Books in the AMS Chelsea Publishing series

A translation of Landau's famous "Elementare Zahlentheorie" with added exercises.

Growing out of a course designed to teach Gauss's Disquisitiones Arithmeticae to honours-level undergraduates, this volume focuses on Gauss's theory of binary quadratic forms. It is suitable for use as a textbook in a course or self-study by students who possess a basic familiarity with abstract algebra.

This famous work is a textbook that emphasises the conceptual and historical continuity of analytic function theory. The second volume broadens from a textbook to a textbook-treatise, covering the "canonical" topics, and other topics nearer the expanding frontier of analytic function theory. In the latter category are the chapters on majorisation and on functions holomorphic in a half-plane.

Quantum mechanics is arguably the most successful physical theory. It provides the structure underlying all of our electronic technology, and much of our mastery over materials. Suitable for undergraduates with minimal mathematical preparation, this title presents a logical path to understanding what quantum mechanics is about.

Presents the study of Riemannian manifolds through specializing the theory of connections on principle bundles and affine connections. This work emphasizes the geometry of Riemannian manifolds, so that the theorems of Hopf-Rinow, Hadamard-Cartan, and Cartan's local isometry theorem are included, but no elliptic operator theory.

Covers groups of linear transformations, especially Fuchsian groups, fundamental domains, and functions that are invariant under the groups, including the classical elliptic modular functions and Poincare theta series. This book also covers conformal mappings, uniformization, and connections between automorphic functions.

Suitable for an undergraduate first course in ring theory, this work discusses the various aspects of commutative and noncommutative ring theory. It begins with basic module theory and then proceeds to surveying various special classes of rings (Wedderbum, Artinian and Noetherian rings, hereditary rings and Dedekind domains.).

The six-volume collection, Generalized Functions gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. The unifying theme of Volume 6 is the study of representations of the general linear group of order two over various fields and rings of number-theoretic nature.

Contains an account of the foundations of the theory of commutative normed rings without, however, touching upon the majority of its analytic applications. Intended for those who have knowledge of the elements of the theory of normed spaces and of set-theoretical topology, this title is based on [the authors'] paper written in 1940.

Emphasizes the conceptual and historical continuity of analytic function theory. This work covers topics including elliptic functions, entire and meromorphic functions, as well as conformal mapping. It features chapters on majorization and on functions holomorphic in a half-plane.

The six-volume collection, Generalized Functions, published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. The main goal of Volume 4 is to develop the functional analysis setup for the universe of generalized functions.

The six-volume collection, Generalized Functions, published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. Volume 2 is devoted to detailed study of generalized functions as linear functionals on appropriate spaces of smooth test functions.

This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has avoided any presumption that the reader has knowledge of mathematical concepts until they are presented in the book.

This flexible text is organised into two parts: Part I treats the theory of measure and integration over abstract measure spaces; Part II is more specialised, and includes regular measures on locally compact spaces, the Riesz-Markoff theorem on the measure-theoretic representation of positive linear forms, and Haar measure on a locally compact group.

Includes Gauss' number-theoretic works. This title provides papers that include a fourth, fifth, and sixth proof of the Quadratic Reciprocity Law, researches on biquadratic residues, quadratic forms, and other topics. It also includes an appendix and concludes with a commentary on the papers.

By 'combinatory analysis', the author understands the part of combinatorics now known as 'algebraic combinatorics'. He presents the classical results of the outstanding 19th century school of British mathematicians.

Based on lectures given by the author at the University of Chicago in 1956, this work covers such topics as recurrence, the ergodic theorems, and a general discussion of ergodicity and mixing properties. It is suitable for use for a one-semester course in ergodic theory or for self-study.

Presents a series of problems of progressive interest in the subject of Mathematical Probability.

Presents an introduction to the basic ideas of the theory of large deviations and makes a suitable package on which to base a semester-length course for advanced graduate students with a background in analysis and some probability theory. This book also covers various non-uniform results.

Focuses on the study of continued fractions in the theory of analytic functions, rather than on arithmetical aspects. This book provides discussions of orthogonal polynomials, power series, infinite matrices and quadratic forms in infinitely many variables, definite integrals, the moment problem and the summation of divergent series.