Product Description

This is a softcover reprint of the English translation of 1968 of N. Bourbaki's, ThTorie des Ensembles (XXXXX).

Customer Reviews (4)

A Comparison
It seems like theres enough information here (and elsewhere) about the Bourbaki series in general so I wont comment on that. This review is written for someone that wants to learn set theory and is written with an eye to the other options available.

The Bad:

1) No Comparisons - This book constructs one system of axioms for set theory. There is no comparison of this theory with other theories, nor is there any in depth analysis of the axioms and thier interrealtion. You would find this stuff in most other introductory set theory books, but not here.

2) Light Exposition - Set theory and mathematical logic are subjects where results are subtle, and you need to tease out these subtleties by constantly thinking about the theorems. This book, unlike other set theory books, doesnt point out these subtle things and so the burden is left to the reader. (It is a huge burden for the unintiated!)

3) Typographical Errors - There are a few typographical errors. Some of these are obvious, some are not; the ones that are not obvious are devastating, since a proof will become incomprehensible with a few misplaced symbols.

4) Proofs Are Condensed - The proofs offered are written very concisely. There is very little in the proof to help the reader follow along and as such you need to think a bit about what is going on.

The Good:

1) Great System - The particular system of axioms used is rather standard so it wont be unfamiliar. What is especially great is that they go so in depth with the background logic; they actually use part of the logical system and the axioms of set theory to prove the axiom of choice.

2) Rigour - The book is incredibly rigorous. Everything is done with great precision without being long winded.

3) Generality - Theorems are proved in the most general form possible. This is incredibly good if you are interested in using the theorems in many other branches of mathematics. Its also interesting to see exactly how general theorems can get.

4) Structures - This book, unlike other set theory books, focuses heavily on creating mathematical structures from set theoretical objects. If you plan to persue model theory then this is a godsend.

I would not recommend this book to someone who has not already had an aquiantance with axiomatic set theory. I would not recommend this book to anyone that likes to solve mathematical problems: the focus here is on theory and not problem solving. Finally i would not recommend this book to anyone that has even the slightest trouble following rigorous mathematical proofs.

This is a unique book that should be read by good mathematicians after an introduction to set theory; especially if they plan to persue model theory or (obviously) the rest of the Bourbaki series.

Reading Axiomatic Set Theory before this book is more than adequate. Reading Set Theory and Its Philosophy: A Critical Introduction before or afterwards will make up for the shortcomings of this book.

A Wonderful Book
Today, I have just finished reading the first chapter of this amazing book, and I am definitely looking forward to see the rest of it.

Elements of Mathematics. Theory of Sets
I am neither qualified nor competent to rate any work of "Nicolas Bourbaki"; I will "borrow" from "Wikipedia"about "Nicolas Bourbaki" the following information:
"Nicolas Bourbaki is the collective pseudonym under which a group of mainly French 20th-century mathematicians wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. With the goal of founding all of mathematics on set theory, the group strove for utmost rigour and generality, creating some new terminology and concepts along the way.

While Nicolas Bourbaki is an invented personage, the Bourbaki group is officially known as the Association des collaborateurs de Nicolas Bourbaki ("association of collaborators of Nicolas Bourbaki"), which has an office at the cole Normale Suprieure in Paris."

Euclid in the XX century
Some historians of Mathematics believe that Euclid, in his great treatise (the Elements) joined together in a consistent way all known Mathematics of his time. Polishing the work of his predecessors, he made important contributions of his own. More than two thousand years later Bourbaki suceeded in making a similar thing with the Mathematics of his time. After the important contributions of the XIX century mathematicians in the foundations of Analysis and of the XX century in Logic, a new way of working with Mathematics emerged. Mathematics did not deal anymore just with numbers, or geometrical figures, or whatever, but with a general and abstract concept called Structure. Much of the development and spreading of this concept is due to the monumental treatise of Bourbaki - the treatise not incidentally is called the Elements of Mathematics. Rewriting all known Mathematics in a very peculiar way, and searching perfect and absolute rigour, Bourbaki perhaps reinvented Mathematics. And it is indisputable its influence in the basic trends of this area of human enterprise. For Bourbaki, the basis of Mathematics is Theory of Sets (including Mathematical Logic). Resting upon it we find Algebra and the Algebraic Structures. Above Algebra is Topology, where we finally meet real numbers. It is said that Bourbaki only wrote about subjects that he considered terminated in a certain way, giving it a final perfected form, but for myself I prefer to think that his intention was similar to Euclid: organize the knowledge. Theory of Sets is the first book of the treatise, that counts ten books to this date and provides the safe foundation on which the whole stuff rests. But it can - and probably must - be read independently of the mysticism involving the treatise, and in my opinion is the best book ever written on the subject, showing what it is all about. Today the Theory of Sets is evolving in unforeseen directions, and of course those directions are not present in Bourbaki's work (search for Thomas Jech's book Set Theory if you want to know what they are doing right now). But the real intention of the classical Theory of Sets, its real purpose and meaning, is no better explained - and I doubt that it can be better explained - than by Bourbaki. ... Read more

