Libros de Álgebra, página 7 de 27

Juan F. NavarroEl Álgebra Lineal y, particularmente, la estructura algebraica de espacio vectorial, constituye uno de los pilares en los que se fundamenta la formación de cualquier ingeniero. Este texto aborda el estudio del espacio vectorial y el espacio vectorial euclideo desde una perspectiva clasica. En el libro se exponen con claridad y detalle los aspectos teoricos basicos, y se profundiza en otros que pueden motivar el interes del alumno por las Matematicas en general. Ademas, la resolucion de una amplia variedad de problemas facilita la comprension de los elementos teoricos.

A Thorough Guide to Elementary Matrix Algebra and Implementation in R Basics of Matrix Algebra for Statistics with R provides a guide to elementary matrix algebra sufficient for undertaking specialized courses, such as multivariate data analysis and linear models. It also covers advanced topics, such as generalized inverses of singular and rectangular matrices and manipulation of partitioned matrices, for those who want to delve deeper into the subject. The book introduces the definition of a matrix and the basic rules of addition, subtraction, multiplication, and inversion. Later topics include determinants, calculation of eigenvectors and eigenvalues, and differentiation of linear and quadratic forms with respect to vectors. The text explores how these concepts arise in statistical techniques, including principal component analysis, canonical correlation analysis, and linear modeling. In addition to the algebraic manipulation of matrices, the book presents numerical examples that illustrate how to perform calculations by hand and using R. Many theoretical and numerical exercises of varying levels of difficulty aid readers in assessing their knowledge of the material. Outline solutions at the back of the book enable readers to verify the techniques required and obtain numerical answers. Avoiding vector spaces and other advanced mathematics, this book shows how to manipulate matrices and perform numerical calculations in R. It prepares readers for higher-level and specialized studies in statistics.

Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This second edition of this acclaimed text presents results of both classic and recent matrix analysis using canonical forms as a unifying theme and demonstrates their importance in a variety of applications. This thoroughly revised and updated second edition is a text for a second course on linear algebra and has more than 1,100 problems and exercises, new sections on the singular value and CS decompositions and the Weyr canonical form, expanded treatments of inverse problems and of block matrices, and much more.

TEXTO GENERAL

Este manual se ha preparado o pensado en el estudiante habitual de un Grado en Economía o de ADE o de grados afines propios de las facultades de Economía y Empresa. En este texto el lector podrá encontrar recogidos, explicados e ilustrados con ejemplos, la mayoria de los conceptos y herramientas propias del Algebra Lineal que va a utilizar a lo largo de su formacion en cualquiera de los grados referidos anteriormente. De singular relevancia es que para la preparacion de esta edicion se han revisado los manuales de econometria, estadistica y matematicas avanzadas, a fin de que el lector pueda encontrar en estas paginas aquellas herramientas propias del Algebra Lineal que se le van a demandar desde estas asignaturas indicadas.El texto ademas contiene un amplio apendice que pretende explicar e ilustrar aquellos conceptos o tecnicas elementales de matematicas que se suelen dar por conocidas en los cursos iniciales de los grados de Economia y ADE, por los que el lector probablemente encuentre utilidad en la obra, mas alla de aquella directamente relacionada con Algebra Lineal.Ambos autores cuentan con una dilatada experiencia docente en la materia. Mariano Matilla Garcia es actualmente Catedratico de Universidad en la UNED especializado en metodos cuantitativos para la Economia y Empresa, ambito en el que ha publicado numerosos articulos de investigacion en revistas de primer nivel internacional, asi como varios manuales de matematicas, econometria y analisis microeconomico. Compagina su labor docente con la editor asociado de la Revista de Estadistica Española y de la Revista de Economia Aplicada. Julian Rodriguez Ruiz ha sido Catedratico de la UNED en el departamento de Economia Aplicada Cuantitativa en asignaturas prioritariamente de matematicas para las Economia y la Empresa: calculo diferencial, programacion lineal y optimizacion. Actualmente colabora activamente con el departamento de Economia Aplicada y Estadistica tanto en aspectos docentes, como de investigacion y supervision de estudiantes.

This proceedings book brings selected works from two conferences, the 2nd Brazil-Mexico Meeting on Singularity and the 3rd Northeastern Brazilian Meeting on Singularities, that were hold in Salvador, in July 2015. All contributions were carefully peer-reviewed and revised, and cover topics like Equisingularity, Topology and Geometry of Singularities, Topological Classification of Singularities of Mappings, and more. They were written by mathematicians from several countries, including Brazil, Spain, Mexico, Japan and the USA, on relevant topics on Theory of Singularity, such as studies on deformations, Milnor fibration, foliations, Catastrophe theory, and myriad applications. Open problems are also introduced, making this volume a must-read both for graduate students and active researchers in this field.

