Topology Books

This classic textbook has been used successfully by instructors and students for nearly three decades. This timely new edition offers minimal yet notable changes while retaining all the elements,...

This classic textbook has been used successfully by instructors and students for nearly three decades. This timely new edition offers minimal yet notable changes while retaining all the elements,...

Math and Art: An Introduction to Visual Mathematics explores the potential of mathematics to generate visually appealing objects and reveals some of the beauty of mathematics. It includes numerous...

Math and Art: An Introduction to Visual Mathematics explores the potential of mathematics to generate visually appealing objects and reveals some of the beauty of mathematics. It includes numerous...

Topological phases of quantum materials and brane charges in M-theory are measured by extraordinary cohomology theories defined on orbifold spacetimes. Geometric Orbifold Cohomology presents a...

This book is an ambitious but optimistic treatment of the subject of topology. Not only does Elements of Topology: Theory and Practice, Second Edition treat the standard basic material on point-set...

This book offers a rigorous, comprehensive, and modern presentation of the most traditional concepts in measure theory and integration. Building on the classical foundations, it introduces the theory...

Near Vector Spaces and Related Topics provides a systematic treatment of the introductory theory of near vector spaces, as well as a range of associated areas.Since many topics in nonlinear analysis...

Representation Theory and C*-algebras is devoted to the representation theory of solvable Lie groups and the associated non-commutative harmonic analysis including the study of C*-algebras. It...

In The Mind of Complex Numbers and the Subject in Analyses, Raul Moncayo uses the complex plane to evaluate analytic outcomes. Moncayo’s approach provides a study of the process and outcomes of...

Borel Games are multiplayer games with infinite horizon and general payoff functions. These types of games, first introduced by Gale and Stewart (1953), were studied within descriptive set theory in...

This volume argues that concepts from the theory of computation—including information theory, formal languages, and discrete structures—might provide novel paths towards a solution to the problem of...

Optimization Methods for Finite Element Analysis and Design describes recent developments in Finite Element Methods (FEM). It gives a brief introduction of the applications of AI-based...

Smooth Topological Design of Continuum Structures focuses on the use of a newly-proposed topology algorithm for structural optimization called Smooth-Edged Material Distribution for Optimizing...

Smooth Topological Design of Continuum Structures focuses on the use of a newly-proposed topology algorithm for structural optimization called Smooth-Edged Material Distribution for Optimizing...

The Tutte Polynomial touches on nearly every area of combinatorics as well as many other fields, including statistical mechanics, coding theory, and DNA sequencing. It is one of the most studied...

"Data Science Foundations is most welcome and, indeed, a piece of literature that the field is very much in need of…quite different from most data analytics texts which largely ignore foundational...

Basic Analysis V: Functional Analysis and Topology introduces graduate students in science to concepts from topology and functional analysis, both linear and nonlinear. It is the fifth book in a...

The Unconscious as Space explores the experience of being and the practice of psychoanalysis by thinking of the unconscious in mathematical terms.Anca Carrington introduces mathematical models of...

Lorentz Geometry is a very important intersection between Mathematics and Physics, being the mathematical language of General Relativity.Learning this type of geometry is the first step in properly...

Curves for the Mathematically Curious is a thoughtfully curated collection of ten mathematical curves, selected by Julian Havil for their significance, mathematical interest, and beauty. Each chapter...

Visual Differential Geometry and Forms fulfils two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham...

Mathematical Analysis with Topological Examples: A Narrative Approach for Undergraduates offers an introduction to elementary analysis for undergraduates studying mathematics or any related...

Mathematical Analysis with Topological Examples: A Narrative Approach for Undergraduates offers an introduction to elementary analysis for undergraduates studying mathematics or any related...

Alexandrov spaces are defined via axioms similar to those of the Euclid axioms but where certain equalities are replaced with inequalities. Depending on the signs of the inequalities, we obtain...

This book represents a novel approach to differential topology. Its main focus is to give a comprehensive introduction to the classification of manifolds, with special attention paid to the case of...

This textbook offers an accessible introduction to translation surfaces. Building on modest prerequisites, the authors focus on the fundamentals behind big ideas in the field: ergodic properties of...

We develop a unified theory of Eulerian spaces by combining the combinatorial theory of infinite, locally finite Eulerian graphs as introduced by Diestel and Kuehn with the topological theory of...

The connective topological modular forms spectrum, $tmf$, is in a sense initial among elliptic spectra, and as such is an important link between the homotopy groups of spheres and modular forms. A...

This book introduces advanced undergraduates to Riemannian geometry and mathematical general relativity. The overall strategy of the book is to explain the concept of curvature via the Jacobi...

This book serves as an introduction to number theory at the undergraduate level, emphasizing geometric aspects of the subject. The geometric approach is exploited to explore in some depth the...

This two-volume set containts parts I and II. Each volume is a collection of articles written in memory of Boris Dubrovin (1950-2019). The authors express their admiration for his remarkable...

The theory of persistence modules originated in topological data analysis and became an active area of research in algebraic topology. This book provides a concise and self-contained introduction to...

Among the many beautiful and nontrivial theorems in geometry found in Geometry Revisited are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. A nice proof is given of...

This book is a concrete introduction to abstract algebra and number theory. Starting from the basics, it develops the rich parallels between the integers and polynomials, covering topics such as...

The main topic of the book is amenable groups, i.e., groups on which there exist invariant finitely additive measures. It was discovered that the existence or non-existence of amenability is...

This volume contains the proceedings of the virtual conference on Cyclic Cohomology at 40: Achievements and Future Prospects, held from September 27-October 1, 2021 and hosted by the Fields Institute...

Discrete Morse theory is a powerful tool combining ideas in both topology and combinatorics. Invented by Robin Forman in the mid 1990s, discrete Morse theory is a combinatorial analogue of Marston...

The theory of geometric structures on manifolds which are locally modeled on a homogeneous space of a Lie group traces back to Charles Ehresmann in the 1930s, although many examples had been studied...

This volume contains the proceedings of the conference Dynamics: Topology and Numbers, held from July 2-6, 2018, at the Max Planck Institute for Mathematics, Bonn, Germany. The papers cover diverse...

Geometry: The Line and the Circle is an undergraduate text with a strong narrative that is written at the appropriate level of rigor for an upper-level survey or axiomatic course in geometry...

This book contains the proceedings of the AMS Special Session on Topology of Biopolymers, held from April 21-22, 2018, at Northeastern University, Boston, MA. The papers cover recent results on the...

This book on two-dimensional geometry uses a problem-solving approach to actively engage students in the learning process. The aim is to guide readers through the story of the subject, while giving...

This volume contains the proceedings of the 2017 Georgia International Topology Conference, held from May 22-June 2, 2017, at the University of Georgia, Athens, Georgia. The papers contained in this...

This volume contains the proceedings of the CRM Workshops on Probabilistic Methods in Spectral Geometry and PDE, held from August 22-26, 2016 and Probabilistic Methods in Topology, held from November...

This volume contains the proceedings of the 2016 Summer School on Fractal Geometry and Complex Dimensions, in celebration of Michel L. Lapidus's 60th birthday, held from June 21-29, 2016, at...

Computational methods to approximate the solution of differential equations play a crucial role in science, engineering, mathematics, and technology. The key processes that govern the physical...

This volume contains the proceedings of the ICM 2018 satellite school and workshop $K$-theory conference in Argentina. The school was held from July 16-20, 2018, in La Plata, Argentina, and the...