Product Description

This is the softcover reprint of the 1971 English translation of the first four chapters of Bourbaki’s Topologie Generale. It gives all basics of the subject, starting from definitions. Important classes of topological spaces are studied, and uniform structures are introduced and applied to topological groups. In addition, real numbers are constructed and their properties established.

Customer Reviews (2)

a solid introduction
this book is a bit denser than most other introductory general topology books. But it does quite exhaustive survey of important concepts pertaining to general topology.

Since Bourbaki series builds upon its previous materials, many set theoretic ideas and terminologies are used without explanations. So unless one does have access to their previous book "Theory of Sets" there will be some minor frustrations/annoyances when reading this book.

For the content, it starts with open set axioms for the topology like any other intro. topology text.
Then Bourbaki shows how the neighborhood system determines a unique topology on a set and conversely. Next topic covered is continuity and the initial and final topology induced by a family of mappings and defines subset, product, and quotient topology in terms of the these two natural constructions. After covering these topics Bourbaki covers quotient various quotient mapping and some useful criteria for determining when the map from quotient space to the codomain after the canonical decomposition of a map becomes homeomorphism.

Next topic covered is open and closed mapping along with equivalence relations being open or closed.

After discussing general continuity without any major restrictions on the topological spaces, Bourbaki then introduces typical restrictions; namely compactness, Hausdorff, and regular conditions.

Unlike many other major introductory topology books, Bourbaki does not talk about sequences nor nets in order to define compactness( quasi-compactness as Bourbaki calls it). Instead, he uses filters to define compactness. Using Zorn's lemma, existence of ultrafilter is shown and Tychnoff's theorem is proven using filter property in a very slick fashion.
Also, there is a short section on germs, although this is not used in the rest of this book in any significant ways.
Then, Bourbaki moves on to the topic of the limit and cluster(accumulation) point of a function of filtered space into a topological space and shows how the definition limit of a sequence or nets can be retrieved from a definition of limits of a function with respect to a filter.

After covering this necessary tool or terminology, Bourbaki then covers Hausdorff space and regular space. Extension of a continuous function of a dense subset into a regular space, by continuity is shown in a very slick fashion.After covering this he does the typical stuff associated with compactness, paracompactness, and connectedness. These three sections are very similar to other intro. topology text in its content but with terminology adjusted for use of filter in these concepts.

However, Bourbaki offers something you do not typically see in intro. topology text, in this section; proper mapping and inverse system.
Proper mapping is shown as an alternative criterion for determining compactness, and other use of proper mappings are illustrated.

Next section of this book is uniform space, which is a generalization of pseudo-metric spaces.
Here, Bourbaki shows how a notion of completeness can be generalized to the setting of uniform spaces and introduces notion of Cauchy filter.The major result of this section is the construction of Hausdorff completion of a uniform space. This construction is essentially same as the construction of real numbers from Cauchy sequences of rational numbers but Bourbaki maintains the vocabulary of Cauchy filter. Also, instead of working with equivalent classes of Cauchy filters(or sequences if you prefer), Bourbaki uses a system of representatives called minimal Cauchy filters.

Section 3 of this book, covers topological group. Using how a neighborhood systems determines a unique topology, he quickly determines criterion for existence of suitable topology such that this topology is compatible with the pre-existing algebraic structure; i.e. all the algebraic operations become continuous with this topology. Thus the completion stuff one might see in Lang's Algebra or in Atiyah's intro. commutative algebra will makes more sense after reading this section.
Then the usual stuff of completion of topological group, ring, field, module is shown using tools developed in previous two sections.Also, using inverse system he does a few approximation stuff, which one can skip without disrupting further reading.

