Bøger i Graduate Texts in Mathematics serien

This textbook on algebraic topology updates a popular textbook from the golden era of the Moscow school of I. a deeper and broader treatment of topics in comparison to most beginning books on algebraic topology;

First Edition sold over 2500 copies in the Americas; New Edition contains three new chapters and two new appendices

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.

Anyone who has studied abstract algebra and linear algebra as an undergraduate can understand this book. The first six chapters provide material for a first course, while the rest of the book covers more advanced topics.

Basic properties, homotopy classification, and characteristic classes of fibre bundles have become an essential part of graduate mathematical education for students in geometry and mathematical physics.

In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations.

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. He then taught for ten years on the faculty of Brown University, and moved to his present position at Yale in 1960.

This third edition contains new material on maximum modulus algebras and subharmonicity, the hull of a smooth curve, integral kernels, perturbations of the Stone-Weierstrass Theorem, boundaries of analytic varieties, polynomial hulls of sets over the circle, areas, and the topology of hulls.

This introduction to the representation theory of compact Lie groups follows Herman Weyl's original approach. It discusses all aspects of finite-dimensional Lie theory, consistently emphasizing the groups themselves. Each section contains a range of exercises, and 24 figures help illustrate geometric concepts.

This graduate text, while focusing on locally convex topological vector spaces, covers most of the general theory needed for application to other areas of functional analysis. Includes over 100 exercises with varying levels of difficulty.

First textbook-level account of basic examples and techniques in this area. Suitable for self-study by a reader who knows a little commutative algebra and algebraic geometry already.

Organizing the basic material of complex analysis in a unique manner, the authors of this versatile book aim is to present a precise and concise treatment of those parts of complex analysis that should be familiar to every research mathematician.

While Hardy and Bergman spaces are established subjects in the literature on analytic functions, Fock spaces remain virgin territory. This book meets the need for a focused presentation of key results and techniques and includes new and simpler proofs.

This text provides a systematic treatment of all the basic analytic and geometric aspects of Bergman's classic theory of the kernel and its invariance properties. Each chapter includes illustrative examples and a collection of exercises.

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 cyclotomic fields, or modular forms."Lang's books are always of great value for the graduate student and the research mathematician.

Grothendieck's beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.

Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ ential topology, etc.), we concentrate our attention on concrete prob lems in low dimensions, introducing only as much algebraic machin ery as necessary for the problems we meet.

This is an introduction to Galois Theory along the lines of Galois's Memoir on the Conditions for Solvability of Equations by Radicals. It puts Galois's ideas into historical perspective by tracing their antecedents in the works of Gauss, Lagrange, Newton, and even the ancient Babylonians.

Aimed at graduate math students, this classic work is a systematic exposition of general topology and is intended to be a reference and a text. As a reference, it offers a reasonably complete coverage of the area, resulting in a more extended treatment than normally given in a course.

Written by three authorities in the field, this book contains all the main theorems of the field with complete proofs. As both notation and techniques of rational homotopy theory have been considerably simplified, the book presents modern elementary proofs for many results that were proven ten or fifteen years ago.

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.

We have also tried, this time with an eye to both the student and the mature mathematician, to give a many-sided treatment of our topics, not hesitating to offer several proofs of one and the same result when we thought that something might be learned, as to methods, from each of the proofs."

The term "weakly differentiable functions" in the title refers to those inte n grable functions defined on an open subset of R whose partial derivatives in the sense of distributions are either LP functions or (signed) measures with finite total variation.

At the same time, the author has managed to include discussions of more advanced topics such as the Gibbs phenomenon, distributions, Sturm-Liouville theory, Cesaro summability and multi-dimensional Fourier analysis, topics which one usually does not find in books at this level.

This text is intended to serve as an introduction to the geometry of the action of discrete groups of Mobius transformations. However, the recent developments have again emphasized the need for hyperbolic geometry, and I have included a comprehensive chapter on analytical (not axiomatic) hyperbolic geometry.

Richard Sharpe erforscht in seinem Buch die Idee der Cartanschen Verbindungen und schliesst damit eine Lucke in der Literatur zur Differentialgeometrie.

Based on a graduate course at the Technische Universitat, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes.

Presents a comprehensive treatment of most of the basic material in differential topology, as far as is accessible without the methods of algebraic topology.

The material presented includes the theory of Borel measures and integration for ~n, the general theory of integration for locally compact Hausdorff spaces, and the first dozen results about invariant measures for groups.