Algebra

The book reports a comparative research project about algebra teaching and learning in four countries.

This book offers a user friendly, hands-on, and systematic introduction to applied and computational harmonic analysis: to Fourier analysis, signal processing and wavelets; and to their interplay and applications.

These are notes from a graduate student course on algebraic topology and K-theory given by Daniel Quillen at the Massachusetts Institute of Technology during 1979-1980.

This book offers a review of the vibrant areas of geometric representation theory and gauge theory, which are characterized by a merging of traditional techniques in representation theory with the use of powerful tools from algebraic geometry, and with strong inputs from physics.

This book, the first of two volumes, contains over 250 selected exercises in Algebra which have featured as exam questions for the Arithmetic course taught by the authors at the University of Pisa.

This book presents the state of the art on numerical semigroups and related subjects, offering different perspectives on research in the field and including results and examples that are very difficult to find in a structured exposition elsewhere.

Originating from the School on Birational Geometry of Hypersurfaces, this volume focuses on the notion of (stable) rationality of projective varieties and, more specifically, hypersurfaces in projective spaces, and provides a large number of open questions, techniques and spectacular results.

Disjunctive Programming is a technique and a discipline initiated by the author in the early 1970's, which has become a central tool for solving nonconvex optimization problems like pure or mixed integer programs, through convexification (cutting plane) procedures combined with enumeration.

Quaternionic and Clifford analysis are an extension of complex analysis into higher dimensions.

This proceedings volume gathers selected, peer-reviewed works presented at the Polynomial Rings and Affine Algebraic Geometry Conference, which was held at Tokyo Metropolitan University on February 12-16, 2018.

This book presents, in a uniform way, several problems in applied mechanics, which are analysed using the matrix theory and the properties of eigenvalues and eigenvectors.

This unique collection of research papers offers a comprehensive and up-to-date guide to algebraic approaches to rough sets and reasoning with vagueness.

This proceedings volume covers a range of research topics in algebra from the Southern Regional Algebra Conference (SRAC) that took place in March 2017.

This edited volume features a curated selection of research in algebraic combinatorics that explores the boundaries of current knowledge in the field.

This textbook demonstrates how differential calculus, smooth manifolds, and commutative algebra constitute a unified whole, despite having arisen at different times and under different circumstances.

This volume collects contributions from speakers at the INdAM Workshop "e;Birational Geometry and Moduli Spaces"e;, which was held in Rome on 11-15 June 2018.

This textbook provides an introduction to representations of general *-algebras by unbounded operators on Hilbert space, a topic that naturally arises in quantum mechanics but has so far only been properly treated in advanced monographs aimed at researchers.

This textbook demonstrates the strong interconnections between linear algebra and group theory by presenting them simultaneously, a pedagogical strategy ideal for an interdisciplinary audience.

Based on the authors' research experience, this two-volume reference textbook focuses on the theory of generalized locally Toeplitz sequences and its applications.

This volume contains extended abstracts outlining selected talks and other selected presentations given by participants of the workshop "e;Positivity and Valuations"e;, held at the Centre de Recerca Matematica (CRM) in Barcelona from February 22nd to 26th, 2016.

This textbook introduces the representation theory of algebras by focusing on two of its most important aspects: the Auslander-Reiten theory and the study of the radical of a module category.

This innovative monograph explores a new mathematical formalism in higher-order temporal logic for proving properties about the behavior of systems.

This book is divided into two parts, one theoretical and one focusing on applications, and offers a complete description of the Canonical Grobner Cover, the most accurate algebraic method for discussing parametric polynomial systems.

This volume features selected, refereed papers on various aspects of statistics, matrix theory and its applications to statistics, as well as related numerical linear algebra topics and numerical solution methods, which are relevant for problems arising in statistics and in big data.

This is an in-depth report on the endotrivial modules, an important class of modular representations for finite groups.

This book focuses on recent developments in the theory of vertex algebras, with particular emphasis on affine vertex algebras, affine W-algebras, and W-algebras appearing in physical theories such as logarithmic conformal field theory.

In this partly expository work, a framework is developed for building exotic circle actions of certain classical groups.

This book offers a unified presentation of Fourier theory and corresponding algorithms emerging from new developments in function approximation using Fourier methods.

This textbook offers an innovative approach to abstract algebra, based on a unified treatment of similar concepts across different algebraic structures.

This book presents the main concepts of linear algebra from the viewpoint of applied scientists such as computer scientists and engineers, without compromising on mathematical rigor.

This textbook provides a rigorous mathematical perspective on error-correcting codes, starting with the basics and progressing through to the state-of-the-art.

This monograph is the first comprehensive treatment of multiplicity-free induced representations of finite groups as a generalization of finite Gelfand pairs.

This book explores the application of field theory (patterns of interaction) to Russian economic history, and how social and political fields mediate the influences of institutions, structures, discourses and ideologies in the creation and dissemination of economic thinking, theory and practice.

This proceedings volume gathers selected, peer-reviewed papers presented at the 2nd International Conference on Mathematics and its Applications in Science and Engineering - ICMASE 2021, which was virtually held on July 1-2, 2021 by the University of Salamanca, Spain.

This book, the second of two volumes, contains approximately 350 exercises in Algebra which have featured exam questions for the Algebraic Structure and Algebra I courses taught by the authors at the University of Pisa.

Groups and Symmetries: From Finite Groups to Lie Groups presents an introduction to the theory of group representations and its applications in quantum mechanics.

This book is dedicated to the structure and combinatorics of classical Hopf algebras.

This book provides a visual and intuitive coverage of the core theory of linear models.

This research monograph develops the theory of relative nonhomogeneous Koszul duality.

This book develops a new theory in convex geometry, generalizing positive bases and related to Caratheordory's Theorem by combining convex geometry, the combinatorics of infinite subsets of lattice points, and the arithmetic of transfer Krull monoids (the latter broadly generalizing the ubiquitous class of Krull domains in commutative algebra)This new theory is developed in a self-contained way with the main motivation of its later applications regarding factorization.

Providing a timely description of the present state of the art of moduli spaces of curves and their geometry, this volume is written in a way which will make it extremely useful both for young people who want to approach this important field, and also for established researchers, who will find references, problems, original expositions, new viewpoints, etc.

This volume contains research papers and surveys reflecting the topics discussed at the EMS Summer School on Multigraded Algebra and Applications held in Romania in August 2016.

This book is the second volume of an intensive "e;Russian-style"e; two-year undergraduate course in abstract algebra, and introduces readers to the basic algebraic structures - fields, rings, modules, algebras, groups, and categories - and explains the main principles of and methods for working with them.

This volume presents recent advances in the field of matrix analysis based on contributions at the MAT-TRIAD 2015 conference.

This book consists of two parts.

This carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields.

Held during algebraic topology special sessions at the Vietnam Institute for Advanced Studies in Mathematics (VIASM, Hanoi), this set of notes consists of expanded versions of three courses given by G.

This textbook is an introduction to the theory of infinity-categories, a tool used in many aspects of modern pure mathematics.

This book uncovers mathematical structures underlying natural intelligence and applies category theory as a modeling language for understanding human cognition, giving readers new insights into the nature of human thought.