Galois Theory: Lectures Delivered at the University of Notre Dame by Emil Artin (Notre Dame Mathematical Lectures, Number 2) (Dover Books on Mathematics)

Evariste Galois was the Beethoven of mathematics because he was able to "see" mathematical ideas with his entire being. This volume delves deeply into his mathematics but it is presented in a way accessible to anyone willing to put in a little effort. The primary role of Galois theory in the proof of Tanyama-Shimura conjecture and, by implication, the proof of Fermat's Last Theorem speaks volumes about this mathematician's genius. This book is well worth the effort and acts as a springboard to other cutting edge mathematics like Elliptic Curves, Modular Forms, Langlands Program, and eventually Riemann Hypothesis. Galois had a passion for mathematics that reflected the Romanticism of the early nineteenth century. Definitely give this book the old college try.

This was a fun and interesting read

This is a cute little book that guides the reader into Galois theory starting all the way from the review of linear algebra and polynomial rings over fields and progressing all the way to the Fundamental theorem. There are moreover many nice sections on Finite fields, Noether equations, Kummer extensions and as a final chapter the application to solvability by radicals of a general polynomial and the ruler and compass constructions. So the book is pretty self-contained and contains lots of good stuff. Also, Artin has a knack of giving very down-to-earth proofs that could be characterized as computational (rather than conceptual). It depends on everyone's preference whether they like this approach but for me it was very refreshing change of pace (compared to abstract and ofter almost magical proofs e.g. from commutative algebra). In any case, patient reader will walk away from this book with a feeling of having built the subject from the ground up. Nevertheless, I can't give it 5 stars because the book is very lacking in exercises. There are some applications scattered here and there (e.g. on symmetric extensions of function fields and on symmetric functions) but this is hopelessly insufficient to solidify the knowledge gained from the theorems. To properly understand Galois theory one needs to get their hands dirty by investigating splitting fields and Galois groups of all kinds of polynomials and paying close attention to the interaction of roots and group actions. In this regard the book leaves the reader completely on their own and so should be complemented by some additional source of exercices.

Es una reimpresión de una vieja edición del libro. Vale la pena por el precio.

Not helpful to almost anyone who hasn’t already learned Galois theory. As the abstract algebra prereqs for the work would almost only be guilted in the context of a course or text that ended with coverage of Galois theory. Nor is the text focused on broad ideas or intuition. However. If you have seen Galois theory and would like to look at another take on it (as is valuable for subjects in general) then this is a reasonably concise text that one may find interesting.

Any student (graduate or undergraduate) who is learning Galois theory will benefit greatly from reading this book. Artin has a very elegant style of writing and many parts of the book read like a novel. At its current price, there's no reason to not buy this book; you may actually want to buy a few extra copies as they make great gifts and/or stocking stuffers. I would also recommend Artin's Geometric Algebra.

great book but the kindle version is packed full of typos and misprints. get the latest dover edition and you're all set.

Self-instruction. Not for everyone. Replaces an older book in my library.

Marbelous! a masterpiece!

Da neofita ho letto diverse presentazioni della teoria di Galois, ma nessuna ha la stessa chiarezza, oltre che compattezza della trattazione di Emil Artin. Credo che l'esposizione presentata in questo breve testo sia diventata la presentazione standard de facto della teoria di Galois nell'algebra del XX secolo. Come spesso accade la fonte risulta spesso più chiara delle riproposizioni successive. Il difetto che si riscontra in tanti altri testi successivi -incluso quello di Michael Artin, figlio di Emil- è la presenza di riferimenti ad altri risultati e proposizioni, mentre questo testo è pressoché autocontenuto. Un altro difetto che spesso si riscontra è non chiarire bene la natura degli enti matematici che sono oggetto delle proposizioni: capita spesso nell'algebra di partire da un campo F per definire un altro campo su altri enti, per esempio sull'insieme degli omomorfismi da F ad un altro campo F'. E' la potenza (e la croce) dell'algebra, ma l'importante è che chi espone chiarisca al lettore il salto concettuale che sta compiendo senza dare nulla per scontato. Emile Artin si preoccupa di farlo. L'unico neo è la mancanza di esempi o esercizi.

Ce livre d'un mathématicien reconnu a le mérite de présenter l'essentiel de la théorie de Galois d'une manière claire,abrégée et simple.Il s'adresse toutefois à un lecteur qui a déjà des notions de mathématiques (bac et bac+1).Dommage qu'il soit écrit en anglais et non en français.

The book is more like a compilation of definitions and theorem. The concepts are not explained. Quality of paper is pathetic. Printing quality is equally bad so much so that the number '0' is not distinguishable from the letter 'o'.

Great book, very easy to understand and gets straight to the point