Section 4 is the last section of this book, and Bourbaki finally talks about real number. Since he talked about completion of topological group, he defines real number as the Hausdorff completion of rational numbers considered as an additive topological group. After this consideration many results just fall out; such as rational line being dense in real, etc.

After this characterization supreme property of a bounded set of real number is proved using Archimedes' Axiom(which is proved also). Then the usual criterion of compactness and connectedness in real line is proved.Here the proof of these facts are not given in the standard way deriving contradiction using supreme property. So it is interesting to see how the previous materials are used to prove these well know facts.

Then monotone convergence of a function from directed set into a real number is discussed and its consequences are discussed;limsup, upper envelope of a family of continuous functions, etc. Also, upper and lower continuity is discussed and some familiar results are discussed in brief fashion.

Finally, Bourbaki talks about series of real number and standard facts such as Cauchy's convergence criterion, alternating series test, etc are given along with n-ary expansion of real numbers.

And this is where part 1 of this book ends.

My overall impression is that this book(just like other Bourbaki book) is very user friendly, in that it does each proof very carefully. However, due to its constant build of a long logical chains, you really cannot read this book like a typical textbook; meaning you cannot skip around and the entire book must be read in a linear fashion.

Also, the filter and uniform stuff is not typically covered in the introductory topology courses so to a novice this stuff might not be useful to your classwork(at least for the undergraduate or beginning graduate level). However, reading this book broadens your view on general topology for this book explains ideas behind the common concepts you encounter in other courses; such as use of filtration in a module to define a topology in an algebra course.

Anyway, it seems to me that the biggest disadvantage of reading Bourbaki is its inefficiency.Meaning, stuff you really wanna see is not discussed unless you read through first 200 or 300 pages of this wonderful book.And this is probably the main reason why Bourbaki is not used as a standard text anymore;not because categorical language is not used as some might argue. So to a student with not enough studying time, this book will not useful when it is needed.

the book that the experts study
i recently ordered "A GENERAL TOPOLOGY WORKBOOK" by Iain Adamson, as i very much wish to understand the mathematics of topology.as i would do with any other book, i started by reading the introduction and suggested readings.Mr. Adamson highly recommends the BOURBAKI series on topology as a reference material.he ascribes to this series as his text of choice and further states that this is the text that he has studied the most closely.it is for this reason that i am ordering this series.

i extend my thanks to mr. adamson for the recommendation.with the plethora of choices in study materials and a limited budget, i needed to narrow my scope and decide which text would best serve me.

thanks again:-) ... Read more

Product Description

This is the softcover reprint of the English translation of Bourbaki's text Groupes et Algèbres de Lie, Chapters 7 to 9. It completes the previously published translations of Chapters 1 to 3 (3-540-64242-0) and 4 to 6 (978-3-540-69171-6) by covering the structure and representation theory of semi-simple Lie algebras and compact Lie groups. Chapter 7 deals with Cartan subalgebras of Lie algebras, regular elements and conjugacy theorems. Chapter 8 begins with the structure of split semi-simple Lie algebras and their root systems. It goes on to describe the finite-dimensional modules for such algebras, including the character formula of Hermann Weyl. It concludes with the theory of Chevalley orders. Chapter 9 is devoted to the theory of compact Lie groups, beginning with a discussion of their maximal tori, root systems and Weyl groups. It goes on to describe the representation theory of compact Lie groups, including the application of integration to establish Weyl's formula in this context. The chapter concludes with a discussion of the actions of compact Lie groups on manifolds. The nine chapters together form the most comprehensive text available on the theory of Lie groups and Lie algebras.

Product Description

Intégration is the sixth and last of the Books that form the core of the Bourbaki series; it draws abundantly on the preceding five Books, especially General Topology and  Topological Vector Spaces, making it a culmination of the core six. The power of the tool thus fashioned is strikingly displayed in Chapter II of the author's Théories Spectrales [MR  35 #4725], an exposition, in a mere 38 pages, of abstract harmonic analysis and the structure of locally compact abelian groups.

