Algebra Books

A complete quick reference guide for all aspects of Linear Algebra.

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 abstract algebra textbook takes an integrated approach that highlights the similarities of fundamental algebraic structures among a number of topics. The book begins by introducing groups,...

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,...

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...

Power series provide a technique for constructing examples of commutative rings. In this book, the authors describe this technique and use it to analyse properties of commutative rings and their...

Hopf algebras have been shown to play a natural role in studying questions of integral module structure in extensions of local or global fields. This book surveys the state of the art in Hopf-Galois...

Galois theory is the culmination of a centuries-long search for a solution to the classical problem of solving algebraic equations by radicals. In this book, Bewersdorff follows the historical...

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...

Erdos asked how many distinct distances must there be in a set of $n$ points in the plane. Falconer asked a continuous analogue, essentially asking what is the minimal Hausdorff dimension required of...

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...

Articles in this volume are based on talks given at the International Workshop on Hopf Algebras and Tensor Categories, held from September 9-13, 2019, at Nanjing University, Nanjing, China. The...

Unitary representations of groups play an important role in many subjects, including number theory, geometry, probability theory, partial differential equations, and quantum mechanics. This monograph...

This volume contains the combined Proceedings of the Second International Meeting on Commutative Algebra and Related Areas (SIMCARA) held from July 22-26, 2019, at the Universidade de Sao Paulo, Sao...

Over 1 million sold to college and high school students supporting better test scores, grades, and improved skills - a best-selling reference for over 25 years. As a college student or being college...

In college or college bound, the importance of algebra in an academic career is so large it can determine your future path and college major. This solid prerequisite course can pave the way for...

This guide outlines basic algebraic equations, formulas, properties & operations.

Brush up on your first year of college-level math with our new College Algebra guide! Pinpointed essentials of college algebra are covered in our easy-to-access format that includes succinct...

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 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...

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...

This book is a lightly edited version of the unpublished manuscript Maximal Cohen-Macaulay modules and Tate cohomology over Gorenstein rings by Ragnar-Olaf Buchweitz. The central objects of study are...

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...

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...

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...

The construction of a $C^{*}$-algebra from a locally compact groupoid is an important generalization of the group $C^{*}$-algebra construction and of the transformation group $C^{*}$-algebra...

It presents several themes of contemporary representation theory together with some new tools, such as stable ?-categories, stable derivators, and contramodules. In the first part, expanded lecture...

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 a systematic account of the impressive developments in the theory of symmetric manifolds achieved over the past 50 years. It contains detailed and friendly, but rigorous, proofs of the...

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...

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,...

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...

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...

This volume contains the proceedings of the international conference Model Theory of Modules, Algebras and Categories, held from July 28-August 2, 2017, at the Ettore Majorana Foundation and Centre...

This volume contains the proceedings of the Conference on Representation Theory and Algebraic Geometry, held in honor of Joseph Bernstein, from June 11-16, 2017, at the Weizmann Institute of Science...

This volume contains a collection of papers on algebraic curves and their applications. While algebraic curves traditionally have provided a path toward modern algebraic geometry, they also provide...

Nonassociative mathematics is a broad research area that studies mathematical structures violating the associative law $x(yz)=(xy)z$. The topics covered by nonassociative mathematics include...

For thirty years, the biennial international conference AGC$^2$T (Arithmetic, Geometry, Cryptography, and Coding Theory) has brought researchers to Marseille to build connections between arithmetic...

This volume contains the proceedings of the Arizona Winter School 2016, which was held from March 12-16, 2016, at The University of Arizona, Tucson, AZ. In the last decade or so, analytic methods...

This volume contains the proceedings of the Research Workshop of the Israel Science Foundation on Groups, Algebras and Identities, held from March 20-24, 2016, at Bar-Ilan University and the Hebrew...