dirichlet's Collected Works"".

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Matrix theory is a classical topic of algebra that had originated, in its current form, in the middle of the 19th century. It is remarkable that for more than 150 years it continues to be an active area of research full of new discoveries and new applications. This presents modern perspectives of matrix theory at the level accessible to graduate students.

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Contains lecture notes from most of the courses presented at the 50th anniversary edition of the Seminaire de Mathematiques Superieure in Montreal. This 2011 summer school was devoted to the analysis and geometry of metric measure spaces, and featured much interplay between this subject and the emergent topic of optimal transportation.

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This book introduces graduate students and researchers in mathematics and the sciences to the multifaceted subject of the equations of hyperbolic type, which are used, in particular, to describe propagation of waves at finite speed. Among the topics presented are nonlinear geometric optics, the asymptotic analysis of short wavelength solutions, and nonlinear interaction of such waves.

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Suitable for an undergraduate first course in ring theory, this work discusses the various aspects of commutative and noncommutative ring theory. It begins with basic module theory and then proceeds to surveying various special classes of rings (Wedderbum, Artinian and Noetherian rings, hereditary rings and Dedekind domains.).

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Presents an introductory course on the methods of computing asymptotics of probabilities of rare events: the theory of large deviations. The book combines large deviation theory with basic statistical mechanics, namely Gibbs measures with their variational characterization and the phase transition of the Ising model, in a text intended for a one semester or quarter course.

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Presents possible paths to studying mathematics and falling in love with it, via teaching two important skills: thinking creatively while still obeying the rules, and making connections between problems, ideas, and theories. The book encourages you to apply the newly acquired knowledge to problems and guides you along the way.

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A monograph that deals with the mathematical theory of Huygens' principle in optics and its application to the theory of diffraction. It concerns with the general theory of the solution of the partial differential equations governing the propagation of light.

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Suitable as a text for both Riemannian geometry and for the analysis and geometry of symmetric spaces, this title features chapters on differential geometry and Lie groups. It also includes a chapter on functions on symmetric spaces, that gives an introduction to the study of spherical functions, and the theory of invariant differential operators.

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Emphasizes the conceptual and historical continuity of analytic function theory. This work covers topics including elliptic functions, entire and meromorphic functions, as well as conformal mapping. It features chapters on majorization and on functions holomorphic in a half-plane.

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Gives an overview of classical topics in fluid dynamics, focusing on the kinematics and dynamics of incompressible inviscid and Newtonian viscous fluids, and including some material on compressible flow. It illustrates the mathematical methods of classical fluid dynamics.

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Contains lectures presented at the 3rd Regional Geometry Institute at Park City in 1993. This text offers an introduction to Hodge theory and intersection homology based on simple topological ideas of Lefschetz and an overview of the interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.

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Contrasts combinatorial games, which have complete information and no chance moves, with those of classical game theory. This book introduces a theory of numbers, including infinitesimals and transfinite numbers, which has emerged as a special case of the theory of games. It also describes impartial games.

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Presents Brownian motion and deals with stochastic integrals and differentials, including Ito lemma. This book is devoted to topics of stochastic integral equations and stochastic integral equations on smooth manifolds. It is suitable for graduate students and researchers interested in probability, stochastic processes, and their applications.

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Superalgebras are algebras containing positively-signed and negatively-signed variables. This book contains some topics in superalgebras and symbolic method in invariant theory.

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Deals with the Ricci flow, and the convergence theory for the Ricci flow. This title focuses on preserved curvature conditions, such as positive isotropic curvature. It is suitable for graduate students and researchers.

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Chronicles Henri Poincaré's journey in algebraic topology between 1892 and 1904, from his discovery of the fundamental group to his formulation of the Poincaré conjecture. For the first time in English translation, one can follow every step (and occasional stumble) along the way, with the help of translator John Stillwell's introduction and editorial comments.

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Contains papers presented by speakers at the AMS-IMS-SIAM Joint Summer Research Conference on Conformal Field Theory, Topological Field Theory and Quantum Groups, held at Mount Holyoke College in June 1992. This work deals with one aspect of conformal field theory, namely, vertex operator algebras or superalgebras and their representations.

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Algebraic Geometry has been at the centre of much of mathematics for hundreds of years. It is not an easy field to break into, despite its humble beginnings in the study of circles, ellipses, hyperbolas, and parabolas. This text consists of a series of exercises, plus some background information and explanations, starting with conics and ending with sheaves and cohomology.

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Markov processes are among the most important stochastic processes for both theory and applications. This book develops the general theory of these processes, and applies this theory to various special examples.

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There is a deep and fundamental relationship between the differential equations that occur in the calculus of variations and partial differential equations of the first order: in particular, to each such partial differential equation there correspond variational problems. This book discusses this basic fact.

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A collection of one hundred short essays, that offers a tour through contemporary and everyday mathematics. It includes topics that range from pure mathematics to applications of mathematics to observations about the mathematics that surrounds us in daily life. It is suitable for those who read the science section of a newspaper or magazine.

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Develops three related tools that are useful in the analysis of partial differential equations (PDEs), arising from the classical study of singular integral operators: pseudodifferential operators, paradifferential operators, and layer potentials. This work focuses on the treatment of PDE in the presence of relatively little regularity.

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Contains twenty-two papers presented at the International Conference in Combinatorics, held in Jerusalem in May 1993. This title describes developments in algebraic combinatorics, enumeration, graph and hypergraph theory, combinatorial geometry, and geometry of polytopes and arrangements.

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We have been curious about numbers - and prime numbers - since antiquity. One notable direction this century in the study of primes has been the influx of ideas from probability. This book intends to provide insights into the prime numbers and to describe how a sequence so tautly determined can incorporate such a striking amount of randomness.

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Contains a collection of papers devoted primarily to transcendental number theory and diophantine approximations. This title includes a text of the author's invited address on his work on the theory of transcendental numbers to the 1978 International Congress of Mathematicians in Helsinki.

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Resolution of Singularities has long been considered as being a difficult to access area of mathematics. This volume is intended for readers who are not yet experts but always wondered about the intricacies of resolution. It provides a gentle and comprehensive introduction to this amazing field.

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A collection of papers that addresses a variety of problems and approaches for predicting spatial effects in ecological systems. It discusses the spatial dynamics of natural systems and the impact of economic and sociological changes, as well as the adaptation methods from statistical lattice physics.

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The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. There have been striking developments in the mathematics of 3-dimensional manifolds. This book introduces some of these important developments.

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Oliver Heaviside is probably best known to the majority of mathematicians for the Heaviside function in the theory of distribution. His main research activity concerned the theory of electricity and magnetism. This book brings together many of Heaviside's published and unpublished notes and short articles written between 1891 and 1912.

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Deals with the interplay of computational commutative algebra and the theory of convex polytopes. This title centers around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties.

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This flexible text is organised into two parts: Part I treats the theory of measure and integration over abstract measure spaces; Part II is more specialised, and includes regular measures on locally compact spaces, the Riesz-Markoff theorem on the measure-theoretic representation of positive linear forms, and Haar measure on a locally compact group.

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Focuses on the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. This title begins with an introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem. It then gives a presentation of homogeneous spaces in which the main goal is to find formulas for their curvature.

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The goal of this book is to analyse in detail Ulam's problem for increasing subsequences of random permutations, and domino tilings of the Aztec diamond. Other examples are also described along the way, but in less detail. The book is self-contained, and develops enough of the theory from each area that a general reader can learn the subject directly from the text.

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