Search results for ""author american mathem american mathem""

Based on a capstone course that the author taught to upper division undergraduate students with the goal to explain and visualize the connections between different areas of mathematics and the way different subject matters flow from one another, this book is suitable for those with a basic knowledge of high school mathematics.

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Nature tries to minimize the surface area of a soap film through the action of surface tension. The process can be understood mathematically by using differential geometry, complex analysis, and the calculus of variations. This book employs ingredients from each of these subjects to tell the mathematical story of soap films.

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Counterexamples are remarkably effective for understanding the meaning, and the limitations, of mathematical results. This title looks at some of the major ideas of several complex variables by considering counterexamples to what might seem like reasonable variations or generalizations.

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Mathematics education research in undergraduate mathematics has increased significantly over the years. This book presents an introduction for educational research, and surveys the more commonly used research methods, along with their rationales and assumptions. It is of practical interest to university-based research mathematicians.

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Based on a course entitled 'Wigner measures and semiclassical limits of nonlinear Schrodinger equations,' this book applies the theory of semiclassical pseudodifferential operators to the study of various high-frequency limits of equations from quantum mechanics.

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Contains lectures that focus on fundamentals of the modern theory of linear elliptic and parabolic equations in Holder spaces. This title shows that this theory - including some issues of the theory of nonlinear equations - is based on some general and extremely powerful ideas and some simple computations.

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Contains the proceedings of the first DIMACS workshop. This work covers topics including multicommodity flows, graph matchings and colorings, the traveling salesman problem, integer programming and complexity theory. It is suitable for researchers in combinatorics and combinatorial optimization.

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Presents the characteristic zero invariant theory of finite groups acting linearly on polynomial algebras. The author assumes basic knowledge of groups and rings, and introduces more advanced methods from commutative algebra along the way. The theory is illustrated by numerous examples.

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A guide to Line Complex.

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Presents an understanding of scattering theory, starting with basic principles and extending to research. This work presents a comprehensive exposition of the theory, covering different methods (of trace class and smooth perturbations) and approaches (time dependent and stationary) and discussing the relationships among them.

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A cipher is a scheme for creating coded messages for the secure exchange of information. This book develops various encryption schemes, and also introduces the reader to number theory. It places the study of integers and their properties in the context of cryptology.

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Contains papers presented at a conference held in April 2007 at the CRM in Montreal honouring the remarkable contributions of John McKay. This title features the papers that cover a wide range of topics, including group theory, symmetries, modular functions, and geometry, with focus on 2 areas: 'Monstrous Moonshine' and the 'McKay Correspondence'.

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Contains 15 articles based on invited talks given at an AMS Special Session on 'Stochastic Inequalities and Their Applications' held at Georgia Institute of Technology (Atlanta). This book includes articles that offer a comprehensive picture of this area of mathematical probability and statistics.

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Based on a course given by the author at the Mechanics-Mathematics Faculty of Moscow University, this book covers mathematical analysis. It includes bibliography and indexes.

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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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