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

Presents an introduction to algebraic topology via its most classical and elementary segment centered at the notions of fundamental group and covering space. This book is suitable for a course on general and beginning algebraic topology.

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Based on lectures given at the CBMS Workshop on the Combinatorics of Large Sparse Graphs, this work presents fresh perspectives in graph theory and helps to contribute to a sound scientific foundation for our understanding of discrete networks that permeate the information age.

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Determining the invariant subspaces of any given transformation and writing the transformation as an integral in terms of invariant subspaces is a fundamental problem. This book presents the foundations of the theory of triangular and Jordan representations of bounded linear operators in Hilbert space.

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Gives an exposition of the relations among the following three topics: monoidal tensor categories (such as a category of representations of a quantum group), 3-dimensional topological quantum field theory, and 2-dimensional modular functors (which naturally arise in 2-dimensional conformal field theory).

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Presents lectures delivered at a workshop held at the Chinese Academy of Sciences (Bejing). Suitable as a text for a graduate course on wireless communication, this title includes the following articles: ""Nonlinear Systems Control"", ""Adaptive Control of Discrete-Time Nonlinear Systems with Structural Uncertainties"", and ""Networks and Learning"".

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Contains papers presented at the conference, 'Computational Perspectives on Number Theory' held at the University of Illinois at Chicago in honor of the retirement of A O L Atkin. This work covers a range of topics, including algebraic number theory, $p$-adic modular forms and modular curves.

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Integrating ideas from category theory, algebra and combinatorics, this monograph is organised into three parts: category theory; combinatorics and geometry; and an examination of how ideas in Parts I and II lead to a unified approach to Hopf algebras.

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Offers details of Grothendieck's constructions and laying bare how the important classes of operators are a consequence of the abstract operations on tensor norms. This book shows how the classical Banach spaces ($C(K)$'s, Hilbert spaces, and the spaces of integrable functions) fit naturally within the mosaic that Grothendieck constructed.

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Describes the essence of the orbit method for non-experts and gives a detailed exposition of the method. This work can be used as a text for a graduate course, as well as a handbook for non-experts and a reference book for research mathematicians and mathematical physicists.

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Takes a novel approach to the standard introductory material on groups, rings, and fields. This title offers a semi-historical journey through the early decades of the subject as it emerged in the revolutionary work of Euler, Lagrange, Gauss, and Galois. It focuses on the central problem of studying the solutions of polynomial equations.

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Suitable for pre-college teachers, this text starts where Euclid starts, and covers the basics of plane Euclidean geometry. It features problems that are well-suited to exploration using the tools of dynamic geometry software. It includes a CD of solutions to select problems, created using Texas Instruments' TI-Nspire[trademark] Learning Software.

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The nonlinear Schrodinger equation has received a great deal of attention from mathematicians, particularly because of its applications to nonlinear optics. This book presents various mathematical aspects of the nonlinear Schrodinger equation. It studies both problems of local nature and problems of global nature.

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Riesz space (or a vector lattice) is an ordered vector space that is simultaneously a lattice. A topological Riesz space (also called a locally solid Riesz space) is a Riesz space equipped with a linear topology that has a base consisting of solid sets. This book presents a study (with complete proofs) of topological Riesz spaces.

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Shows how to explain concepts, demonstrate computational procedures, and lead students through problem-solving techniques. This book describes the foundations of arithmetic, along with a selection of topics from geometry. It is suitable for a college course in mathematics for prospective elementary school teachers.

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Presents the Dirichlet problem for harmonic functions twice: once using the Poisson integral for the unit disk and again in an informal section on Brownian motion, where the reader can understand intuitively how the Dirichlet problem works for general domains. This book is suitable for a first-year course in complex analysis.

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Includes articles written by A N Kolmogorov's students and colleagues and his personal accounts of shared experiences and lifelong mathematical friendships. This volume includes the following articles: ""On A N Kolmogorov"" by V I Arnol'd, ""In Memory of A N Kolmogorov"" by S M Nikol'skii, and ""A Few Words on A N Kolmogorov"" by P S Aleksandrov.

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Offers a review of high school geometry, and discusses special points associated with triangles, circles and certain associated lines, Ceva's theorem, vector techniques of proof, and compass-and-straightedge constructions. This book focuses on interesting theorems and on the techniques that can be used to prove them.

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Contains various developments and research arising from the conference on the 'Legacy of the Inverse Scattering Transform' held at Mount Holyoke College (South Hadley, MA). This book reviews major research results in the inverse scattering transform (IST) and on the application of IST to classical problems in differential geometry.

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Reflects the themes of student learning and calculus. This volume includes overviews of calculus reform in France and in the US and large-scale and small-scale longitudinal comparisons of students enrolled in first-year reform courses and in traditional courses. It concludes with a study of a concept that overlaps the areas of focus, quantifiers.

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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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