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

Everyone knows some of the basics of probability, perhaps enough to play cards. Beyond the introductory ideas, there are many wonderful results that are unfamiliar to the layman. This book is suitable for those who would like to learn more about mathematical probability and has had a one-year undergraduate course in analysis.

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Number theory is the equal of Euclidean geometry - some would say it is superior to Euclidean geometry - as a model of pure, logical, deductive thinking. This title explains number theory in a way that gives deductive reasoning, including algorithms and computations, the central role.

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Introduces the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators and spectral theory of self-adjoint operators. This work presents the theorems and methods of abstract functional analysis and applications of these methods to Banach algebras and theory of unbounded self-adjoint operators.

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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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Building on the basic techniques of separation of variables and Fourier series, this presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems – rectangular, cylindrical, and spherical.

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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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Consists of thirty lectures on diverse topics, covering much of the mathematical landscape. This title helps reader learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology.

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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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Research in string theory has generated a rich interaction with algebraic geometry, with exciting work that includes the Strominger-Yau-Zaslow conjecture. This monograph builds on lectures at the 2002 Clay School on Geometry and String Theory that sought to bridge the gap between the languages of string theory and algebraic geometry.

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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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Offers a modern, up-to-date introduction to quasiconformal mappings from an explicitly geometric perspective, emphasizing both the extensive developments in mapping theory during the past few decades and the remarkable applications of geometric function theory to other fields, including dynamical systems, Kleinian groups, geometric topology, differential geometry, and geometric group theory.

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The Berkeley Math Circle (BMC) started in 1998 as one of the very first maths circles in the US. Over the last decade and a half, 100 instructors have shared their passion for mathematics by delivering over 800 BMC sessions. This second volume is based on a dozen of these sessions, encompassing a variety of enticing and stimulating mathematical topics.

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Operads are mathematical devices that describe algebraic structures of many varieties and in various categories. Operads are particularly important in categories with a good notion of 'homotopy', where they play a key role in organizing hierarchies of higher homotopies. This book offers an introduction describing the development of operad theory.

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Deals with the topic of game theory. This textbook discusses the general game models including deterministic, strategic, sequential, bargaining, coalition, and fair division games. It emphasises on the process of mathematical modeling.

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A guide to Line Complex.

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Presents an introduction to differential geometry. This book then introduces Lie groups and Lie algebras. It concludes with the classification of symmetric spaces by means of the Killing-Cartan classification of simple Lie algebras over $\mathbf{C}$ and Cartan's classification of simple Lie algebras over $\mathbf{R}$.

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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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Presents an integrated development of the theory of several complex variables and complex algebraic geometry, leading to proofs of Serre's celebrated GAGA theorems relating the two subjects, and including applications to the representation theory of complex semisimple Lie groups. This text includes a treatment of the local theory.

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Based on a series of lectures at the PCMI summer school, this volume gives an introduction to the advanced techniques behind recent developments in algebraic and analytic geometry. The lectures contain many illustrative examples, detailed computations, and new perspectives on the topics presented.

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Treats free probability theory, which has been extensively developed since the early 1980s. This work focuses on entropy and the random matrix model approach. It is suitable as a reference for mathematicians interested in free probability theory and can serve as a text for an advanced graduate course.

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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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Presents an account of the theory of probability measures on complete metric spaces. This title includes a description of the basics of topology on the set of measures. It discusses regularity, tightness, and perfectness of measures, properties of sampling distributions, and metrizability and compactness theorems.

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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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Contains historical background and discussion of results for each chapter, References, and an Index.

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Introduces students with diverse backgrounds to various types of mathematical analysis that are commonly needed in scientific computing. This title treats the subject of numerical analysis from a mathematical point of view, offering an analysis of methods for scientific computing with appropriate motivations and proofs.

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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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