This is a softcover reprint of chapters four through seven of the 1990 English translation of the revised and expanded version of Bourbaki’s Algebre. Much material was added or revised for this edition, which thoroughly establishes the theories of commutative fields and modules over a principal ideal domain.
--This text refers to the
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5.0 out of 5 stars
The BEST of The BEST New Math Bible,
By Wu Bing "Cornelius" (Singapore) - See all my reviews
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This review is from: Algebra II: Chapters 4-7 (Elements of Mathematics) (Chapters 4-7 Pt. 2) (Paperback)
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expelled the Math genius Evariste Galois) , headed by Andre Weil, realised that French Math Textbooks were outdated and decided to form a Math Study Group nicknamed "Bourbaki" consisted of a few bright ENS classmates, met regularly in the Cafe near Jardin de Luxembourg in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 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.
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First Sentence:
Let I be a set. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
setwise coprime, relative separable closure, symmetric rational fractions, relative algebraic closure, ordered field structure, etale algebra, abelian closure, separating transcendence basis, composite extensions, separable algebraic extension, commutative monoid structure, polynomial law, group annihilated, coprime elements, exceptional extension, algebraically closed extension, infinite integral domain, separable algebraic closure, principal ideal domain, pure transcendental extension, finite transcendence degree, convex subgroup, ordered extension, unital homomorphism, principal fractional ideals Key Phrases - Capitalized Phrases (CAPs): (learn more)
Set Theory, Historical Note, Mac Lane, Substitutions Let New!
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Front Cover | First Pages | Index | Back Cover | Surprise Me!
Let I be a set. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
setwise coprime, relative separable closure, symmetric rational fractions, relative algebraic closure, ordered field structure, etale algebra, abelian closure, separating transcendence basis, composite extensions, separable algebraic extension, commutative monoid structure, polynomial law, group annihilated, coprime elements, exceptional extension, algebraically closed extension, infinite integral domain, separable algebraic closure, principal ideal domain, pure transcendental extension, finite transcendence degree, convex subgroup, ordered extension, unital homomorphism, principal fractional ideals Key Phrases - Capitalized Phrases (CAPs): (learn more)
Set Theory, Historical Note, Mac Lane, Substitutions Let New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 4
books:
- History of Hindu Mathematics ( two Vol. set) by Bibhutibhushan Datta in Back Matter
- Gesammelte Abhandlungen. Erster Band: Zahlentheorie (AMS Chelsea Publishing) by David Hilbert on page 123
- The Collected Mathematical Papers of Henry John Stephen Smith (AMS Chelsea Publishing) by J. W. L. Glaisher in Back Matter
- Opera Omnia by Girolamo Cardano on page 303
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