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

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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Presents a comprehensive introduction to free probability theory, a highly noncommutative probability theory with independence based on free products instead of tensor products. This title provides basic examples of this kind of theory by convolution operators on free groups and by the asymptotic behavior of large Gaussian random matrices.

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Covers topics including fundamental notions such as homeomorphisms, homotopy equivalence, fundamental groups and higher homotopy groups, homology and cohomology, fiber bundles, spectral sequences and characteristic classes. This work considers objects and examples including the torus, the Mobius strip, the Klein bottle and closed surfaces.

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This manual is written to accompany Mathematical Interest Theory, by Leslie Jane Federer Vaaler and James Daniel. It includes detailed solutions to the odd-numbered problems. There are solutions to 239 problems, and sometimes more than one way to reach the answer is presented.

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This book picks up the history of mathematics from where Sherlock Holmes in Babylon left it. The 40 articles of Who Gave You the Epsilon? continue the story of the development of mathematics into the nineteenth and twentieth centuries. It is ideal for those interested in the history of mathematics.

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In these volumes, a reader will find all of John Tate's published mathematical papers-spanning more than six decades-enriched by new comments made by the author. Included also is a selection of his letters. His letters give us a close view of how he works and of his ideas in process of formation.

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Features a unified derivation of the mathematical theory of the three classical types of invariant random matrix ensembles - orthogonal, unitary, and symplectic. This book presents a proof of universality for orthogonal and symplectic ensembles corresponding to generalized Gaussian type weights.

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Offering an introduction to Berkovich analytic spaces and to potential theory and rational iteration on the Berkovich line, this book contains applications to arithmetic geometry and arithmetic dynamics. It presents a description of the topological structure of the Berkovich projective line and then introduces the Hsia kernel.

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Surveys matching theory, with an emphasis on connections with other areas of mathematics and on the role matching theory has played, and continues to play, in the development of some of these areas. This book discusses basic results on the existence of matchings and on the matching structure of graphs, as well as the impact of matching theory.

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Linear algebra is the study of vector spaces and the linear maps between them. It underlies much of modern mathematics and is widely used in applications. Written for students with some mathematical maturity and an interest in abstraction and formal reasoning, this book is suitable for an advanced undergraduate course in linear algebra.

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Presents the proceedings from the conference on low dimensional topology held at the University of Madeira (Portugal). This work focuses on the Poincare conjecture, characterizations of $PL$-manifolds, covering quadratic forms of links and to categories in low dimensional topology that appear in connection with conformal and quantum field theory.

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Includes survey papers on applications of group theory in cryptography, research papers on various aspects of statistical group theory, and papers on more traditional combinatorial group theory. The book is suitable for graduate students and research mathematicians interested in group theory and its applications to cryptography.

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Presents an overview of the basic methods and concepts in mechanics of applied mathematics or related fields. This book introduces Newton's law, action principles, Hamilton-Jacobi theory, geometric wave theory, analytical and numerical statistical mechanics, discrete and continuous quantum mechanics, and quantum path-integral methods.

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Offers an introduction to large deviations. This book is divided into two parts: theory and applications. It presents basic large deviation theorems for i i d sequences, Markov sequences, and sequences with moderate dependence. It also includes an outline of general definitions and theorems.

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Contains four essays on expository writing of books and papers at the research level and at the level of graduate texts.

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