This textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout.
This textbook offers an accessible, modern introduction at undergraduate level to an area known variously as general topology, point-set topology or analytic topology with a particular focus on helping students to build theory for themselves.
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.
This edited collection of chapters, authored by leading experts, provides a complete and essentially self-contained construction of 3-fold and 4-fold klt flips.
This work is an introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions, and classes of ordered sets.
Topology is a major area of mathematics concerned with properties that are preserved undercontinuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing, although the notion of stretching employed in mathematics is not quite the everyday notion: see below and the definition of homeomorphism for details of the mathematical notion.
In this book, experts in different fields of mathematics, physics, chemistry and biology present unique forms of knots which satisfy certain preassigned criteria relevant to a given field.
Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explore similar systems that instead evolve on differentiable manifolds.
Introduction to Large Truncated Toeplitz Matrices is a text on the application of functional analysis and operator theory to some concrete asymptotic problems of linear algebra.
This book aims to fill the gap in the available literature on supermanifolds, describing the different approaches to supermanifolds together with various applications to physics, including some which rely on the more mathematical aspects of supermanifold theory.
This textbook on combinatorial commutative algebra focuses on properties of monomial ideals in polynomial rings and their connections with other areas of mathematics such as combinatorics, electrical engineering, topology, geometry, and homological algebra.
This volume covers many diverse topics related in varying degrees to mathematics in mind including the mathematical and topological structures of thought and communication.
The Magic Theorem: a Greatly-Expanded, Much-Abridged Edition of The Symmetries of Things presents a wonder- fully unique re-imagining of the classic book, The Symmetries of Things.
In mathematics, general topology or point-set topology is the branch of topology which studies properties of topological spaces and structures defined on them.
This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves.
Providing an accessible approach to a special case of the Rank Theorem, the present text considers the exact finiteness properties of S-arithmetic subgroups of split reductive groups in positive characteristic when S contains only two places.
This definitive synthesis of mathematician Gregory Margulis's research brings together leading experts to cover the breadth and diversity of disciplines Margulis's work touches upon.
This rapid and concise presentation of the essential ideas and results of algebraic topology follows the axiomatic foundations pioneered by Eilenberg and Steenrod.
