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Galois Theory
Ian Stewart's Galois Theory has been in print for 30 years. Resoundingly popular, it still serves its purpose exceedingly well. Yet mathematics education has changed considerably since 1973, when theory took precedence over examples, and the time has come to bring this presentation in line with more modern approaches.
To this end, the story now begins with polynomials over the complex numbers, and the central quest is to understand when such polynomials have solutions that can be expressed by radicals. Reorganization of the material places the concrete before the abstract, thus motivating the general theory, but the substance of the book remains the same.
To this end, the story now begins with polynomials over the complex numbers, and the central quest is to understand when such polynomials have solutions that can be expressed by radicals. Reorganization of the material places the concrete before the abstract, thus motivating the general theory, but the substance of the book remains the same.
328 pages, Paperback
First published October 19, 1989
17 people are currently reading
375 people want to read
About the author
Ian Stewart
269 books758 followersIan Nicholas Stewart is an Emeritus Professor and Digital Media Fellow in the Mathematics Department at Warwick University, with special responsibility for public awareness of mathematics and science. He is best known for his popular science writing on mathematical themes.
--from the author's website
Librarian Note: There is more than one author in the GoodReads database with this name. See other authors with similar names.
--from the author's website
Librarian Note: There is more than one author in the GoodReads database with this name. See other authors with similar names.
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Displaying 1 - 5 of 5 reviews
July 22, 2009
One of the great romantic stories of mathematics. For non-mathematicians, here's a brief summary.
You probably recall learning how to solve quadratic equations, and with the right prompting can still perhaps mumble minus-b-plus-or-minus-square-root-of-b-squared-minus-four-a-c-all-over-two-a. It's a little harder, but you can also solve cubic (third degree) and quartic (fourth degree) equations in a similar way. But although people tried for hundreds of years, no one could figure out how to do the same thing with equations of fifth degree or higher.
Finally, in 1832, 20 year old Évariste Galois figured out why it was actually impossible, shortly before he had to fight a duel in which he knew his chances of survival were negligible. He spent all night writing down the proof, interspersing the mathematics with frantic comments of "I have no time!" and was duly killed the next day. His work was decades ahead of his contemporaries, and it was ages before anyone recognized its importance.
Or at least, that's the legend every mathematician imbibes together with his mother's milk. I just looked him up on Wikipedia, and was shocked to discover how many factual errors there were. The one which surprised me most: the Norwegian mathematician Abel had already proved the insolubility of quintics by radicals a few years earlier. How could I not have known that!? Also, he had submitted a part of the theory for publication earlier in the year, and had it rejected. I know from my own experience that this is what usually happens the first time you try to publish anything that contains new ideas.
But, even if the story has been improved a bit, Galois theory is amazingly beautiful and elegant, and this book does a good job of explaining it. You don't need a huge amount of math - it was one of the first serious algebra books I read, while I was still at high school, and got me started on the whole subject.
______________________________________
A postscript that mathematicians may find interesting. There's a section about Abel in Erobreren, the Norwegian novel I'm currently reading. The way Kjærstad tells it, Norwegians are well aware that Abel was first, and consider that the treatment he received from the French Academy of Sciences was absolutely disgraceful. Kjærstad is particularly vitriolic about Cauchy, whom he considers to have been the main culprit.
Remarkably, Abel also died young, in tragic circumstances, and it was years before people acknowledged his genius. The more I hear about this, the more surprised I become that I hadn't discovered the Abel story years ago!
______________________________________
Would you believe it, there's a Galois theory joke in La Disparition. It's based on the fact that people in the novel who discover the secret of their world are immediately killed by it, Galois's tragic end, and the choice of letter often used to represent the identity element in a group. But no more spoilers!
You probably recall learning how to solve quadratic equations, and with the right prompting can still perhaps mumble minus-b-plus-or-minus-square-root-of-b-squared-minus-four-a-c-all-over-two-a. It's a little harder, but you can also solve cubic (third degree) and quartic (fourth degree) equations in a similar way. But although people tried for hundreds of years, no one could figure out how to do the same thing with equations of fifth degree or higher.
Finally, in 1832, 20 year old Évariste Galois figured out why it was actually impossible, shortly before he had to fight a duel in which he knew his chances of survival were negligible. He spent all night writing down the proof, interspersing the mathematics with frantic comments of "I have no time!" and was duly killed the next day. His work was decades ahead of his contemporaries, and it was ages before anyone recognized its importance.
Or at least, that's the legend every mathematician imbibes together with his mother's milk. I just looked him up on Wikipedia, and was shocked to discover how many factual errors there were. The one which surprised me most: the Norwegian mathematician Abel had already proved the insolubility of quintics by radicals a few years earlier. How could I not have known that!? Also, he had submitted a part of the theory for publication earlier in the year, and had it rejected. I know from my own experience that this is what usually happens the first time you try to publish anything that contains new ideas.
But, even if the story has been improved a bit, Galois theory is amazingly beautiful and elegant, and this book does a good job of explaining it. You don't need a huge amount of math - it was one of the first serious algebra books I read, while I was still at high school, and got me started on the whole subject.
______________________________________
A postscript that mathematicians may find interesting. There's a section about Abel in Erobreren, the Norwegian novel I'm currently reading. The way Kjærstad tells it, Norwegians are well aware that Abel was first, and consider that the treatment he received from the French Academy of Sciences was absolutely disgraceful. Kjærstad is particularly vitriolic about Cauchy, whom he considers to have been the main culprit.
Remarkably, Abel also died young, in tragic circumstances, and it was years before people acknowledged his genius. The more I hear about this, the more surprised I become that I hadn't discovered the Abel story years ago!
______________________________________
Would you believe it, there's a Galois theory joke in La Disparition. It's based on the fact that people in the novel who discover the secret of their world are immediately killed by it, Galois's tragic end, and the choice of letter often used to represent the identity element in a group. But no more spoilers!
August 22, 2007
Spare a thought for poor Evariste Galois, the French genius who jotted down the outline for a whole branch of mathematics (which is still bearing fruit almost 200 years after his death) in a single night before being killed the next morning in a duel over a prostitute. He was twenty years old.
Galois theory is so elegant and far-reaching, it packs an emotional wallop. (If you like that kind of thing, that is, which I do)
Galois theory is so elegant and far-reaching, it packs an emotional wallop. (If you like that kind of thing, that is, which I do)
September 2, 2023
Awesome introductory book with the proper historical context of the development of Galois theory. Gives a good foundation to move towards more abstract algebra and category theory.
Want to read
April 20, 2022Abstract algebra
January 11, 2023
Interesting book, explores the 400 year long history of galois theory and extrapolates the ideas present.
Displaying 1 - 5 of 5 reviews