Universitext

Now in a thoroughly revised and expanded second edition, this textbook offers a comprehensive and self-contained introduction to numerical methods in probability, with particular emphasis on stochastic optimization and its applications in …

This textbook offers an accessible introduction to Functional Analysis, providing a solid foundation for students new to the field. It is designed to support learners with no prior background in the subject and serves as an effective guide for …

This textbook offers a self-contained introduction to probability, covering all topics required for further study in stochastic processes and stochastic analysis, as well as some advanced topics at the interface between probability and functional …

Algebraic Geometry is a huge area of mathematics which went through several phases: Hilbert's fundamental paper from 1890, sheaves and cohomology introduced by Serre in the 1950s, Grothendieck's theory of schemes in the 1960s and so on. This book …

The theory of elliptic functions and modular forms is rich and storied, though it has a reputation for difficulty. In this textbook, the authors successfully bridge foundational concepts and advanced material. Following Weierstrass’s approach to …

Diagrammatic Algebra provides the intuition and tools necessary to address some of the key questions in modern representation theory, chief among them Lusztig’s conjecture. This book offers a largely self-contained introduction to diagrammatic …

This graduate textbook provides a natural and structured introduction to Continuum Theory, guiding readers from fundamental concepts to advanced topics. It covers classical results such as locally connected continua, indecomposable continua, arcs …

This textbook offers an elementary introduction to noncommutative rings and algebras. Beginning with the classical theory of finite-dimensional algebras, it then develops a more general structure theory of rings, grounded in modules and tensor …

This text is based on lectures delivered by the first author on various, often nonstandard, parts of knot theory and related subjects. By exploring contemporary topics in knot theory including those that have become mainstream, such as skein …

This book provides a foundation for arithmetic topology, a new branch of mathematics that investigates the analogies between the topology of knots, 3-manifolds, and the arithmetic of number fields. Arithmetic topology is now becoming a powerful …

This book provides a new, comprehensive, and self-contained account of Oka theory as an introduction to function theory of several complex variables, mainly concerned with the Three Big Problems (Approximation, Cousin, Pseudoconvexity) that were …

This textbook provides a modern introduction to advanced concepts and methods of mathematical analysis.

The first three parts of the book cover functional analysis, harmonic analysis, and microlocal analysis. Each chapter is designed to provide …

This textbook offers a rigorous introduction to the foundations of Riemannian Geometry, with a detailed treatment of homogeneous and symmetric spaces, as well as the foundations of the General Theory of Relativity.

Starting with the basics of …

This textbook presents the spectral theory of self-adjoint operators on Hilbert space and its applications in quantum mechanics. Based on a course taught by the author in Paris, the book not only covers the mathematical theory but also provides …

This text provides a concise introduction, suitable for a one-semester special topicscourse, to the remarkable properties of Gaussian measures on both finite and infinitedimensional spaces. It begins with a brief resumé of probabilistic results in …

This textbook provides a concise, visual introduction to Hopf algebras and their application to knot theory, most notably the construction of solutions of the Yang–Baxter equations.

Starting with a reformulation of the definition of a group in …

This text covers a first course in bilinear maps and tensor products intending to bring the reader from the beginning of functional analysis to the frontiers of exploration with tensor products. Tensor products, particularly in …

This book provides an introduction to the broad topic of the calculus of variations. It addresses the most natural questions on variational problems and the mathematical complexities they present.
Beginning with the scientific modeling that …

This textbook offers a complete one-semester course in probability, covering the essential topics necessary for further study in the areas of probability and statistics.

The book begins with a review of the fundamentals of measure theory and …

This textbook provides a first introduction to category theory, a powerful framework and tool for understanding mathematical structures. Designed for students with no previous knowledge of the subject, this book offers a gentle approach to …