Algebra

The unifying theme of this collection of papers by the very creative Russian mathematician I.

This introduction is designed for graduate students who have some knowledge of finite groups and general topology, but is otherwise self-contained.

Symmetric designs are an important class of combinatorial structures which arose first in the statistics and are now especially important in the study of finite geometries.

This book will be of use to professional mathematicians working in algebraic geometry, complex-analytical geometry and, to some extent, differential analysis.

In these notes the abstract theory of analytic one-parameter semigroups in Banach algebras is discussed.

This volume introduces and systematically develops the calculus of 2-spinors.

A thorough development of certain classes of matrices that have combinatorial definitions or significance.

Comprehensive text which develops the notion of symmetric generation and applies the technique to sporadic simple groups.

An integrated approach for new graduate students, emphasising connections with game theory, optimisation, mathematical programming and statistics.

An introduction, suitable for beginning graduate students, showing connections to other areas of mathematics.

Third in a three part set, this volume introduces topos theory and the idea of sheaves.

Second in a three part set, this volume introduces important classes of categories (abelian, monadic, fibred, etc.

First of a 3-volume work giving a detailed account of what should be known by all working in, or using category theory.

This book is devoted entirely to the theory of finite fields.

The real, rational, complex and p-adic numbers are discussed in detail in this comprehensive work.

Orthogonal polynomials of several variables, approximation theory, symmetry-group methods.

The book is a self-contained introduction to the results and methods in classical invariant theory.

A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.

For advanced undergraduates and graduates, introducing physicists to the mathematical aspects of group theory, and mathematicians to its physics applications.

An introduction to the ordinary and modular representation theory of finite groups, with special emphasis on computational aspects.

This volume examines the impact of the ''Monstrous Moonshine'' paper on mathematics and theoretical physics.

This account of totally positive matrices treats their central properties with full proofs and a complete bibliography.

An elegant book that is sure to become the standard introduction to synthetic differential geometry.

A self-contained introduction to the representation theory of the symmetric groups, including an exhaustive exposition of the Okounkov–Vershik approach.

An up-to-date account of algebraic statistics and information geometry, which also explores the emerging connections between these two disciplines.

A complete and clear account of the classification of unitary reflection groups, which arise naturally in many areas of mathematics.

Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.

This truly elementary book on categories introduces retracts, graphs, and adjoints to students and scientists.

This book presents a coherent and unified account of classical and more advanced techniques for analyzing the performance of randomized algorithms.

A rigorous construction and uniqueness proof for the Monster group, detailing its relation to Majorana involutions.

This book presents an accessible and engaging approach to geometric group theory; ideal for advanced undergraduates.

This book is an introduction to semisimple Lie algebras.

A self-contained and elementary presentation of Lie group theory, with numerous exercises and worked examples ideal for a graduate course.

Combines algebra and statistics to explore the interplay between symmetry-related research questions and their statistical analysis.

The first comprehensive introduction to the role of Property (T), with applications to an amazing number of fields within mathematics.

Self-contained text, ideal for graduate students new to the area and researchers.

Monograph exploring the connections that forcing makes with descriptive set theory and other areas of mathematics.

This book presents research in model theory and its applications to valued fields.

Volume three of this modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field.

First text to focus on exciting area of group-theoretic research: the question ''how many groups of order n are there?

Volume two of this modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field

Provides an elementary but up-to-date introduction to the representation theory of algebras.

A stand-alone textbook in matrix algebra for econometricians and statisticians - advanced undergraduates, postgraduates and teachers.

A systematic geometro-topological approach to vanishing cycles appearing in non-proper fibrations; contains the latest research findings.

A rapid route for graduate students and researchers to the frontiers of research in this evergreen subject, first published in 2005.

A monograph on Moonshine, a mathematical physics topic, for graduate students and researchers.

Combining a concrete perspective with an exploration-based approach, Exploratory Galois Theory develops Galois theory at an entirely undergraduate level.

The first modern, comprehensive introduction to central simple algebras for graduate students and researchers.

This book presents the theory of free ideal rings (firs) in detail.

This book presents a self-contained graduate-level introduction to the topic of L-functions.