Bøger i Translations of Mathematical Monographs serien

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.

This book, together with the companion volume, Fermat's Last Theorem: The Proof, presents in full detail the proof of Fermat's Last Theorem given by Wiles and Taylor. With these two books, the reader will be able to see the whole picture of the proof to appreciate one of the deepest achievements in the history of mathematics.

Presents an introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. This book also include a chapter on infinite-dimensional generalizations of Euclidean and affine geometries.

Treats inverse problems in the theory of small oscillations of systems with finitely many degrees of freedom, which requires finding the potential energy of a system from the observations of its oscillations.

In the area of mathematical logic, a great deal of attention is now being devoted to the study of nonclassical logics. This book intends to present the most important methods of proof theory in intuitionistic logic and to acquaint the reader with the principal axiomatic theories based on intuitionistic logic.

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.

Discusses the geometry and arithmetic of elliptic curves. This book includes modern interpretations of some famous classical algebraic theorems such as Abel's theorem on the lemniscate and Hermite's solution of the fifth degree equation by means of theta functions.

Considers integer solutions for systems of linear inequalities, equations, and congruences along with the construction and theoretical analysis of integer programming algorithms. This book analyzes the complexity of algorithms dependent upon two parameters: the dimension, and the maximal modulus of the coefficients.

The main goal of this book is to present the so-called birational Arakelov geometry, which can be viewed as an arithmetic analog of the classical birational geometry. After explaining classical results about the geometry of numbers, the author starts with Arakelov geometry for arithmetic curves, and continues with Arakelov geometry of arithmetic surfaces and higher-dimensional varieties.

Provides historical background and a complete overview of the qualitative theory of foliations and differential dynamical systems. Senior mathematics majors and graduate students with background in multivariate calculus, algebraic and differential topology, differential geometry, and linear algebra will find this book an accessible introduction.

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.

Focuses on the fundamentals of a theory, which is an analog of affine algebraic geometry for partial differential equations. This work describes applications of Secondary Calculus ranging from algebraic geometry to field theory, classical and quantum, including areas such as characteristic classes, differential invariants and variational calculus.

Presents an introduction to real analysis. This text covers real numbers, the notion of general topology, and a brief treatment of the Riemann integral, followed by chapters on the classical theory of the Lebesgue integral on Euclidean spaces; the differentiation theorem and functions of bounded variation; Lebesgue spaces; and distribution theory.

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.

Based on courses taught by the author at Moscow State University, this book features such topics as the theory of Banach and Hilbert tensor products, the theory of distributions and weak topologies, and Borel operator calculus. It contains many examples illustrating the general theory presented, as well as multiple exercises to help the reader.

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.

The mean curvature of a surface is an extrinsic parameter measuring how the surface is curved in the three-dimensional space. A surface whose mean curvature is zero at each point is a minimal surface, and it is known that such surfaces are models for soap film. This book presents many examples of constant mean curvature surfaces.

Presents an exposition of spherical functions on compact symmetric spaces, from the viewpoint of Cartan-Selberg. This title treats compact symmetric pairs, spherical representations for compact symmetric pairs, the fundamental groups of compact symmetric spaces, and the radial part of an invariant differential operator.

The space of all Riemann surfaces (the so-called moduli space) plays an important role in algebraic geometry and its applications to quantum field theory. This book focuses on the study of topological properties of this space and of similar moduli spaces, such as the space of real algebraic curves, and the space of mappings.

In a very broad sense, 'spaces' are objects of study in geometry, and 'functions' are objects of study in analysis. There are, however, deep relations between functions defined on a space and the shape of the space, and the study of these relations is the main theme of Morse theory. This book describes Morse theory for finite dimensions.

Studies boundary value problems are from two points of view; solvability, unique or otherwise, and the effect of various smoothness properties of the given functions on the smoothness of the solutions. This title includes various chapters that introduce the various function spaces typical of modern Russian-style functional analysis.

Reproduces the doctoral thesis written by a remarkable mathematician, Sergei V Kerov. This book discusses the properties of the distribution of the normalized cycle length in a random permutation and the limiting shape of a random (with respect to the Plancherel measure) Young diagram.

Intended for students wishing to deepen their knowledge of mathematical analysis and for those teaching courses in this area, this title contains problems, some of which are well-known theorems in analysis. It also includes brief but detailed solutions to most of the problems.