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

Algebraic curves and compact Riemann surfaces comprise the most developed and arguably the most beautiful portion of algebraic geometry. This book provides a foundation to proceed to advanced texts in general algebraic geometry, complex manifolds, and Riemann surfaces, as well as algebraic curves.

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The Fourier coefficients of modular forms are of widespread interest as an important source of arithmetic information. This book covers the Eichler-Selberg/Hijikata trace formula for the traces of Hecke operators on spaces of holomorphic cusp forms of weight $\mathtt{k}>2$ for congruence subgroups of $\operatorname{SL}_2(\mathbf{Z})$.

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A comprehensive and up-to-date treatment of sieve methods. The theory of the sieve is developed thoroughly with complete and accessible proofs of the basic theorems. A wide range of applications are included, both to traditional questions, and to areas pr

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Emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, inner functions, invariant metrics, and mapping theory, this title is intended for the student with a background in real and complex variable theory, harmonic analysis, and differential equations.

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Algorithmic number theory is a branch of number theory, which, in addition to its mathematical importance, has substantial applications in computer science and cryptography. This book describes the various algorithms used in cryptography.

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Covers quadratic and higher forms. This book presents methods of attacking whole classes of problems.

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Includes articles that introduce readers to mathematical methods of classical and quantum mechanics and the link between these two theories: quantization and semiclassical analysis. This title introduces graduate students with a basic knowledge of mathematics into areas of active research.

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Wavelet analysis has had a great impact in areas such as approximation theory, harmonic analysis, and scientific computation. This book focuses on applications of wavelets to numerical solutions of partial differential equations and integral equations, image processing and facial recognition, and computer vision.

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Contains the proceedings of the Moonshine workshop held at the Centre de Recherches Mathematiques (CRM) in Montreal. This work presents the various classical Moonshine themes, namely the Monster simple group and other finite groups, automorphic functions and forms and related congruence groups, and vertex algebras and their representations.

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Emil Artin was one of the great mathematicians of the twentieth century. He had the rare distinction of having solved two of the famous problems posed by David Hilbert in 1900. He showed that every positive definite rational function of several variables was a sum of squares. This book gathers a selection of his writings.

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Presents a systematic approach to conformal field theory with gauge symmetry from the point of view of complex algebraic geometry. This book also presents the basic facts of the theory of compact Riemann surfaces and the representation theory of affine Lie algebras.

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Presents the proceedings of the Joint Summer Research Conference on Algebraic $K$-theory held at the University of Washington in Seattle. This work includes an account of Voevodsky's proof of the Milnor conjecture relating the Milnor $K$-theory of fields to Galois cohomology.

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Presents the theory and applications of Fourier series and integrals, eigenfunction expansions, and related topics, on a level suitable for advanced undergraduates. This title includes material on Bessel functions, orthogonal polynomials, and Laplace transforms.

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Contains proceedings of the research conference on algebraic $K$-theory that took place in Poznan, Poland, in September 1995. This book covers topics such as: $K$-theory of fields and rings of integers; $K$-theory of elliptic and modular curves; and, theory of motives, motivic cohomology, Beilinson conjectures.

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Mirror symmetry began when theoretical physicists made some astonishing predictions about rational curves on quintic hypersurfaces in four-dimensional projective space. This book presents a comprehensive monograph on mirror symmetry, covering the original observations by the physicists.

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Includes discussion of smoothness, differentiability, and analyticity, the idea of local coordinates and coordinate transformation, and a detailed explanation of the Whitney imbedding theorem (both in weak and in strong form). This book describes the notion of the area of a figure on the plane and the volume of a solid body in space.

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Although division algebras are a very classical object, this book presents this 'classical' material in a new way, highlighting various approaches and fresh theorems, and illuminating the connections with a variety of areas in mathematics. It is based on lectures on division algebras given at a conference held at Colorado State University.

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Presents a comprehensive exposition of the modern theory of valued and ordered fields. This title presents the classical aspects of such fields: their arithmetic, topology, and Galois theory. It emphasizes the close connections and interplay between valuations and orderings, and to a large extent, studies them in a unified manner.

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Presents proceedings from the AMS short course, Trends in Optimization 2004, held at the Joint Mathematics Meetings in Phoenix (AZ). This book describes Lovasz's fundamental algorithm for producing a short vector in a lattice by basis reduction.

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Part of ""Colloquium Series"", this book presents systematic treatment of orthogonal polynomials.

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Ideas from quantum field theory and string theory have had considerable impact on mathematics. In 1996-97 the Institute for Advanced Study (Princeton, NJ) organized a special year-long program designed to teach mathematicians the basic physical ideas which underlie the mathematical applications. These volumes are a written record of the program.

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Based on classes in probability for advanced undergraduates held at the IAS/Park City Mathematics Institute (Utah), this title is derived from both lectures (Chapters 1-10) and computer simulations (Chapters 11-13) that were held during the program. It concludes with a number of problems ranging from routine to very difficult.

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Presents a coherent account of matrix theory with a view to applications in mathematics, theoretical physics, statistics, and electrical engineering.

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Presents a systematic treatment of results on the theory and numerical analysis of the Navier-Stokes equations for viscous incompressible fluids. Considered are the linearized stationary case, the nonlinear stationary case, and the full nonlinear time-dependent case. This title introduces the relevant mathematical tools at each stage.

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Throughout the history of mathematics, maximum and minimum problems have played an important role in the evolution of the field. This book presents fifteen 'stories' that acquaint readers with the central concepts of the theory of maxima and minima, as well as with its illustrious history.

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Offers a celebration of mathematical problem solving at the level of the high school American Invitational Mathematics Examination. It is intended, in part, as a resource for comprehensive study and practice for the AIME competition for students, teachers, and mentors. However, this book is also intended for anyone who enjoys solving problems as a recreational pursuit.

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This is the third volume of problems that cover the USA Mathematical Olympiad (USAMO) and the International Mathematical Olympiad (IMO) to be published by the MAA in its Problem Book series.

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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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