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

Presents an introduction to set theory for beginning graduate students who want to get a grounding in those aspects of set theory used extensively throughout other areas of mathematics. This book contains topics that include formal languages and models, the power and limitation of the Axiomatic Method, and the Axiom of Choice.

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Presents the theory of elliptic functions and its applications. Suitable primarily for engineers who work with elliptic functions, this work is also intended for those with background in the elements of mathematical analysis and the theory of functions contained in the first two years of mathematics and physics courses at the college level.

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Focuses on integrable systems and symmetries presents new results on applications of symmetries and integrability techniques to the case of equations defined on the lattice. This relatively new field has many applications, for example, in describing the evolution of crystals and molecular systems defined on lattices.

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Offers advice on various aspects of math circle operations. This book includes topics such as creative means for getting the word out to students, sound principles for selecting effective speakers, guidelines for securing financial support, and tips for designing a math circle session.

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Quantum groups are certain families of Hopf algebras that are deformations of universal enveloping algebras of Kac-Moody algebras. This book aims to provide an elementary introduction to the theory of quantum groups and crystal bases, focusing on the combinatorial aspects of the theory.

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Among all areas of mathematics, algebra is one of the best suited to find applications within the frame of our booming technological society. This book contains thirty-eight articles that encompass the proceedings of the International Conference on Algebra and Its Applications (Athens, OH, 1999).

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Offers expository introductions to superalgebras, supermanifolds, classical field theory, free quantum theories, and super Poincare groups. This book also covers specific models and describes some of their geometric features. It explains the classical supersymmetric field theories that are basic for applications in quantum mechanics.

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Focuses on differential calculus in infinite dimensions and those applications in infinite dimensional differential geometry and global analysis not involving Sobolev completions and fixed point theory. This work discusses the existence of smooth partitions of unity, the foundations of manifold theory in infinite dimensions and differential forms.

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Develops an arithmetic analog of the theory of ordinary differential equations, where functions are replaced by integer numbers, the derivative operator is replaced by a 'Fermat quotient operator', and differential equations (viewed as functions on jet spaces) are replaced by 'arithmetic differential equations'.

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Contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Geometric Group Theory and Computer Science held at Mount Holyoke College (South Hadley, MA). This work features articles about insights from computer experiments, applications of formal language theory, decision problems, and complexity problems.

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Covers the key topics of numerical methods. This work covers topics including 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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Covers such topics as tangent spaces to sub varieties of projective spaces and complex tori, projections of algebraic varieties, classification of Severi varieties, higher secant varieties, and classification of Scorza varieties over an algebraically closed field of characteristic zero.

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Presents papers by those who participated in Dynkin's seminar on Lie groups and Lie algebras in the late 1950s and early 1960s. This book features several aspects of modern developments in Lie groups and Lie algebras, including theory of invariants superalgebras arithmetic applications connections with mathematical physics.

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Introduces the notion of topological degree and develops its basic properties. This book uses these properties in the discussion of bifurcation theory (the possible branching of solutions as parameters vary), including the proof of Rabinowitz's global bifurcation theorem. It is suitable as a graduate level textbook and a supplementary course text.

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Contains results about the global dynamics defined by a class of delay differential equations which model basic feedback mechanisms and arise in a variety of applications such as neural networks. This book describes the geometric structure of a fundamental invariant set, which in special cases is the global attractor.

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The Teichmuller space $T(X)$ is the space of marked conformal structures on a given quasi conformal surface $X$. This book uses quasi conformal mapping to give a unified and up-to-date treatment of $T(X)$. It offers a treatment of deformations of complex structures on infinite Riemann surfaces.

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Contains articles written by the workshop participants from the conference on 'Crystallographic Groups and Their Generalizations', held at Katholieke Universiteit Leuven, Kortrijk (Belgium). This book includes such topics as the theory of affine structures and polynomial structures, and affine Schottky groups and crooked tilings.

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Presents the proceedings of a conference on 'Harmonic Analysis and Number Theory' held at McGill University (Montreal). The papers are dedicated to the memory of Carl Herz, who had deep interests in both harmonic analysis and number theory.

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The study of natural and social phemomena indicates that the future development of many processes depends not only on their present state, but also on their history. Such processes can be described mathematically by using the machinery of equations with aftereffect. This book presents control theory for hereditary systems of various types.

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Illustrates how simple observations can be made the starting point of rich and fruitful theories and how the same theme recurs in seemingly unrelated disciplines. Mark Kac conveyed his infectious enthusiasm for mathematics and its applications in his lectures, papers, and books. Two of his papers won Chauvenet awards for expository excellence.

