Search results for ""MP-AMM American Mathematical""

Presents the proceedings of a conference held at the University of California at Riverside in February 1995, that focused on the interplay between the theory of Lie algebras of prime characteristic, quantum groups and Lie superalgebras.

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Offers an elementary, self-contained presentation of the integration processes developed by Lebesgue, Denjoy, Perron, and Henstock. This book contains over 230 exercises (with solutions) that illustrate and expand the material. It is suitable for first-year graduate students who have background in real analysis.

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Covers key topics of numerical methods. This book includes such topics as interpolation, the fast Fourier transform, iterative methods for solving systems of linear and nonlinear equations, numerical methods for solving ODEs, numerical methods for matrix eigenvalue problems, approximation theory, and computer arithmetic.

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Tries to display the value (and joy!) of starting from a mathematically amorphous problem and combining ideas from diverse sources to produce new and significant mathematics - mathematics unforeseen from the motivating problem. This book focuses on aperiodic tilings; the best-known example is the 'kite and dart' tiling.

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This is the second volume of the book on the proof of Fermat's Last Theorem by Wiles and Taylor (the first volume is published in the same series). Here the detail of the proof announced in the first volume is fully exposed. The book also includes basic materials and constructions in number theory and arithmetic geometry that are used in the proof.

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This is the first book to be devoted entirely to the potential theory of the heat equation, and thus deals with time dependent potential theory. Its purpose is to give a logical, mathematically precise introduction to a subject where previously many proofs were not written in detail, due to their similarity with those of the potential theory of Laplace's equation.

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Explores concepts such as the index of composition and the index of isolation of an integer. This book displays several tables of particular families of numbers, including the list of all 88 narcissistic numbers and the list of the eight known numbers which are not prime powers but which can be written as the sum of cubes of their prime factors.

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Presents complex algebraic curves. This book covers a range of topics from conics and cubics to theta functions, Jacobians, and questions of moduli. It is suitable for those preparing a course on the topic of complex curves.

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Contains papers presented at the conference on Banach Algebras and Several Complex Variables held June 21-24, 1983, to honor Professor Charles E Rickart upon his retirement from Yale University. This work includes articles that present advances in topics related to Banach algebras, function algebras and infinite dimensional holomorphy.

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Group-theoretic methods have taken an increasingly prominent role in analysis. Some of this change has been due to the writings of Sigurdur Helgason. This book is an introduction to such methods on spaces with symmetry given by the action of a Lie group.

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Provides an elementary introduction to $p$-adic analysis from the number theory perspective. With over 100 exercises, it will acquaint the non-expert with the basic ideas of the theory and encourage the novice to enter this fertile field of research. The main focus of the book is the study of $p$-adic $L$-functions and their analytic properties.

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The field of differential topology underwent a dramatic development period between 1955 and 1965. This collection of articles contains original papers and expository lectures. It includes commentary by the author, filling in some of the historical context, and outlining developments in the field. It provides an understanding of the subject.

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Presents an introduction to probability and statistics. This book covers topics that include the axiomatic setup of probability theory, polynomial distribution, finite Markov chains, distribution functions and convolution, the laws of large numbers (weak and strong), characteristic functions, the central limit theorem, and Markov processes.

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Presents a view about the experience of being a department head.

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Presents an introduction to differential geometry through differential forms, emphasizing their applications in various areas of mathematics and physics. This work focuses on Stokes' theorem, the classical integral formulas and their applications to harmonic functions and topology.

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In a very broad sense, 'spaces' are objects of study in geometry, and 'functions' are objects of study in analysis. There are, however, deep relations between functions defined on a space and the shape of the space, and the study of these relations is the main theme of Morse theory. This book describes Morse theory for finite dimensions.

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The study of the zeroes of polynomials, which for one variable is essentially algebraic, becomes a geometric theory for several variables. This book looks at the classic entry point to the subject: plane algebraic curves. It presents an introduction to algebraic geometry, which assumes the standard undergraduate mathematical topics.

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Explains the problems that must be resolved in order to procure a rigorous development of the calculus and shows the student how to deal with those problems. Starting with the real line, this book also covers finite-dimensional spaces and metric spaces.

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The space of all Riemann surfaces (the so-called moduli space) plays an important role in algebraic geometry and its applications to quantum field theory. This book focuses on the study of topological properties of this space and of similar moduli spaces, such as the space of real algebraic curves, and the space of mappings.

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Presents an introduction to the theory of functions of several complex variables and their singularities, with special emphasis on topological aspects. This book includes such topics as Riemann surfaces, holomorphic functions of several variables, classification and deformation of singularities, and fundamentals of differential topology.

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Presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. This book starts with the basics of polytope theory. It introduces Schlegel and Gale diagrams as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes.

