Libros de Álgebra, página 19 de 28

Durante los días 25, 26 y 27 de junio de 1993 tuvo lugar un acontecimiento realmente extraordinario: una ecuación matemática conseguía colarse en la primera página de los principales diarios: xn + yn = zn Justo la misma ecuacion que habia obsesionado sin descanso, durante casi cuatrocientos años, a algunos de los matematicos mas grandes de todos los tiempos: Euler, Gauss, Dirichlet, Kummer o Serre, empeñados en resolver, infructuosamente, el enigma planteado por un aficionado frances, Pierre de Fermat, un magistrado de provincias que habia lanzado su desafio despues de muerto desde el estrecho margen de un viejo libro de aritmetica. El reto de Fermat es una invitacion a compartir esa frenetica aventura, cargada de ingenio, rivalidades, momentos de inspiracion y tambien de amargas decepciones, en la que Fermat consiguio arrastrar a cientos de personas, incluyendo a algunos de los genios de la historia de las matematicas, y que no llego a su fin hasta 1994, cuando Andrew Wiles anuncio que habia resuelto definitivamente el problema. El que fuera durante siglos el enigma sin resolver mas famoso de la historia de las matematicas mantiene hoy en dia todo su atractivo, despues de afectar de manera profunda a practicamente todas las ramas de esta ciencia, un camino que ahora puede volver a recorrer cualquier persona interesada en las matematicas o que simplemente disfrute con los desafios al ingenio.

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.

En este libro –nos dice el autor en su prólogo- se parte de unas ideas sencillas de lógicay conjuntos que formalizan, hasta donde es posible en un nivel elemental, el lenguajeque se usará a todo lo l

Este VOLUMEN 1 contiene 2 capítulos: I. Sistemas de ecuaciones lineales y matrices II. Espacios vectoriales y aplicaciones lineales Este es el primer volumen de un curso de Álgebra Lineal dividido en dos, que totalizan cuatro capítulos y 20 lecciones. En conjunto, se cubre todo lo que a veces se denomina geometría vectorial, y se corresponde con los temarios de la materia que con motivo de los nuevos planes de estudios se han implantado en las Facultades de Ciencias, en particular Físicas y Matemáticas, en la Facultad de Informática y en la Escuelas Técnicas. Basados en nuestra experiencia, tras haber impartido cursos similares durante muchísimos años hemos pretendido escribir un texto muy directo, despojándolo de todos los formalismos evitables sin menoscabar el rigor ni en los enunciados ni en las pruebas de los mismos. En todo caso, nuestro objetivo esencial es explicar el significado verdadero de las cosas. Este curso se completa con el VOLUMEN 2 que también se compone de 2 capítulos: III. Clasificación de endomorfismos IV. Formas bilineales y formas cuadráticas (…) Como pauta general, los ejemplos son muy numerosos y parte central de la exposición. Además, cada lección concluye con una colección de 15 problemas y ejercicios de dificultad variable. Al final de cada capítulo hay una sección con 50 cuestiones verdadero/falso con las que el lector podrá contrastar cómo ha asimilado los conceptos estudiados. Se incluyen en un apéndice las soluciones de todos los ejercicios, problemas y cuestiones propuestos en él. También hemos incluido una lista de símbolos que suele ser de ayuda para encontrar con rapidez el significado de una notación, y un índice terminológico, para la búsqueda correspondiente. Hay además una lista breve de lecturas recomendadas.(...)

From the reviews:"The author has attempted an ambitious and most commendable project. He assumes only a modest knowledge of algebraic topology on the part of the reader to start with, and he leads the reader systematically to the point at which he can begin to tackle problems in the current areas of research centered around generalized homology theories and their applications...The author has sought to make his treatment complete and he has succeeded. The book contains much material that has not previously appeared in this format. (...)

This is an English translation of the now classic "Algebre Locale - Multiplicites" originally published by Springer as LNM 11, in several editions since 1965. It gives a short account of the main theorems of commutative algebra, with emphasis on modules, homological methods and intersection multiplicities ("Tor-formula"). Many modifications to the original French text have been made by the author for this English edition: they make the text easier to read, without changing its intended informal character.

The subject of this book is the solution of stiff differential equations and of differential-algebraic systems (differential equations with constraints). The book is divided into four chapters. The beginning of each chapter is of introductory nature, followed by practical applications, the discussion of numerical results, theoretical investigations on the order and accuracy, linear and nonlinear stability, convergence and asymptotic expansions. Stiff and differential-algebraic problems arise everywhere in scientific computations (e.g., in physics, chemistry, biology, control engineering, electrical network analysis, mechanical systems). Many applications as well as computer programs are presented.