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Contains such topics as Symmetric Sets, Principle of Duality, most of the 'Algebra' of Sets, Partially Ordered Sets, Arbitrary Sets of Complexes, Normal Types, Initial and Final Ordering, Complexes of Real Numbers, General Topological Spaces, Euclidean Spaces, and the Special Methods Applicable in the Euclidean Plane.

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Suitable for a first year graduate course on global analysis, this title proves the basics of Fourier transforms, Sobolev theory and interior regularity at the same time as symbol calculus, culminating in beautiful results in global analysis, real and complex.

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A monograph that is concerned with Galois theoretical embedding problems of so-called Brauer type with a focus on 2-groups and on finding explicit criteria for solvability and explicit constructions of the solutions. It also considers questions of reducing the embedding problems and reformulating the solvability criteria.

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Offers an easily accessible form a coherent account of matrix theory with a view to applications in mathematics, theoretical physics, statistics, and electrical engineering. This title includes individual chapters that have been kept as far as possible independent of each other.

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Brings together both the classical and current aspects of deformation theory. The presentation is mostly self-contained, assuming only basic knowledge of commutative algebra, homological algebra and category theory. In the interest of readability, some technically complicated proofs have been omitted when a suitable reference was available.

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Ricci flow is a powerful technique using a heat-type equation to deform Riemannian metrics on manifolds to better metrics in the search for geometric decompositions. With the fourth part of their volume on techniques and applications of the theory, the authors of this volume discuss long-time solutions of the Ricci flow and related topics.

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Aims to give an exposition of generalized (co)homology theories that can be read by mathematicians who are not experts in algebraic topology. This work starts with basic notions of homotopy theory and then introduces the axioms of generalized (co)homology theory. It focuses on spectral sequences and their use in generalized cohomology theories.

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One of the greatest accomplishments in the history of cryptography occurred in 1940 when Arne Beurling broke the German code used for strategic military communications. This work describes Beurling's attack on the G-Schreiber system as well as attacks on other wartime crypto systems, noting high points from the history of Swedish cryptology.

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Traces the thread of pi through the long history of mathematics. This book touches upon many major subjects in mathematics: geometry (of course), number theory, Galois theory, probability, transcendental numbers, analysis, and, as their crown jewel, the theory of elliptic functions, which connects many of the other subjects.

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The concept of 'wave packet analysis' originates in Carleson's famous proof of almost everywhere convergence of Fourier series of $L^2$ functions. This work emphasizes the classical successes (Carleson's theorem and the Hilbert transform) in the main development.

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The influence of Thurston's hyperbolization theorem on the geometry and topology of 3-manifolds has been tremendous. This book presents a proof of the hyperbolization theorem for 3-manifolds that fiber over the circle, following the plan of Thurston's original proof, though the double limit theorem is dealt with in a different way.

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In the area of mathematical logic, a great deal of attention is now being devoted to the study of nonclassical logics. This book intends to present the most important methods of proof theory in intuitionistic logic and to acquaint the reader with the principal axiomatic theories based on intuitionistic logic.

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Presents an exposition of spherical functions on compact symmetric spaces, from the viewpoint of Cartan-Selberg. This title treats compact symmetric pairs, spherical representations for compact symmetric pairs, the fundamental groups of compact symmetric spaces, and the radial part of an invariant differential operator.

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Focuses on equations from toric varieties and Grassmannians. Not only is much known about these, but such equations are common in applications. There are three main themes: upper bounds on the number of real solutions, lower bounds on the number of real solutions, and geometric problems that can have all solutions be real.

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Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This book provides a general perspective on coarse structures. It discusses results on asymptotic dimension and uniform embeddings into Hilbert space.

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Suitable for readers who want to learn about the Newtonian $N$-body problem, this book contains simple explanations of the apparent 'looping' orbit of Mars and the unexpected 'Sunrise, Sunset' behavior as viewed from Mercury. It also covers the weird dynamics exhibited by Saturn's F-ring.

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Studies boundary value problems are from two points of view; solvability, unique or otherwise, and the effect of various smoothness properties of the given functions on the smoothness of the solutions. This title includes various chapters that introduce the various function spaces typical of modern Russian-style functional analysis.

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Provides an account of the triangulated theory of motives. The book’s purpose is to introduce Motivic Cohomology, to develop its main properties, and finally to relate it to other known invariants of algebraic varieties and rings such as Milnor K-theory, étale cohomology, and Chow groups.

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Contains essays on Ramanujan and his work. This book includes survey articles in areas that are influenced by Ramanujan's mathematics.

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