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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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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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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Introduces algebraic geometric coding theory. This book covers linear codes, including cyclic codes, and both bounds and asymptotic bounds on the parameters of codes. Algebraic geometry is introduced, with particular attention given to projective curves, rational functions and divisors.

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Suitable for those who wish to explore elementary methods in modern number theory, this book offers an introduction to elementary prime number theory, including Dirichlet's theorem on primes in arithmetic progressions, the Brun sieve, and the Erdos-Selberg proof of the prime number theorem.

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Symplectic geometry and the theory of Fourier integral operators are modern manifestations of themes that have occupied a central position in mathematical thought. This book intends to develop these themes, and present some of the advances, using the language of differential geometry as a unifying influence.

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Presents two essential and apparently unrelated subjects that include, microlocal analysis and the theory of pseudo-differential operators, a basic tool in the study of partial differential equations and in analysis on manifolds; and the Nash-Moser theorem, that is fundamentally important in geometry, dynamical systems, and nonlinear PDE.

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Starts with necessary information about matrices, algebras, and groups. This title then proceeds to representations of finite groups. It includes several chapters dealing with representations and characters of symmetric groups and the closely related theory of symmetric polynomials.

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'The International Conference on Hyperbolic Problems: Theory, Numerics and Applications', 'HYP2008', was held at the University of Maryland from June 9-14, 2008. This title contains articles that cover a range of multi-disciplinary topics addressing theoretical, modeling and computational issues arising under the umbrella of 'hyperbolic PDEs'.

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One of the most active areas in mathematics is the topic of 'additive combinatorics'. This book brings together key researchers from different areas, sharing their insights in articles meant to inspire mathematicians coming from various backgrounds.

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Describes in monograph form important applications in numerical methods of linear algebra. This book studies the behavior of the resolvent of a matrix under the perturbation by low rank matrices. It also introduces the basics of value distribution theory of meromorphic scalar functions.

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Presents an overview of nonlinear conversation laws. This book describes the theory of asymptotic equivalence between conservation laws and singular kinetic equations. It is suitable for researchers and advanced graduate students in the areas of nonlinear partial differential equations and nonlinear analysis.

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