Product Description
This book is an English translation of the last French edition of Bourbaki's Functions of a Real Variable. The first chapter is devoted to derivatives, Taylor expansions, the finite increment's theorem, convex functions. In the second chapter, primitives and integrals (on arbitrary intervals) are studied, as well as their dependence with respect to parameters. Classical functions (exponential, logarithmic, circular and inverse circular) are investigated in the third chapter. The fourth chapter gives a thorough treatment of differential equations (existence and unicity properties of solutions, approximate solutions, dependence on parameters) and of systems of linear differential equations. The local study of functions (comparison relations, asymptotic expansions) is treated in chapter V, with an appendix on Hardy fields. The theory of generalized Taylor expansions and the Euler-MacLaurin formula are presented in the sixth chapter, and applied in the last one to the study of the Gamma function on the real line as well as on the complex plane. Although the topics of the book are mainly of an advanced undergraduate level, they are presented in the generality needed for more advanced purposes: functions allowed to take values in topological vector spaces, asymptotic expansions are treated on a filtered set equipped with a comparison scale, theorems on the dependance on parameters of differential equations are directly applicable to the study of flows of vector fields on differential manifolds, etc. ... Read more

Product Description
Nicolas Bourbaki's multi-volume treatise "The Elements of Mathematics" contains, in each volume, a section or chapter devoted to the history of the subject. This book collects together these historical segments, without any claim to establishing a complete or chronological history of mathematics, but with an emphasis on the emergence, development and interaction of the leading ideas of the mathematical theories presented in the "Elements". In particular, the book provides a highly readable account of the evolution of algebra, geometry, infinitesimal calculus, and of the concepts of number and structure, from the Babylonian era through to the 20th century. ... Read more

Customer Reviews (1)

Good source, but rather incomplete.
I really expected more from such a title and such an author (group of authors as a matter of fact). The book does not cover the history of all important branches of modern mathematics, and those included are nottreated in a complete manner. Their major lacks occur in 20th centurymathematics. There's a lot of topics and names missing, for example:algebraic geometry, coding theory, dynamical systems, harmonic analysis,complex analysis, multidimensional complex analysis, hypercomplex analysis,approximation theory,... ; Samuel Eilenberg, Norman Steenrod, SalomonLefschetz, Elias Stein, Alberto Calderón, Peter Lax, Abraham Besicovitch,Michael Atiyah, Wendell Fleming, Witold Hurewicz...

Eventhough theBourbaki group has made a great effort to synthesize and standarize a lotof branches of modern mathematics the actual product of their work (theElements of Mathematics, the Fascicules of Results, etc.) may well becomeobsolete and forgotten because of their limited perspective. Nevertheless,the book contains some useful data that will prove valuable to thoseinterested in mathematics' history, above all, the first essay on thefoundations of mathematics.

Contents: Foundations of Mathematics, Logic,Set Theory; Notation, Combinatorial Analysis; The Evolution of Algebra;Linear Algebra and Multilinear Algebra; Polynomials and Commutative Fields;Divisibility, Ordered Fields; Commutative Algebra, Algebraic Number Theory;Non-Commutative Algebra; Quadratic Forms, Elementary Geometry; TopologicalSpaces; Uniform Spaces; Real Numbers; Exponentials and Logarithms;n-Dimensional Spaces; Complex Numbers, Measurement of Angles; MetricSpaces; Infinitesimal Calculus; Asymptotic Expansions; The Gamma Function;Function Spaces; Topological Vector Spaces; Integration in Locally CompactSpaces; Haar Measure, Convolution; Integration in Non-Locally CompactSpaces; Lie Groups and Lie Algebras; Groups Generated by Reflections; RootSystems.

