Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory: 50 (Graduate Texts in Mathematics)

Description

This introduction to algebraic number theory via the famous problem of "Fermats Last Theorem" follows its historical development, beginning with the work of Fermat and ending with Kummers theory of "ideal" factorization. The more elementary topics, such as Eulers proof of the impossibilty of x+y=z, are treated in an uncomplicated way, and new concepts and techniques are introduced only after having been motivated by specific problems. The book also covers in detail the application of Kummers theory to quadratic integers and relates this to Gauss'theory of binary quadratic forms, an interesting and important connection that is not explored in any other book. Review: good for insights into mathematics and its nature - This is a good book to read about mathematics. All of us have witnessed, at least the ones who have strong interests in math, how often mathematics amounts to little more than gamesmanship, and often trivial at that. Fermat's Last Theorem in this respect is a good case study, because the work on the theorem started out as little more than the typical game-playing, and it gradually grew beyond that to connect up with the great river of mathematics, right at its heart. Prof. Edwards discussion gives one an opportunity to trace this curious evolution and to gain some insights into mathematics and how, from humble beginnings, a mathematics problem that piques the interest of people can grow into something of perennial interest. I'm only about 1/3 of the way through the book, but have found it to be fascinating reading. Review: Unconvincing experience - The book had a bad smell, and after returning it to the seller, it took three weeks to receive the refund