Libros de Álgebra, página 8 de 28

Incluye 622 problemas totalmente resueltosCompleta cobertura de los fundamentos y conceptos clave del algebra linealContiene 475 problemas suplementarios con solucion indicadaMas de 150 ejemplos intercalados en la teoria, para reforzar los conceptos aprendidos

Preface.- 1 Linear Algebra and Optimization: An Introduction.- 2 Linear Transformations and Linear Systems.- 3 Eigenvectors and Diagonalizable Matrices.- 4 Optimization Basics: A Machine Learning View.- 5 Advanced Optimization Solutions.- 6 Constrained Optimization and Duality.- 7 Singular Value Decomposition.- 8 Matrix Factorization.- 9 The Linear Algebra of Similarity.- 10 The Linear Algebra of Graphs.- 11 Optimization in Computational Graphs.- Index.

Segona edició corregida i augmentada d'aquesta obra, que ofereix una clara i concisa introducció a l'àlgebra. El seu objectiu, el gran teorema de Galois sobre la resolubilitat d'equacions polinòmique

Computer algebra systems allow students to work on mathematical models more efficiently than in the case of pencil and paper. The use of such systems also leads to fewer errors and enables students to work on complex and computationally intensive models. Aimed at undergraduates in their second or third year, this book is filled with examples from a wide variety of disciplines, including biology, economics, medicine, engineering, game theory, physics, and chemistry. The text includes a large number of Maple(R) recipes.

This research monograph presents many new results in a rapidly developing area of great current interest. Guillemin, Ginzburg, and Karshon show that the underlying topological thread in the computation of invariants of G-manifolds is a consequence of a linearization theorem involving equivariant cobordisms. The book incorporates a novel approach and showcases exciting new research. During the last 20 years, ``localization'' has been one of the dominant themes in the area of equivariant differential geometry. Typical results are the Duistermaat-Heckman theory, the Berline-Vergne-Atiyah-Bott localization theorem in equivariant de Rham theory, and the ``quantization commutes with reduction'' theorem and its various corollaries. To formulate the idea that these theorems are all consequences of a single result involving equivariant cobordisms, the authors have developed a cobordism theory that allows the objects to be non-compact manifolds. A key ingredient in this non-compact cobordism is an equivariant-geometrical object which they call an ``abstract moment map''. This is a natural and important generalization of the notion of a moment map occurring in the theory of Hamiltonian dynamics. The book contains a number of appendices that include introductions to proper group-actions on manifolds, equivariant cohomology, Spin${mathrm{c $-structures, and stable complex structures. It is geared toward graduate students and research mathematicians interested in differential geometry. It is also suitable for topologists, Lie theorists, combinatorists, and theoretical physicists. Prerequisite is some expertise in calculus on manifolds and basic graduate-level differential geometry.

The Separable Galois Theory of Commutative Rings, Second Edition provides a complete and self-contained account of the Galois theory of commutative rings from the viewpoint of categorical classification theorems and using solely the techniques of commutative algebra. Along with updating nearly every result and explanation, this edition contains a new chapter on the theory of separable algebras. The book develops the notion of commutative separable algebra over a given commutative ring and explains how to construct an equivalent category of profinite spaces on which a profinite groupoid acts. It explores how the connection between the categories depends on the construction of a suitable separable closure of the given ring, which in turn depends on certain notions in profinite topology. The book also discusses how to handle rings with infinitely many idempotents using profinite topological spaces and other methods.

Algebraic groups play much the same role for algebraists as Lie groups play for analysts. This book is the first comprehensive introduction to the theory of algebraic group schemes over fields that includes the structure theory of semisimple algebraic groups, and is written in the language of modern algebraic geometry. The first eight chapters study general algebraic group schemes over a field and culminate in a proof of the Barsotti-Chevalley theorem, realizing every algebraic group as an extension of an abelian variety by an affine group. After a review of the Tannakian philosophy, the author provides short accounts of Lie algebras and finite group schemes. The later chapters treat reductive algebraic groups over arbitrary fields, including the Borel-Chevalley structure theory. Solvable algebraic groups are studied in detail. Prerequisites have also been kept to a minimum so that the book is accessible to non-specialists in algebraic geometry.

A completely reworked new edition of this superb textbook. This key work is geared to the needs of the graduate student. It covers, with proofs, the usual major branches of groups, rings, fields, and modules. Its inclusive approach means that all of the necessary areas are explored, while the level of detail is ideal for the intended readership. The text tries to promote the conceptual understanding of algebra as a whole, doing so with a masterful grasp of methodology. Despite the abstract subject matter, the author includes a careful selection of important examples, together with a detailed elaboration of the more sophisticated, abstract theories

Whilst being a research monograph presenting new original results, the book is essentially self-contained and contains an introductory chapter reviewing the necessary preliminaries.The unifying techniques introduced in this book have applications beyond Mathematics.Good balance and integration between theoretical results and examples/applications.The book gets the reader to the core aspects of topos theory and the ways in which it can be applied to shed light on a variety of different mathematical subjects.