Extensive references (not common in Bourbaki writings); nicesoftbound. ... Read more

Product Description
This is the softcover reprint of the English translation of 1972 (available from Springer since 1989) of the first 7 chapters of Bourbaki's 'Algbre commutative'. It provides a very complete treatment of commutative algebra, enabling the reader to go further and study algebraic or arithmetic geometry. The first 3 chapters treat in succession the concepts of flatness, localization and completions (in the general setting of graduations and filtrations). Chapter 4 studies associated prime ideals and the primary decomposition. Chapter 5 deals with integers, integral closures and finitely generated algebras over a field (including the Nullstellensatz). Chapter 6 studies valuation (of any rank), and the last chapter focuses on divisors (Krull, Dedekind, or factorial domains) with a final section on modules over integrally closed Noetherian domains, not usually found in textbooks. Useful exercises appear at the ends of the chapters. ... Read more

Customer Reviews (1)

the next step
For some reason, I got this idea in my head that I didn't need any algebra books besides Atiyah & Macdonald, Lang and maybe Eisenbud. Not true. I think this is considered to be one of the "good" Bourbaki books. Anyway, if you "do algebra", you will probably find this book worth having eventually. The font is fine, perhaps a point small for my taste, and the printing is clear, not like those hack photocopy jobs that some of the publishers use for old books (I'm looking at you Addison-Wesley) ... Read more

Product Description
Intégration is the sixth and last of the Books that form the core of the Bourbaki series; it draws abundantly on the preceding five Books, especially General Topology andTopological Vector Spaces, making it a culmination of the core six. The power of the tool thus fashioned is strikingly displayed in Chapter II of the author's Théories Spectrales [MR35 #4725], an exposition, in a mere 38 pages, of abstract harmonic analysis and the structure of locally compact abelian groups.

The present volume comprises Chapters 1-6 in English translation (a second volume will contain the remaining Chapters 7-9). The individual fascicles of the original French edition have been extensively reviewed [Chs. 1--4, MR 14, 960, 2e édn. MR 36 #2763; Ch. 5, MR 18, 881, 2e edn. MR 35 #322; Ch.6, MR 23 #A2033; Chs. 7-8, MR31 #3539; Ch. 9, MR 43 #2183].

Chapters 1-5 received very substantial revisions in a second edition, including changes to some fundamental definitions. Chapters 6-8 are based on the first editions of Chs. 1-5. The English edition has given the author the opportunity to correct misprints, update references, clarify the concordance of Chapter 6 with the second editions of Chapters 1-5, and revise the definition of a key concept in Chapter 6 (measurable equivalence relations). ... Read more

Product Description
This is the softcover reprint of the English translation of 1975 (available from Springer since 1989) of the first 3 chapters of Bourbaki's 'Groupes et algèbres de Lie'. The first chapter describes the theory of Lie algebras, their derivations, their representations and their enveloping algebras. In Ch. 2, free Lie algebras are introduced in order to discuss the exponential, logarithmic and the Hausdorff series. Ch. 3 deals with the theory of Lie groups over R and C and ultrametric fields. It describes the connections between their local and global properties, and the properties of their Lie algebras. It is one of the very best references on this subject. ... Read more

Customer Reviews (1)

great as references, and..
...even better when supplemented by other texts (be wary though, as the notation of Bourbaki is not universally accepted).
I'd buy themsimply for their sparkling clarity and careful attention to rigour (esp. Commalg, Lie theory and integration).
These arewonderfully crafted, masterful expositions, and shouldnot, by any means, be overlooked by the (aspiring) pure mathematician.

Cheers,
A. ... Read more

Product Description
This is the softcover reprint of the English translation of 1996 (available from Springer since 1989) of the later chapters of Bourbaki's 'Topologie générale'. It completes the treatment of general topology begun in Part I (Ch. 1-4, also available in English in softcover). The real numbers having been introduced in Ch. 4, the first chapters of this volume study subgroups and quotients of R (with applications to the 'measurement of magnitudes' and to the log and exp functions), then real vector spaces and projective spaces, then the additive groups Rn (subgroups, quotients, homomorphisms, infinite sums and products). Analogous properties are then studied for complex numbers, in Ch.8. Chapter 9 illustrates the use of real numbers in general topology, studying different important kinds of topological spaces: uniformizable, metric, normal Baire, Polish, Borel spaces.The final chapter deals with the various topologies of function spaces,ending with a section on approximation of functions. ... Read more

