Geometry Books

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...

Olive Whicher's groundbreaking book presents an accessible - non-mathematician's - approach to projective geometry. Profusely illustrated, and written with fire and intuitive genius, this work will...

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...

This book uses finite field theory as a hook to introduce the reader to a range of ideas from algebra and number theory. It constructs all finite fields from scratch and shows that they are unique up...

This book is the third of a three-volume set of books on the theory of algebras, a study that provides a consistent framework for understanding algebraic systems, including groups, rings, modules,...

This book is the second of a three-volume set of books on the theory of algebras, a study that provides a consistent framework for understanding algebraic systems, including groups, rings, modules,...

This volume contains the proceedings of the 18th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, held (online) from May 31 to June 4, 2021. For over thirty years,...

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...

This volume contains the proceedings of the 2019 Lluis A. Santalo Summer School on $p$-Adic Analysis, Arithmetic and Singularities, which was held from June 24-28, 2019, at the Universidad...

This book gives a self-contained account of applications of category theory to the theory of representations of algebras. Its main focus is on 2-categorical techniques, including 2-categorical...

This book is the ninth volume in a series whose goal is to furnish a careful and largely self-contained proof of the classification theorem for the finite simple groups. Having completed the...

This book provides an elementary analytically inclined journey to a fundamental result of linear algebra: the Singular Value Decomposition (SVD). SVD is a workhorse in many applications of linear...

The goal of this book is to present a portrait of the $n$-dimensional Cremona group with an emphasis on the 2-dimensional case. After recalling some crucial tools, the book describes a naturally...

This volume contains the proceedings of the workshop Crossing the Walls in Enumerative Geometry, held in May 2018 at Snowbird, Utah. It features a collection of both expository and research articles...

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...

Vladimir Abramovich Rokhlin (8/23/1919-12/03/1984) was one of the leading Russian mathematicians of the second part of the twentieth century. His main achievements were in algebraic topology, real...

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 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...

Strengthen your trigonometry skills and grades with this powerful and simple tool for reviewing and referencing the most important core concepts. Quickly find that answer you need in 6 laminated...

The point, line, plane and solid objects represent the first three dimensions, but a kind of reversal of space is involved in the ascent to a fourth dimension. Steiner leads us to the brink of this...

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 the tenth in a series of volumes whose aim is to provide a complete proof of the classification theorem for the finite simple groups based on a fairly short and clearly enumerated set of...

This book is an introduction to the geometry of complex algebraic varieties. It is intended for students who have learned algebra, analysis, and topology, as taught in standard undergraduate courses...

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...

Articles in this volume are based on lectures given at three conferences on Geometry at the Frontier, held at the Universidad de la Frontera, Pucon, Chile in 2016, 2017, and 2018. The papers cover...

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 book is an introduction to Hopf algebras in braided monoidal categories with applications to Hopf algebras in the usual sense. The main goal of the book is to present from scratch and with...

This volume contains selected expository lectures delivered at the 2018 Maurice Auslander Distinguished Lectures and International Conference, held April 25-30, 2018, at the Woods Hole Oceanographic...

This book is a collection of articles on abelian varieties and number theory dedicated to Gerhard Frey's 75th birthday. It contains original articles by experts in the area of arithmetic and...

A polynomial identity for an algebra (or a ring) $A$ is a polynomial in noncommutative variables that vanishes under any evaluation in $A$. An algebra satisfying a nontrivial polynomial identity is...

The Seventh ARTA ('Advances in Representation Theory of Algebras VII') conference took place at the Instituto de Matematicas of the Universidad Nacional Autonoma de Mexico, in Mexico City, from...

Systems of polynomial equations can be used to model an astonishing variety of phenomena. This book explores the geometry and algebra of such systems and includes numerous applications. The book...

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...

Borel's Conjecture entered the mathematics arena in 1919 as an innocuous remark about sets of real numbers in the context of a new covering property introduced by Emile Borel. In the 100 years since,...

Linear Algebra for the Young Mathematician is a careful, thorough, and rigorous introduction to linear algebra. It adopts a conceptual point of view, focusing on the notions of vector spaces and...

This book is the first of two volumes on linear algebra for graduate students in mathematics, the sciences, and economics, who have: a prior undergraduate course in the subject; a basic understanding...

Algebraic Geometry Codes: Advanced Chapters is devoted to the theory of algebraic geometry codes, a subject related to several domains of mathematics. On one hand, it involves such classical areas as...

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 volume contains the proceedings of the conference A Panorama on Singular Varieties, celebrating the 70th birthday of Le Dung Trang, held from February 7-10, 2017, at the University of Seville,...

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...

The theory of complex dynamics in one variable, initiated by Fatou and Julia in the early twentieth century, concerns the iteration of a rational function acting on the Riemann sphere. Building on...

Discrete Differential Geometry (DDG) is an emerging discipline at the boundary between mathematics and computer science. It aims to translate concepts from classical differential geometry into a...

Linear Algebra: Concepts and Applications is designed to be used in a first linear algebra course taken by mathematics and science majors. It provides a complete coverage of core linear algebra...