This textbook on homology and cohomology theory is geared towards the beginning graduate student. Singular homology theory is developed systematically, avoiding all unnecessary definitions, terminology, and technical machinery. Wherever possible, th…
The new edition of this thorough examination of the distribution of prime numbers in arithmetic progressions offers many revisions and corrections as well as a new section recounting recent works in the field. The book covers many classical results,…
This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research--- smooth structures, tangent…
This book is based on a course I have given five times at the University of Michigan, beginning in 1973. The aim is to present an introduction to a sampling of ideas, phenomena, and methods from the subject of partial differential equations that can…
This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other par…
This book is meant as a text for a first-year graduate course in analysis. In a sense, it covers the same topics as elementary calculus but treats them in a manner suitable for people who will be using it in further mathematical investigations. The…
This basic introduction to number theory is ideal for those with no previous knowledge of the subject. The main topics of divisibility, congruences, and the distribution of prime numbers are covered. Of particular interest is the inclusion of a proo…
A carefully prepared account of the basic ideas in Fourier analysis and its applications to the study of partial differential equations. The author succeeds to make his exposition accessible to readers with a limited background, for example, those…
Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety…
This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet…
This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear…
This textbook provides a careful treatment of functional analysis and some of its applications in analysis, number theory, and ergodic theory.In addition to discussing core material in functional analysis, the authors cover more recent and advanced…
A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is pres…
This book is an elegant and rigorous presentation of integer programming, exposing the subject's mathematical depth and broad applicability. Special attention is given to the theory behind the algorithms used in state-of-the-art solvers. An abundanc…
A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the Dedekind eta funct…
This text is unique in accepting probability theory as an essential part of measure theory. Therefore, many examples are taken from probability, and probabilistic concepts such as independence and Markov processes are integrated into the text. Also,…
The main goal of these lectures is to introduce the beginner to the finite-dimensional representations of Lie groups and Lie algebras. Intended to serve non-specialists, the concentration of the text is on examples. The general theory is developed m…
This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Co…
"This book succeeds brilliantly by concentrating on a number of core topics...and by treating them in a hugely rich and varied way. The author ensures that the reader will learn a large amount of classical material and perhaps more importantly, will…
This monograph grew out of the notes relating to the lecture courses that I gave at the University of Helsinki from 1977 to 1979, at the Eidgenossische Technische Hochschule Zurich in 1980, and at the University of Minnesota in 1982. The book presum…
A solid introduction to applications of Lie groups to differential equations which have proved to be useful in practice. The computational methods are presented such that graduates and researchers can readily learn to use them. Following an expositi…
Early in the development of number theory, it was noticed that the ring of integers has many properties in common with the ring of polynomials over a finite field. The first part of this book illustrates this relationship by presenting analogues of…
This revised, enlarged edition of Linear Algebraic Groups (1969) starts by presenting foundational material on algebraic groups, Lie algebras, transformation spaces, and quotient spaces. It then turns to solvable groups, general properties of linear…
An introduction to nonstandard analysis based on a course given by the author. It is suitable for beginning graduates or upper undergraduates, or for self-study by anyone familiar with elementary real analysis. It presents nonstandard analysis not j…
This book is intended as a basic text for a one year course in algebra at the graduate level or as a useful reference for mathematicians and professionals who use higher-level algebra. This book successfully addresses all of the basic concepts of al…
This is a second edition of Lang's well-known textbook. It covers all of the basic material of classical algebraic number theory, giving the student the background necessary for the study of further topics in algebraic number theory, such as cycloto…
The basic problem of deformation theory in algebraic geometry involves watching a small deformation of one member of a family of objects, such as varieties, or subschemes in a fixed space, or vector bundles on a fixed scheme. In this new book, Robin…
Based on a graduate course at the Technische Universitat, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The straightforward exposition features many illustrations, and complete proofs for most theorems…
This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "A…
Primarily concerned with the study of cohomology theories of general topological spaces with "general coefficient systems", the parts of sheaf theory covered here are those areas important to algebraic topology. Among the many innovations in this bo…
This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. The reader is assumed to have a basic knowledge of algebra and topology at the first year graduate le…
Kummer's work on cyclotomic fields paved the way for the development of algebraic number theory in general by Dedekind, Weber, Hensel, Hilbert, Takagi, Artin and others. However, the success of this general theory has tended to obscure special facts…
This book emphasizes the isomorphic theory of Banach spaces and techniques using the unifying viewpoint of basic sequences. Its aim is to provide the reader with the necessary technical tools and background to reach the frontiers of research without…
The book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schroedinger operators) and analysis (Dirichlet and Neumann Laplacians,…
Aimed at the novice rather than the connoisseur and stressing the role of examples and motivation, this text is suitable not only for use in a graduate course, but also for self-study in the subject by interested graduate students. More than 400 exe…
This book is first of all designed as a text for the course usually called "theory of functions of a real variable". This course is at present cus tomarily offered as a first or second year graduate course in United States universities, although the…
Functional analysis arose in the early twentieth century and gradually, conquering one stronghold after another, became a nearly universal mathematical doctrine, not merely a new area of mathematics, but a new mathematical world view. Its appearance…
The Fourier transform and the Laplace transform of a positive measure share, together with its moment sequence, a positive definiteness property which under certain regularity assumptions is characteristic for such expressions. This is formulated in…
This textbook gives an introduction to distribution theory with emphasis on applications using functional analysis. In more advanced parts of the book, pseudodi?erential methods are introduced. Distributiontheoryhasbeen developedprimarilytodealwithp…
This introduction to some basic ideas in algebraic topology is devoted to the foundations and applications of homology theory. After the essentials of singular homology and some important applications are given, successive topics covered include att…
This book offers an ideal graduate-level introduction to the theory of partial differential equations. The first part of the book describes the basic mathematical problems and structures associated with elliptic, parabolic, and hyperbolic partial di…
Optimization is everywhere. It is human nature to seek the best option among all that are available. Nature, too, seems to be guided by optimization|many laws of nature have a variational character. Among geometric gures in the plane with a xed peri…
'A Concise Introduction to the Theory of Integration' was once a best-selling Birkhauser title which published 3 editions. This manuscript is a substantial revision of the material. Chapter one now includes a section about the rate of convergence of…
This book offers an ideal introduction to the theory of partial differential equations. It focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. It also develops the…
This book presents the fundamental function spaces and their duals, explores operator theory and finally develops the theory of distributions up to significant applications such as Sobolev spaces and Dirichlet problems. Includes an assortment of wel…
The subject of this book is Complex Analysis in Several Variables. This text begins at an elementary level with standard local results, followed by a thorough discussion of the various fundamental concepts of "complex convexity" related to the remar…
This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, t…
This book has grown out of a set of lecture notes I had prepared for a course on Lie groups in 1966. When I lectured again on the subject in 1972, I revised the notes substantially. It is the revised version that is now appearing in book form. The t…
Fifteen years ago, most mathematicians who worked in the intersection of function theory and operator theory thought that progress on the Bergman spaces was unlikely, yet today the situation has completely changed. For several years, research intere…
About This Book This book is meant to be used by beginning graduate students. It covers basic material needed by any student of algebra, and is essential to those specializing in ring theory, homological algebra, representation theory and K-theory,…