Algebra

This textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises).

MATRIX is Australia's international, residential mathematical research institute.

This book presents the proceedings of the international conference Analytic Aspects in Convexity, which was held in Rome in October 2016.

This book contains the notes of the lectures delivered at an Advanced Course on Combinatorial Matrix Theory held at Centre de Recerca Matematica (CRM) in Barcelona.

This book is intended as a teacher's manual and as an independent-study handbook for students and mathematical competitors.

This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 "e;Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory"e;, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016.

This volume presents an elaborated version of lecture notes for two advanced courses: (Re)Emerging methods in Commutative Algebra and Representation Theory and Building Bridges Between Algebra and Topology, held at the CRM in the spring of 2015.

This contributed volume contains articles written by the plenary and invited speakers from the second international MATHEON Workshop 2015 that focus on applications of compressed sensing.

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 offers an invitation to modern algebra through number systems of increasing complexity, beginning with the natural numbers and culminating with Hamilton's quaternions.

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.

This monograph details several different methods for constructing simple relation algebras, many of which are new with this book.

This rare publication continues an exploratory journey in relational biology, a study of biology in terms of the organization of networked connections in living systems.

The first volume of a pair that charts relation algebras from novice to expert level, this text offers a comprehensive grounding for readers new to the topic.

This monograph presents both classical and recent results in the theory of nilpotent groups and provides a self-contained, comprehensive reference on the topic.

This book focuses on linear time eigenvalue location algorithms for graphs.

This highly readable book aims to ease the many challenges of starting undergraduate research.

The second volume of a pair that charts relation algebras from novice to expert level, this text brings the well-grounded reader to the frontiers of research.

This volume presents a collection of articles highlighting recent developments in commutative algebra and related non-commutative generalizations.

This textbook for graduate and advanced undergraduate students presents the theory of matrix algebra for statistical applications, explores various types of matrices encountered in statistics, and covers numerical linear algebra.

This advanced textbook provides a comprehensive and unified account of the moment problem.

This book provides a rather self-contained survey of the construction of Hadamard states for scalar field theories in a large class of notable spacetimes, possessing a (conformal) light-like boundary.

This self-contained, clearly written textbook on linear algebra is easily accessible for students.

This book collects a series of contributions addressing the various contexts in which the theory of Lie groups is applied.

This volume collects contributions by leading experts in the area of commutative algebra related to the INdAM meeting "e;Homological and Computational Methods in Commutative Algebra"e; held in Cortona (Italy) from May 30 to June 3, 2016 .

Adopting a new universal algebraic approach, this book explores and consolidates the link between Tarski's classical theory of equidecomposability types monoids, abstract measure theory (in the spirit of Hans Dobbertin's work on monoid-valued measures on Boolean algebras) and the nonstable K-theory of rings.

This book focuses on the modeling, processing and visualization of anisotropy, irrespective of the context in which it emerges, using state-of-the-art mathematical tools.

This volume is a tribute to Maxim Kontsevich, one of the most original and influential mathematicians of our time.

This book provides a self-contained introduction to algebraic coding theory over finite Frobenius rings.

This self-contained text presents state-of-the-art results on recurrent sequences and their applications in algebra, number theory, geometry of the complex plane and discrete mathematics.

This book contains selected papers based on talks given at the "e;Representation Theory, Number Theory, and Invariant Theory"e; conference held at Yale University from June 1 to June 5, 2015.

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.

Orthogonal designs have proved fundamental to constructing code division multiple antenna systems for more efficient mobile communications.

This book takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability.

Lie theory is a mathematical framework for encoding the concept of symmetries of a problem, and was the central theme of an INdAM intensive research period at the Centro de Giorgi in Pisa, Italy, in the academic year 2014-2015.

This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems.

This book gives a thorough and entirely self-contained, in-depth introduction to a specific approach to group theory, in a large sense of that word.

The Applications of Computer Algebra (ACA) conference covers a wide range of topics from Coding Theory to Differential Algebra to Quantam Computing, focusing on the interactions of these and other areas with the discipline of Computer Algebra.

This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations.

This textbook provides an accessible introduction to the rich and beautiful area of hyperplane arrangement theory, where discrete mathematics, in the form of combinatorics and arithmetic, meets continuous mathematics, in the form of the topology and Hodge theory of complex algebraic varieties.

This unique and innovative book presents an exciting and complete detail of all the important topics related to the theory of square matrices of order 2.

This monograph is a comprehensive account of formal matrices, examining homological properties of modules over formal matrix rings and summarising the interplay between Morita contexts and K theory.

This book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world.

Based on their research experience, the authors propose a reference textbook in two volumes on the theory of generalized locally Toeplitz sequences and their applications.

To find "e;criteria of simplicity"e; was the goal of David Hilbert's recently discovered twenty-fourth problem on his renowned list of open problems given at the 1900 International Congress of Mathematicians in Paris.

Now in its third decade, the Colorado Mathematical Olympiad (CMO), founded by the author, has become an annual state-wide competition, hosting many hundreds of middle and high school contestants each year.

Mathematical methods and theories with interdisciplinary applications are presented in this book.

Featuring up-to-date coverage of three topics lying at the intersection of combinatorics and commutative algebra, namely Koszul algebras, primary decompositions and subdivision operations in simplicial complexes, this book has its focus on computations.

This book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori's abelian category of mixed motives.

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.