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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 …
Lie Groups, Lie Algebras, and Representations
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 …
Differential Geometry
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 …
Stationary Processes and Discrete Parameter Markov Processes
This textbook explores two distinct stochastic processes that evolve at random: weakly stationary processes and discrete parameter Markov processes. Building from simple examples, …
Homotopical Topology
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, …
Random Walks on Infinite Groups
This text presents the basic theory of random walks on infinite, finitely generated groups, along with certain background material in measure-theoretic probability. The main …
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 …
Partial Differential Equations
This textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors …
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 …
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 …
Measure Theory, Probability, and Stochastic Processes
This textbook introduces readers to the fundamental notions of modern probability theory. The only prerequisite is a working knowledge in real analysis. Highlighting the …
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. …