Libros de Álgebra, página 18 de 28

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.

Homological algebra first arose as a language for describing topological prospects of geometrical objects. As with every successful language it quickly expanded its coverage and semantics, and its contemporary applications are many and diverse. This modern approach to homological algebra, by two leading writers in the field, is based on the systematic use of the language and ideas of derived categories and derived functors. Relations with standard cohomology theory (sheaf cohomology, spectral sequences, etc. ) are described. In most cases complete proofs are given. Basic concepts and results of homotopical algebra are also presented. The book addresses people who want to learn a modern approach to homological algebra and to use it in their work. For the second edition the authors have made numerous corrections.

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

Los ejemplos concretos anteceden a la abstracción con el propósito de facilitar al alumno la comprensión y la adquisición de los conocimientos adaptándose un enfoque basado en vectores en el cual las matrices juegan un papel importante de apoyo. Gracias a la experiencia docente de mas de veinte años de su autor, este libro no solo es facil de entender, sino tambien genera en el alumno un gusto por aprender. Tiene la virtud de contagiar y fomentar en el estudiante la pasion por el algebra lineal. Aqui se le presenta como un punto de entrada a las matematicas que nos conduce y tiene vinculos con muchas ramas de las mismas, incluyendo algebra abstracta, matematicas discretas, calculo, ecuaciones diferenciales, geometria, estadistica, metodos numericos, investigacion de operaciones y sistemas dinamicos.

José; Fernández Bermejo, María Josefa Pérez Blanco

From its history as an elegant but abstract area of mathematics, algebraic number theory now takes its place as a useful and accessible study with important real-world practicality. Unique among algebraic number theory texts, this important work offers a wealth of applications to cryptography, including factoring, primality-testing, and public-key cryptosystems. A follow-up to Dr. Mollin''s popular Fundamental Number Theory with Applications, Algebraic Number Theory provides a global approach to the subject that selectively avoids local theory. Instead, it carefully leads the student through each topic from the level of the algebraic integer, to the arithmetic of number fields, to ideal theory, and closes with reciprocity laws. In each chapter the author includes a section on a cryptographic application of the ideas presented, effectively demonstrating the pragmatic side of theory. In this way Algebraic Number Theory provides a comprehensible yet thorough treatment of the material. Written for upper-level undergraduate and graduate courses in algebraic number theory, this one-of-a-kind text brings the subject matter to life with historical background and real-world practicality. It easily serves as the basis for a range of courses, from bare-bones algebraic number theory, to a course rich with cryptography applications, to a course using the basic theory to prove Fermat''s Last Theorem for regular primes. Its offering of over 430 exercises with odd-numbered solutions provided in the back of the book and, even-numbered solutions available a separate manual makes this the ideal text for both students and instructors.