Algebra I: Chapters 1-3 by N. Bourbaki (PDF)

Description

This softcover reprint of the 1974 English translation of the first three chapters of Bourbaki’s Algebre gives a thorough exposition of the fundamentals of general, linear, and multilinear algebra. The first chapter introduces the basic objects, such as groups and rings. The second chapter studies the properties of modules and linear maps, and the third chapter discusses algebras, especially tensor algebras.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐After Cauchy, Fourier, Galois, French Math dominance in 17th & 18th centuries had been overtaken in 19th century by their defeated (by Napolean) enemy: Germany, which produced the “Prince of Math” Gauss and his bright students and great Gottingen successors (Riemann, Dedekind, Cantor, Kronecker, Wierestrass, Hilbert, Felix Klein, Lindermann, etc).Before World War I, a group of Ecole Normale Superieure students (ENS which,like Ecole Polytechniques, expelled the Math genius Evariste Galois) , headed by Andre Wales, realised that French Math Textbooks were outdated and decided to form a Math Study Group nicknamed “Bourbaki” consisted of a few bright ENS classmates, met regularly in the Cafe near Jardin de Luxembourg in Paris, with the intention to rewrite the entire Mathematics based on the new SET Theory by Cantor, and followed the example of the Greek Euclid’s 13-volume “Elements of Geometry”, called their huge volumes “Elements of Mathematics” (Les Elements de Mathematiques). {Ref: “The artist and the mathematician : the story of Nicolas Bourbaki, the genius mathematician who never existed” by Amir D. Aczel}The Bourbaki books are the “Bible” of New Math, still relevant today for the following reasons:1. As Abel had said of the secret of his Math genius, heeded by his younger successor Galois: “Read Directly from the Master’s works”.2. In the first 16 years of Fields Medal (given every 4 years), 3 out of 4 winners were from Bourbaki Masters.3. The best book written on SET THEROY is still from Bourbaki.I strongly recommend any reputable world-class Reference Library to stock up on the entire series of Bourbaki. The English translation is as good as the French original, if not better, thanks to the additional english explanatory notes by the translators, not available in French version.

⭐I am convinced that this is just the best mathematical book ever written. I know that Bourbaki face criticism these days (where are categories? where are algorithms?), but I noticed a pattern: all of the successful mathematicians I know have read Bourbaki. Even those who criticize it today have read it. Unfortunately, many years ago I was criticizing Bourbaki myself, being affected by the authority of critics, although I didn’t put much effort on understanding Bourbaki’s work. I actually criticized them without reading them first. Shame on me, but this is what most people did then and what most people do now. I am afraid that that the fact the I didn’t read them before have affected my own mathematical education in a very negative way.Of course, all of the fancy moderns explanations of concepts covered in Bourbaki is neat, but for the student they don’t provide a good picture of what’s going on. Even though I see modern treatment of algebra is beneficial, I deeply believe that every single student has to go though building these abstract concepts from scratch. There’s an essay which explains why this way of educating is better, it is called “Don’t dissect a frog: build it”. Bourbaki is the only book which does exactly that and does it very good. And this book is still modern (and in some places more modern than currently publishing books).

⭐Bourbaki understood a great deal of maths. You could say surely no one single person could have done this. You’d be right. The team that is Bourbaki has made a contribution that will live as long as Euclid’s Elements.

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