El programa elegido es el habitual en un curso de un cuatrimestre de duración, por lo que se advierte al estudiante que se dan por sabidos los conocimientos elementales del álgebra lineal:elementos imprescindibles de la teoria de conjuntos, producto cartesiano, correspondencias, aplicaciones,relaciones de equivalencia y de orden, etc., sin que ello signifique que los topicos que se van a desarrollar no sean autosuficientes incluso para aquellos que puedan haber olvidado algunas nociones elementales. Los temas elegidos son imprescindibles para abortar no solo otras materias de matematicas sino tambien de aplicacion en otras asignaturas de la carrera.

Problem solving is an art that is central to understanding and ability in mathematics. With this series of books the authors have provided a selection of problems with complete solutions and test papers designed to be used with or instead of standard textbooks on algebra. For the convenience of the reader, a key explaining how the present books may be used in conjunction with some of the major textbooks is included. Each book of problems is divided into chapters that begin with some notes on notation and prerequisites. The majority of the material is aimed at the student of average ability but there are some more challenging problems. By working through the books, the student will gain a deeper understanding of the fundamental concepts involved, and practice in the formulation, and so solution, of other algebraic problems. Later books in the series cover material at a more advanced level than the earlier titles, although each is, within its own limits, self-contained.

This text provides a supportive environment to help students successfully learn the content of a standard algebra and trigonometry course. By incorporating interactive learning techniques, the Aufmann team helps students to better understand concepts, focus their studying habits, and obtain greater mathematical success. Prerequisite review is include in the textbook (and supporting materials) so that instructors can spend less time covering review material and students can still fill in the gaps in their mathematical knowledge. Integrated Review Notes provided next to examples throughout the text help students see the key prerequisite skills used within the example. For added convenience, these example-specific notes direct students to the page(s) where they can practice and review the skills needed to understand the new concept, thus decreasing students'' frustration and increasing their success. Prepare for the Next Section Exercises, found at the end of the exercise sets, have been carefully selected to review the prerequisite skills students will need in the next section. Next to each exercise is a reference to a section of the text where students can go to review topics they don''t understand. Answers to all of these exercises are provided in the Answer Appendix to help students better understand what they need to do to prepare for the next section. Interactive reading and study support is provided through careful placement of a Question/Answer feature throughout the exposition of the text so that students can check their understanding of concepts, think more critically about the mathematics, and more actively engage in learning mathematics. To support students studying independently, the Answer to each question is conveniently provided as a footnote on the same page as the question. To create a link between the algebraic and visual representations of a solution, increase students'' understanding of the concept presented, and accommodate different learning styles, the authors have provided both an algebraic solution and a graphical solution (represented by either a coordinate grid graph or a graphing calculator screen) for appropriate examples. Focus on Problem Solving at the beginning of every chapter reviews and demonstrates various strategies used by successful problem-solvers. Students become more comfortable with problem-solving and have a collection of tips and strategies to refer t

Today Lie group theoretical approach to differential equations has been extended to new situations and has become applicable to the majority of equations that frequently occur in applied sciences. Newly developed theoretical and computational methods are awaiting application. Students and applied scientists are expected to understand these methods. Volume 3 and the accompanying software allow readers to extend their knowledge of computational algebra. Written by the world's leading experts in the field, this up-to-date sourcebook covers topics such as Lie-Backlund, conditional and non-classical symmetries, approximate symmetry groups for equations with a small parameter, group analysis of differential equations with distributions, integro-differential equations, recursions, and symbolic software packages. The text provides an ideal introduction to modern group analysis and addresses issues to both beginners and experienced researchers in the application of Lie group methods.

Este libro pretende ser una iniciación accesible al estudio de las Variedades Diferenciables. El texto está diseñado para atender a los alumnos de una asignatura determinada: el contenido troncal de Geomatria Diferencial de Variedades del segundo ciclo de los planes de estudios de Ciencias Matematicas.

El concepto de anillo de multiplicación nos permite estudiar bajo el mismo prisma dominios Dedekind, anillos primarios especiales y anillos regulares von Neumann. La obra no sólo recoge y organiza el material existente sino que cuenta con aportaciones originales de los autores publicadas en distintos articulos de investigacion o hasta entonces ineditas. En el trabajo se muestra que los resultados e ideas se pueden aplicar a campos tan diversos como algebra conmutativa, geometria algebraica, teoria de categorias, teoria de anillos, topologias de Gabriel, etc.

I. Resumen teórico: Espacios vectoriales. Matrices. Determinantes. Sistemas de ecuaciones lineales. Aplicaciones lineales. Espacio vectorial euclídeo. Diagonalización de endomorfismos y matrices. Formas cuadraticas. Conicas y cuadraticas. II. Problemas: Espacios vectoriales. Matrices. Determinantes. Sistemas de ecuaciones lineales. Aplicaciones lineales. Espacio vectorial euclideo. Diagonalizacion de endomorfismos y matrices. Formas cuadraticas. Conicas y cuadraticas. III. Bibliografia.