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Contains three papers on the foundations of Grothendieck duality on Noetherian formal schemes and on not-necessarily-Noetherian ordinary schemes. This book presents a self-contained treatment for formal schemes which synthesizes several duality-related topics, such as local duality, formal duality, residue theorems, and dualizing complexes.

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Deals with finite-alphabet stationary processes, which are important in physics, engineering, and data compression. This book gives a careful presentation of the many models for stationary finite-alphabet processes that have been developed in probability theory, ergodic theory, and information theory.

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Gives an introduction to the theory of the integral (called the 'generalized Riemann integral' or the 'Henstock-Kurzweil integral') that corrects the defects in the classical Riemann theory and both simplifies and extends the Lebesgue theory of integration. This book includes a study of measure theory as an application of the integral.

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Character theory is a powerful tool for understanding finite groups. In particular, the theory has been a key ingredient in the classification of finite simple groups. Characters are also of interest in their own right, and their properties are closely related to properties of the structure of the underlying group.

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Contains topics in Hamilton's Ricci flow. This book presents the theory of Ricci solitons, Kahler-Ricci flow, compactness theorems, Perelman's entropy monotonicity and no local collapsing, Perelman's reduced distance function and applications to ancient solutions, and a primer of 3-manifold topology.

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Includes Gauss' number-theoretic works. This title provides papers that include a fourth, fifth, and sixth proof of the Quadratic Reciprocity Law, researches on biquadratic residues, quadratic forms, and other topics. It also includes an appendix and concludes with a commentary on the papers.

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Algebraic number theory is one of the most refined creations in mathematics. This book presents the essential elements of algebraic number theory, including the theory of normal extensions up through a glimpse of class field theory.

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Culminates nearly half a century of the late Alfred Tarski's foundational studies in logic, mathematics, and the philosophy of science. This work shows that set theory and number theory can be developed within the framework of a new, different and simple equational formalism, closely related to the formalism of the theory of relation algebras.

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Presents the basic notions of differential and algebraic topology, which are indispensable for specialists and useful for research mathematicians and theoretical physicists. This title introduces ideas and results that are related to manifolds, cell spaces, coverings and fibrations, and homotopy groups, intersection index.

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The study of group actions on manifolds is the meeting ground of a variety of mathematical areas. In particular, interesting geometric insights can be obtained by applying measure-theoretic techniques. This book provides an introduction to some of the important methods, major developments, and open problems on the subject.

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Presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society in Salvador, Bahia, Brazil. This book presents research on several aspects of model theory, proof theory, algebraic logic, category theory, and connections between logic and computer science.

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Formulated in 1859, Riemann Hypothesis is the most celebrated and multifaceted open problem in mathematics. This book proposes a fresh approach to understand and possibly solve the Riemann Hypothesis. It is suitable for graduate students, experts and nonexperts alike, with an interest in number theory, analysis, dynamical systems, and arithmetic.

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This work is intended for beginning graduate students who already have some background in algebra, including some elementary theory of groups, rings and fields. The expositions and proofs are intended to present Galois theory in as simple a manner as possible, sometimes at the expense of brevity.

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Lie groups and algebraic groups are important in many major areas of mathematics and mathematical physics. We find them in diverse roles, notably as groups of automorphisms of geometric structures, as symmetries of differential systems, or as basic tools in the theory of automorphic forms. This book looks at their development.

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Contains translations of papers on propositional satisfiability and related logical problems which appeared in ""Problemy Sokrashcheniya Perebora"", published in Russian in 1987.

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Symplectic methods are key ingredients in the study of dynamical systems, differential equations, algebraic geometry, topology, mathematical physics and representations of Lie groups. This book presents an introduction to symplectic geometry, assuming only a general background in analysis and familiarity with linear algebra.

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Algebraic curves have many special properties that make their study rewarding. This work presents the various aspects of curves and emphasizes connections with algebra. It covers topics in the geometry of algebraic curves, such as line and vector bundles, the Riemann-Roch Theorem, divisors, coherent sheaves, and zeroth and first cohomology groups.

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Aims to treat a theory of elliptic boundary value problems in domains without singularities and in domains with conical or cuspidal points. This work focuses on fundamental results of the theory: estimates for solutions in different function spaces, regularity assertions and asymptotic formulas for the solutions near singular points.

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Covers basic notions of probability and statistics, vectors, exponential, logarithmic, and trigonometric functions, and an introduction to differentiation and integration.

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Starting with few prerequisites beyond linear algebra, the author charts an expert course from Witt's classical theory of quadratic forms, quaternion and Clifford algebras, Artin-Schreier theory of formally real fields, and structural theorems on Witt rings, to the theory of Pfister forms, function fields, and field invariants.

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