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Graduate Texts in Mathematics

Graduate Texts in Mathematics

Readings in Mathematics

216 Jahrgänge | 1980 - 2019


Graduate Texts in Mathematics bridge the gap between passive study and creative understanding, offering graduate-level introductions to advanced topics in mathematics. The volumes are carefully written as teaching aids and highlight characteristic features of the theory. Although these books are frequently used as textbooks in graduate courses, they are also suitable for individual study.Series Editors:

Sheldon Axler, San Francisco State University
Kenneth Ribet, University of California, Berkeley

Advisory Board:
Alejandro Adem, University of British Columbia
David Eisenbud, University of California, Berkeley & MSRI
Brian C. Hall, University of Notre Dame
Patricia Hersh, North Carolina State University
J.F. Jardine, University of Western Ontario
Jeffrey C. Lagarias, University of Michigan
Ken Ono, Emory University
Jeremy Quastel, University of Toronto
Fadil Santosa, University of Minnesota
Barry Simon, California Institute of TechnologyRavi Vakil, Stanford UniversitySteven H. Weintraub, Lehigh UniversityMelanie Matchett Wood, University of California, Berkeley

Alle Bücher der Reihe Graduate Texts in Mathematics

2019 | Buch


This textbook is the second volume of a pair that presents the latest English edition of the author’s classic, Probability. Building on the foundations established in the preceding Probability-1, this volume guides the reader on to the theory of …

2019 | Buch

Introduction to Real Analysis

Developed over years of classroom use, this textbook provides a clear and accessible approach to real analysis. This modern interpretation is based on the author’s lecture notes and has been meticulously tailored to motivate students and inspire …

2018 | Buch

Binomial Ideals

This textbook provides an introduction to the combinatorial and statistical aspects of commutative algebra with an emphasis on binomial ideals. In addition to thorough coverage of the basic concepts and theory, it explores current trends, results …

2018 | Buch

Introduction to Riemannian Manifolds

​This textbook is designed for a one or two semester graduate course on Riemannian geometry for students who are familiar with topological and differentiable manifolds. The second edition has been adapted, expanded, and aptly retitled from Lee’s …

2017 | Buch

Differential Geometry

Connections, Curvature, and Characteristic Classes

This text presents a graduate-level introduction to differential geometry for mathematics and physics students. The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the …

2017 | Buch

Graph Theory

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 …

2017 | Buch

The Moment Problem

This advanced textbook provides a comprehensive and unified account of the moment problem. It covers the classical one-dimensional theory and its multidimensional generalization, including modern methods and recent developments.

In both the …

2017 | Buch

Functional Analysis, Spectral Theory, and Applications

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 …

2017 | Buch

Modern Real Analysis

This first year graduate text is a comprehensive resource in real analysis based on a modern treatment of measure and integration. Presented in a definitive and self-contained manner, it features a natural progression of concepts from simple to …

2016 | Buch

Riemannian Geometry

Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in …

2016 | Buch

Brownian Motion, Martingales, and Stochastic Calculus

This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional …

2016 | Buch


Volume 1

This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks, martingales, Markov chains, the measure-theoretic foundations of …

2016 | Buch

Topics in Banach Space Theory

This text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises …

2015 | Buch

Operator Theoretic Aspects of Ergodic Theory

Stunning recent results by Host–Kra, Green–Tao, and others, highlight the timeliness of this systematic introduction to classical ergodic theory using the tools of operator theory. Assuming no prior exposure to ergodic theory, this book pro

2014 | Buch

Classical Fourier Analysis

The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular i

2014 | Buch

Modern Fourier Analysis

This text is addressed to 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 d

2014 | Buch

Locally Convex Spaces

For most practicing analysts who use functional analysis, the restriction to Banach spaces seen in most real analysis graduate texts is not enough for their research. This graduate text, while focusing on locally convex topological vector spaces,

2014 | Buch

Integer Programming

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 abunda

2014 | Buch

An Introduction to Markov Processes

This book provides a rigorous but elementary introduction to the theory of Markov Processes on a countable state space. It should be accessible to students with a solid undergraduate background in mathematics, including students from engineering,

2013 | Buch

Functional Analysis, Calculus of Variations and Optimal Control

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. T