The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well establishe......more

A fundamental idea to understanding topological spaces is decomposing them down into simpler components for easier analy......more

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A concise and unified introduction to the foundational concepts of modern topology and geometry Topology and geometry ar......more

A concise and unified introduction to the foundational concepts of modern topology and geometry Topology and geometry ar......more

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This book offers a rigorous, comprehensive, and modern presentation of the most traditional concepts in measure theory a......more

The 20th century saw the development of many of the key concepts and theories in algebraic geometry. However, the evolut......more

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Classical in its approach, this textbook is thoughtfully designed and composed in two parts. Part I is meant for a one-s......more

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In this book, we study the shape of different geometric objects (curves, surfaces, and knots) through small deformation:......more

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This book provides a concise and effective introduction to twisted Rabinowitz-Floer homology, a generalization of Rabino......more

This monograph offers a compelling exploration of structures induced by smooth vector flows on the boundaries of compact......more

An Introduction to Point-Set Topology is intended for use in a beginning topology course for undergraduates or as an ele......more

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Borel Games are multiplayer games with infinite horizon and general payoff functions. These types of games, first introd......more

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The book includes recent articles on various topics studied recently in Banach algebras and abstract harmonic analysis. ......more

This monograph is devoted to the Isomorphism Conjectures formulated by Baum and Connes, and by Farrell and Jones. These ......more

In The Mind of Complex Numbers and the Subject in Analyses, Raul Moncayo uses the complex plane to evaluate analytic out......more

The theme of this book is to establish a link between gauge theory and L -cohomology theory. Although both theories focu......more

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This book focuses on spectral theory for linear operators involving bounded or unbounded demicompact linear operators ac......more

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Optimization Methods for Finite Element Analysis and Design describes recent developments in Finite Element Methods (FEM......more

The Magic Theorem: a Greatly-Expanded, Much-Abridged Edition of The Symmetries of Things presents a wonder- fully unique......more

This book provides an introduction to the theory of connection matrices in the context of combinatorial multivector fiel......more

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This classic text appears here in a new edition for the first time in four decades. The new edition, with the aid of two......more

"A Topological Theory Of Learning" presents a groundbreaking approach to understanding learning processes through the le......more

"Variable Dimension Complexes, Part II: A Unified Approach to Some Combinatorial Lemmas in Topology" presents a rigorous......more

"Variable Dimension Complexes, Part II: A Unified Approach to Some Combinatorial Lemmas in Topology" presents a rigorous......more

This book presents the monodromy group, underlining the unifying role it plays in a variety of theories and mathematical......more

The book introduces (co)homology theory and some of its applications in Algebra and Geometry. It is intended for undergr......more

The book introduces (co)homology theory and some of its applications in Algebra and Geometry. It is intended for undergr......more

This book explores the topological properties of connected and path-connected solution sets for nonlinear equations in B......more

The K-stability of Fano varieties has been a major area of research over the last decade, ever since the Yau-Tian-Donald......more

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An authoritative introduction to the essential features of étale cohomology A. Grothendieck’s work on algebraic geometry......more

An authoritative introduction to the essential features of étale cohomology A. Grothendieck’s work on algebraic geometry......more

This book explores three computational formalisms for solving geometric problems. Part I introduces a trigonometric-base......more

Explore four-dimensional paper constructions inspired by the work of great mathematicians like Möbius, Klein, Boy, Hopf,......more

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This book delves into the intricate world of fixed point theory, focusing on the Krasnoselskii-Mann method to tackle com......more

This monograph covers topics in the cohomology of monoids up through recent developments. Jonathan Leech’s original mono......more

Module theory is a fundamental area of algebra, taught in most universities at the graduate level. This textbook, writte......more

Module theory is a fundamental area of algebra, taught in most universities at the graduate level. This textbook, writte......more

Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are......more

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This volume consists of several papers written by the main participants of the 7th International Colloquium on Different......more

This is the seventh volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an a......more

This book is the result of research initiatives formed during the workshop "Low Dimensional Topology and Number Theory X......more

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This comprehensive guide addresses key challenges at the intersection of data science, graph learning, and privacy prese......more

This book is dedicated to metric spaces and their topology. The book starts with ZFC axioms. The real number system is c......more

This book serves as an introduction to topology, a branch of mathematics that studies the qualitative properties of geom......more

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Symmetry in Geometry and Analysis is a Festschrift honoring Toshiyuki Kobayashi. The three volumes feature 35 selected c......more

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This book seeks to familiarize students with the fundamental concepts and structures of topology. The book covers topics......more

A classic knot is an embedded simple loop in 3-dimensional space. It can be described as a 4-valent planar graph or netw......more

The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum me......more

For over two millennia, the complexities of elementary geometry have challenged learners, burdened by the intricacies of......more

For over two millennia, the complexities of elementary geometry have challenged learners, burdened by the intricacies of......more