Comments on: The Stylings of Nicholas Bourbaki http://www.arsmathematica.net/archives/2006/12/20/bourbaki-in-not-even-wrong-comments/ Dedicated to the mathematical arts. Tue, 02 Dec 2008 02:45:38 +0000 http://wordpress.org/?v=2.5.1 By: Walt http://www.arsmathematica.net/archives/2006/12/20/bourbaki-in-not-even-wrong-comments/#comment-1518 Walt Sat, 23 Dec 2006 06:16:11 +0000 http://www.arsmathematica.net/archives/2006/12/21/bourbaki-in-not-even-wrong-comments/#comment-1518 I think the example of so(3) may be the first time Lie algebras seemed interesting. When I studied vector calculus, I hated the cross product, just because it so obviously did not generalize to higher dimensions. I liked the so(3) explanation, since it obviously did generalize. Bourbaki earned the superfluous 'h' two days ago. (In all these years, I never noticed that it was spelled without the 'h'.) Eisenbud is a terrific book, if you are interested in commutative algebra. (If you're not intrinsically interested in the subject, then I'm not sure the book is so great that it will change your mind.) I think the example of so(3) may be the first time Lie algebras seemed interesting. When I studied vector calculus, I hated the cross product, just because it so obviously did not generalize to higher dimensions. I liked the so(3) explanation, since it obviously did generalize.

Bourbaki earned the superfluous ‘h’ two days ago. (In all these years, I never noticed that it was spelled without the ‘h’.)

Eisenbud is a terrific book, if you are interested in commutative algebra. (If you’re not intrinsically interested in the subject, then I’m not sure the book is so great that it will change your mind.)

]]> By: ComplexZeta http://www.arsmathematica.net/archives/2006/12/20/bourbaki-in-not-even-wrong-comments/#comment-1517 ComplexZeta Fri, 22 Dec 2006 18:22:06 +0000 http://www.arsmathematica.net/archives/2006/12/21/bourbaki-in-not-even-wrong-comments/#comment-1517 Am I to take this as a recommendation for Eisenbud? Am I to take this as a recommendation for Eisenbud?

]]> By: John C. Baez http://www.arsmathematica.net/archives/2006/12/20/bourbaki-in-not-even-wrong-comments/#comment-1516 John C. Baez Fri, 22 Dec 2006 05:51:53 +0000 http://www.arsmathematica.net/archives/2006/12/21/bourbaki-in-not-even-wrong-comments/#comment-1516 Since when is his name spelled 'Nicholas'? Since when is his name spelled ‘Nicholas’?

]]> By: Alexandre Borovik http://www.arsmathematica.net/archives/2006/12/20/bourbaki-in-not-even-wrong-comments/#comment-1515 Alexandre Borovik Thu, 21 Dec 2006 22:44:30 +0000 http://www.arsmathematica.net/archives/2006/12/21/bourbaki-in-not-even-wrong-comments/#comment-1515 "The first time I saw the definition of Lie algebra, my reaction was “Huh?” " It is one of the principal blind spots of undergraduate mathematics - the cross product of vectors in 3-dimensional Euclidean space is occasionally mentioned, but I had not seen an undergraduate textbook which would discuss a fundamental fact: the cross product is the Lie multiplication in the Lie algebra of the group SO(3) of rotations of 3-dimensional Euclidean space. We live inside of a Lie algebra. “The first time I saw the definition of Lie algebra, my reaction was “Huh?” ”

It is one of the principal blind spots of undergraduate mathematics - the cross product of vectors in 3-dimensional Euclidean space is occasionally mentioned, but I had not seen an undergraduate textbook which would discuss a fundamental fact: the cross product is the Lie multiplication in the Lie algebra of the group SO(3) of rotations of 3-dimensional Euclidean space. We live inside of a Lie algebra.

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