Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education. The standard courses in the classical differential geo…
This text on a central area of number theory covers p-adic L-functions, class numbers, cyclotomic units, Fermat's Last Theorem, and Iwasawa's theory of Z_p-extensions. This edition contains a new chapter on the work of Thaine, Kolyvagin, and Rubin,…
This book discusses a variety of problems which are usually treated in a second course on the theory of functions of one complex variable, the level being gauged for graduate students. It treats several topics in geometric function theory as well as…
This rapid and concise presentation of the essential ideas and results of algebraic topology follows the axiomatic foundations pioneered by Eilenberg and Steenrod. The approach of the book is pragmatic: while most proofs are given, those that are pa…
Ah Love! Could you and I with Him consl?ire To grasp this sorry Scheme of things entIre' KHAYYAM People investigating algebraic groups have studied the same objects in many different guises. My first goal thus has been to take three different viewpo…
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…
Homological algebra has found a large number of applications in many fields ranging from finite and infinite group theory to representation theory, number theory, algebraic topology and sheaf theory. In the new edition of this broad introduction to…
This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta functions and Hasse-Weil's theorem as well as Goppa' s al…
This text is an introduction to the modern theory and applications of probability and stochastics. The style and coverage is geared towards the theory of stochastic processes, but with some attention to the applications. In many instances the gist o…
This book treats Jacques Tit's beautiful theory of buildings, making that theory accessible to readers with minimal background. It covers all three approaches to buildings, so that the reader can choose to concentrate on one particular approach. Beg…
Translation of the French Edition
The present volume is the first of three that will be published under the general title Lectures in Abstract Algebra. These vol umes are based on lectures which the author has given during the past ten years at the University of North Carolina, at T…
Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. Thi…
Advanced maths students have been waiting for this, the third edition of a text that deals with one of the fundamentals of their field. This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gr…
This book is about harmonic functions in Euclidean space. This new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bochers Theorem, new exercises and proofs, as well as revisions throughout to i…
William S. Massey Professor Massey, born in Illinois in 1920, received his bachelor's degree from the University of Chicago and then served for four years in the U.S. Navy during World War II. After the War he received his Ph.D. from Princeton Unive…
Assumes only a familiarity with algebra at the beginning graduate level; Stresses applications to algebra; Illustrates several of the ways Model Theory can be a useful tool in analyzing classical mathematical structures
As its title indicates, this book is intended to serve as a textbook for an introductory course in mathematical analysis. In preliminary form the book has been used in this way at the University of Michigan, Indiana University, and Texas A&M Univers…
Intended as a systematic text on topological vector spaces, this text assumes familiarity with the elements of general topology and linear algebra. Similarly, the elementary facts on Hilbert and Banach spaces are not discussed in detail here, since…
This text is aimed at graduate students in mathematics and to interested researchers who wish to acquire an in depth understanding of Euclidean Harmonic analysis. The text covers modern topics and techniques in function spaces, atomic decompositions…
This fourth edition contains several additions. The main ones con cern three closely related topics: Brownian motion, functional limit distributions, and random walks. Besides the power and ingenuity of their methods and the depth and beauty of thei…
Elliptic functions parametrize elliptic curves, and the intermingling of the analytic and algebraic-arithmetic theory has been at the center of mathematics since the early part of the nineteenth century. The book is divided into four parts. In the f…
Can be used as a graduate textContains many exercisesContains new results
Cartan geometries were the first examples of connections on a principal bundle. They seem to be almost unknown these days, in spite of the great beauty and conceptual power they confer on geometry. The aim of the present book is to fill the gap in t…
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…
This text is intended to serve as an introduction to the geometry of the action of discrete groups of Mobius transformations. The subject matter has now been studied with changing points of emphasis for over a hundred years, the most recent developm…
This book explores the theory of strongly continuous one-parameter semigroups of linear operators. A special feature of the text is an unusually wide range of applications such as to ordinary and partial differential operators, to delay and Volterra…
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…
This book focuses on the elementary but essential problems in Riemann-Finsler Geometry, which include a repertoire of rigidity and comparison theorems, and an array of explicit examples, illustrating many phenomena which admit only Finslerian interp…
From the Introduction: "We shall base our discussion on a set-theoretical foundation like that used in developing analysis, or algebra, or topology. We may consider our task as that of giving a mathematical analysis of the basic concepts of logic an…
This book deals with several aspects of what is now called "explicit number theory." The central theme is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or…
Many classical problems in additive number theory are direct problems, in which one starts with a set A of natural numbers and an integer H -> 2, and tries to describe the structure of the sumset hA consisting of all sums of h elements of A. By cont…
"Springer has just released the second edition of Steven Roman's Field Theory, and it continues to be one of the best graduate-level introductions to the subject out there....Every section of the book has a number of good exercises that would make t…
A selection of topics which graduate students have found to be a successful introduction to the field, employing three distinct techniques: geometric topology manoeuvres, combinatorics, and algebraic topology. Each topic is developed until significa…
This book is an introductory text in functional analysis. Unlike many modern treatments, it begins with the particular and works its way to the more general. From the reviews: "This book is an excellent text for a first graduate course in functional…
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 book is designed as a text for a first-year graduate algebra course. As necessary background we would consider a good undergraduate linear algebra course. An undergraduate abstract algebra course, while helpful, is not necessary (and so an adve…
From the reviews: "The book is well written. We find here many examples. Each chapter is followed by exercises, and at the end of the book there are outline solutions to some of them. [...] I especially appreciated the lively style of the book; [...…
SL2(R) gives the student an introduction to the infinite dimensional representation theory of semisimple Lie groups by concentrating on one example - SL2(R). This field is of interest not only for its own sake, but for its connections with other are…
Introduction to Algebraic and Abelian Functions is a self-contained presentation of a fundamental subject in algebraic geometry and number theory. For this revised edition, the material on theta functions has been expanded, and the example of the Fe…
This English edition could serve as a text for a first year graduate course on differential geometry, as did for a long time the Chicago Notes of Chern mentioned in the Preface to the German Edition. Suitable references for ordin ary differential eq…
An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific exam…
The goal of this book is to present local class field theory from the cohomo logical point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions-primarily abelian-of "local" (i.e., compl…
This is the first volume of a three-volume introduction to modern geometry which emphasizes applications to other areas of mathematics and theoretical physics. Topics covered include tensors and their differential calculus, the calculus of variation…
In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas…
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…
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…
A completely reworked new edition of this superb textbook. This key work is geared to the needs of the graduate student. It covers, with proofs, the usual major branches of groups, rings, fields, and modules. Its inclusive approach means that all of…
Some of the central topics in number theory, presnted in a simple and concise fashion. The author covers an amazing amount of material, despite a leisurely pace and emphasis on readability. His heartfelt enthusiasm enables readers to see what is mag…