Algebra

This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof.

This brief presents a solution to the interpolation problem for arithmetically Cohen-Macaulay (ACM) sets of points in the multiprojective space P^1 x P^1.

This book presents an exciting collection of contributions based on the workshop "e;Bringing Maths to Life"e; held October 27-29, 2014 in Naples, Italy.

This textbook on algebraic topology updates a popular textbook from the golden era of the Moscow school of I.

This textbook addresses the mathematical description of sets, categories, topologies and measures, as part of the basis for advanced areas in theoretical computer science like semantics, programming languages, probabilistic process algebras, modal and dynamic logics and Markov transition systems.

This is an introduction to the mathematics behind the phrase "e;quantum Lie algebra"e;.

This book examines the relationship between mathematics and data in the modern world.

This monograph introduces and explores the notions of a commutator equation and the equationally-defined commutator from the perspective of abstract algebraic logic.

This book features a series of lectures that explores three different fields in which functor homology (short for homological algebra in functor categories) has recently played a significant role.

This book constitutes the thoroughly refereed proceedings of the 5th International Conference on Mathematics and Computation in Music, MCM 2015, held in London, UK, in June 2015.

The topic of this book sits at the interface of the theory of higher categories (in the guise of (infinity,1)-categories) and the theory of properads.

The main intention of this book is to describe and develop the conceptual, structural and abstract thinking of mathematics.

Combinatorics plays a prominent role in contemporary mathematics, due to the vibrant development it has experienced in the last two decades and its many interactions with other subjects.

This book, written by an accomplished female mathematician, is the second to explore nonstandard mathematical problems - those that are not directly solved by standard mathematical methods but instead rely on insight and the synthesis of a variety of mathematical ideas.

This book presents a graduate-level course on modern algebra.

This book constitutes the refereed proceedings of the 13th International Conference on Formal Concept Analysis, ICFCA 2015, held in Neja, Spain, in June 2015.

The main goal of this book is to find the constructive content hidden in abstract proofs of concrete theorems in Commutative Algebra, especially in well-known theorems concerning projective modules over polynomial rings (mainly the Quillen-Suslin theorem) and syzygies of multivariate polynomials with coefficients in a valuation ring.

Written by one of the subject's foremost experts, this book focuses on the central developments and modern methods of the advanced theory of abelian groups, while remaining accessible, as an introduction and reference, to the non-specialist.

This text aims to provide graduate students with a self-contained introduction to topics that are at the forefront of modern algebra, namely, coalgebras, bialgebras and Hopf algebras.

Covering topics in graph theory, L-functions, p-adic geometry, Galois representations, elliptic fibrations, genus 3 curves and bad reduction, harmonic analysis, symplectic groups and mould combinatorics, this volume presents a collection of papers covering a wide swath of number theory emerging from the third iteration of the international Women in Numbers conference, "e;Women in Numbers - Europe"e; (WINE), held on October 14-18, 2013 at the CIRM-Luminy mathematical conference center in France.

Analysis, assessment, and data management are core competencies for operation research analysts.

This volume develops the depth and breadth of the mathematics underlying the construction and analysis of Hadamard matrices, and their use in the construction of combinatorial designs.

Extending Griffiths' classical theory of period mappings for compact Kahler manifolds, this book develops and applies a theory of period mappings of "e;Hodge-de Rham type"e; for families of open complex manifolds.

This monograph considers several well-known mathematical theorems and asks the question, "e;Why prove it again?

The topics covered in this book, written by researchers at the forefront of their field, represent some of the most relevant research areas in modern coding theory: codes and combinatorial structures, algebraic geometric codes, group codes, quantum codes, convolutional codes, network coding and cryptography.

This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects.

This book provides the mathematical foundations of networks of linear control systems, developed from an algebraic systems theory perspective.

This monograph is the first book-length treatment of valuation theory on finite-dimensional division algebras, a subject of active and substantial research over the last forty years.

This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side.

Since publication of the initial papers in 2006, compressed sensing has captured the imagination of the international signal processing community, and the mathematical foundations are nowadays quite well understood.

This edited volume highlights the scientific contributions of Volker Mehrmann, a leading expert in the area of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory.

This self-contained monograph explores a new theory centered around boolean representations of simplicial complexes leading to a new class of complexes featuring matroids as central to the theory.

Modern imaging techniques and computational simulations yield complex multi-valued data that require higher-order mathematical descriptors.

Algebra and number theory have always been counted among the most beautiful mathematical areas with deep proofs and elegant results.

The second edition of this highly praised textbook provides an introduction to tensors, group theory, and their applications in classical and quantum physics.

This book is intended as an introduction to fuzzy algebraic hyperstructures.

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Focusing on an approach of solving rigorous problems and learning how to prove, this volume is concentrated on two specific content themes, elementary number theory and algebraic polynomials.

C* tensor categories are a point of contact where Operator Algebras and Quantum Field Theory meet.

This textbook features applications including a proof of the Fundamental Theorem of Algebra, space filling curves, and the theory of irrational numbers.

This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites.

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This is a monograph that details the use of Siegel's method and the classical results of homotopy groups of spheres and Lie groups to determine some Gottlieb groups of projective spaces or to give the lower bounds of their orders.

Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors.

This book gives a general introduction to the theory of representations of algebras.

Investigating the correspondence between systems of partial differential equations and their analytic solutions using a formal approach, this monograph presents algorithms to determine the set of analytic solutions of such a system and conversely to find differential equations whose set of solutions coincides with a given parametrized set of analytic functions.

This edited volume presents a collection of carefully refereed articles covering the latest advances in Automorphic Forms and Number Theory, that were primarily developed from presentations given at the 2012 "e;International Conference on Automorphic Forms and Number Theory,"e; held in Muscat, Sultanate of Oman.

This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students.

In 1842 the Belgian mathematician Eugene Charles Catalan asked whether 8 and 9 are the only consecutive pure powers of non-zero integers.

Gathering and updating results scattered in journal articles over thirty years, this self-contained monograph gives a comprehensive introduction to the subject.