This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course
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 conc
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
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 na
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 anal
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 meth
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
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 curv
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 pragmati
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 algorit
This text provides a masterful and systematic treatment of all the basic analytic and geometric aspects of Bergman's classic theory of the kernel and its invariance properties. These include calculati
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 tec
This textbook assumes only a basic knowledge of functional analysis, giving the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special e
This textbook on algebraic topology updates a popular textbook from the golden era of the Moscow school of I. M. Gelfand. The first English translation, done many decades ago, remains very much in dem
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 c
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
?Since its birth as a mathematical discipline, ergodic theory has had a strong operator theoretic flavor. This graduate text focuses on the interplay between ergodic theory and operator theory in hope
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
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 pragmati
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 algorit
The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It coversclassical topics such as interpolation, Fourier series, the Fourier t
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 coversmodern topics and
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, Schrödinger operators
A central problem in additive number theory is the growth of sumsets. If A is a finite or infinite subset of the integers and the lattice points, or more generally, of any abelian group or semigroup G
