- Tapa blanda: 180 páginas
- Editor: American Mathematical Society; Edición: illustrated Edition (12 de octubre de 2006)
- Colección: Student Mathematical Library
- Idioma: Inglés
- ISBN-10: 0821838172
- ISBN-13: 978-0821838174
- Valoración media de los clientes: Sé el primero en opinar sobre este producto
- Clasificación en los más vendidos de Amazon: nº348.785 en Libros en idiomas extranjeros (Ver el Top 100 en Libros en idiomas extranjeros)
- Ver el Índice completo
Galois Theory for Beginners: A Historical Perspective (Student Mathematical Library) (Inglés) Tapa blanda – 12 oct 2006
|Nuevo desde||Usado desde|
Los clientes que compraron este producto también compraron
Descripción del producto
Reseña del editor
Galois theory is the culmination of a centuries-long search for a solution to the classical problem of solving algebraic equations by radicals. In this book, Bewersdorff follows the historical development of the theory, emphasizing concrete examples along the way. As a result, many mathematical abstractions are now seen as the natural consequence of particular investigations. Few prerequisites are needed beyond general college mathematics, since the necessary ideas and properties of groups and fields are provided as needed. Results in Galois theory are formulated first in a concrete, elementary way, then in the modern form. Each chapter begins with a simple question that gives the reader an idea of the nature and difficulty of what lies ahead. The applications of the theory to geometric constructions, including the ancient problems of squaring the circle, duplicating the cube, and trisecting an angle, and the construction of regular $n$-gons are also presented. This book is suitable for undergraduates and beginning graduate students.
No es necesario ningún dispositivo Kindle. Descárgate una de las apps de Kindle gratuitas para comenzar a leer libros Kindle en tu smartphone, tablet u ordenador.
Obtén la app gratuita:
Detalles del producto
Si eres el vendedor de este producto, ¿te gustaría sugerir ciertos cambios a través del servicio de atención al vendedor?
Opiniones de clientes
|5 estrellas (0%)|
|4 estrellas (0%)|
|3 estrellas (0%)|
|2 estrellas (0%)|
|1 estrella (0%)|
Opiniones de clientes más útiles en Amazon.com
This book on Galois theory is of the latter class, because of its emphasis on historical motivation and the many concrete examples given between its covers. The author has done a fine job of relating to the reader just how Galois theory arose and why its form as Galois discovered it, is very different than what one will find in modern books on the subject. Galois definitely was a "modern" mathematician in the sense that he emphasized studying mathematical objects according to the transformations they can support. This paradigm dominates contemporary pure mathematics, leaving applied mathematicians the worry of how to extract reality and numbers from highly esoteric constructions and theories.
As the author explains brilliantly and originally, it was the desire to find solutions of higher degree polynomials in terms of radicals that motivated Abel and Galois to investigate to what extent this is possible. But before reading this book most readers will already have known this reason for Galois theory. What the author brings to the book is an appreciation of the efforts and failures in finding a general formula for the solution of the quintic equation, either by analogs of completing the square or by using certain transformations that simplified the equation. Readers will also learn of the resistance to negative numbers and complex numbers when they were first proposed, and how ruler and compass constructions can be expressed in terms of purely algebraic manipulations.
It is amazing to read also that Galois' ideas were not accepted right away, taking a couple of decades before they were appreciated and only because a certain mathematician advocated them and eventually got them into print. By modern standards Galois would be labeled as an amateur, but given the impact of his ideas, he finds himself immortalized, and modern algebra would probably not have the form it does without him.
Galois theory is presented only towards the end of the book. Readers already familiar with the solutions of quadratic equations, depressed cubics, cubics, and quartics will find the first half of the book somewhat redundant. But it is nevertheless very pleasant to read, with succinct notes on the historical background, and (mostly) self-contained short sections.
It reads very well all the way to the end. It gets a little harder when Galois theory is introduced. But that's perhaps to be expected. I can't say that I master the subject, but certain things (about polynomial equations) are a great deal clearer for me now.
I do have one reservation (but I did not knock off a star for that): the editing (of this English translation of the German original) is quite poor: there is a typo just about every other page. I am very sensitive to typos, and most readers probably won't (nor should they) care -- but there are some typos in the math here and there, and that's plain unacceptable.