Product Description
The name Bourbaki is known to every mathematician. Many also know something of the origins of Bourbaki, yet few know the full story. In 1935, a small group of young mathematicians in France decided to write a fundamental treatise on analysis to replace the standard texts of the time. They ended up writing the most influential and sweeping mathematical treatise of the twentieth century, Les élements de mathématique. Maurice Mashaal lifts the veil from this secret society, showing us how heated debates, schoolboy humor, and the devotion and hard work of the members produced the ten books that took them over sixty years to write. The book has many first-hand accounts of the origins of Bourbaki, their meetings, their seminars, and the members themselves. He also discusses the lasting influence that Bourbaki has had on mathematics, through both the Élements and the Seminaires. The book is illustrated with numerous remarkable photographs. Readership Students, mathematicians, and historians interested in the group of mathematicians known as Bourbaki. ... Read more

Customer Reviews (3)

Balanced overview of rebarbative biographees
This is a very solid overview of the Bourbaki school, though obviously nothing like a full-fledged biography or monograph. The treatment is slightly more sophisticated than what you might find in a series of Scientific American articles (e.g., the author is confident that readers won't be scared off by an occasional integral sign or 2x2 matrix). I read the French edition, so I can't comment on the translation, though I was abashed to learn that the French adjectival form is not "bourbakien," as I might have guessed, but "bourbachique".

One of the main virtues of the book is that it's frank enough to include many thoughtful criticisms of the Bourbaki style and content. For example, although the Bourbaki were dedicated to following an axiomatic method, they ignored Gödel's incompleteness theorem, aside from an occasional dismissive reference. (That theorem shows that if you start from a system of axioms, you can't deduce all "mathematical truths" from them -- i.e., you can run across some statements that are consistent with the axioms but that cannot be deduced from them). The Bourbaki also ignored category theory, even though one of its inventors (Samuel Eilenberg) was a member of the group for a while. Today category theory is the dominant framework for describing the fundamental structures of mathematics. The Bourbaki also disdained so-called applied mathematics, including probability theory and dynamics, for its lack of "purity," even though it has yielded much mathematical fruit in the past 50 years. (Indeed it represents much of the lasting glory of French mathematics, e.g. the work of Fourier, Legendre, Lebesgue, Henri Poincaré and even Jacques Hadamard, whose seminars were a role model for the Bourbakis' and who supervised the PhDs of two of the group's founding members.) In short, the Bourbaki seem to have ignored or disdained rather lots of stuff. The bourbachique closed-mindedness ultimately contributed to the obsolescence of their approach.

The book's candor is also a bit of a flaw. By the end of the book the members of the group come across as the dogmatic, elitist clique their contemporaries accused them of being. They do seem to have been a livelier bunch in person than what I'd expected from their impersonal, austere, diagram-less presentation of mathematics. But while having a sense of humor was a prerequisite for being invited to join, the examples of their humor are for the most part sophomoric, and occasionally mean-spirited. Readers who already weren't Bourbaki fans might feel vindicated after reading this book; I can't vouch for what their fans might feel. Overall a quite interesting, but not uplifting, brief intellectual biography.

Despite Obvious Flaws, it's a colorful book, providing a clear look at rather common mathematical values and beliefs
For values and beliefs for a large group of mathematicians, this is a helpful book.For Bourbakian values and beliefs have been, by and large, adopted by the academic masses, alas. (expression of a Bourbakian value and a Bourbakian belief from p.75 "basic concepts are treated as abstract entities whose nature and concrete meaning are insignificant") Still, it's a nice tourist guide, even has lots and lots of color snaps.

But the text just reads and feels odd. It might just be due to some weaknesses in the text's translation from the French. All the same, sometimes I have no idea what is being written about or why.

For example, on page 41 I read "the fundamental theorem of algebra, which states that any polynomial with real coefficients has at least one complex root (in other words, there is a complex numer x that makes the expression equal to zero)" WHAT?!?!?!?!?!?! Not only useless, it's nonsense. The basic thought on complex numbers and polynomials with real-valued coefficients is the following. If any polynomial equation with real coefficients has a complex number z as a root, then the complex conjugate of z is also a root of the polynomial equation.

Interesting for fans of Bourbaki's texts
This is very interesting for fans of any of Bourbaki's mathematics texts.It has photos of many of the members taken at their meetings, and information about how the group operated.You'd never know it from the final product, but their original goal was to write a calculus book!Several of the founding members had just begun teaching, and they were unhappy with the standard French calculus text of the day--a multivolume work by Goursat that they considered out of date.They decided to write a little bit of background material on algebra and general topology, and somehow ended up with the books we all know and love.
The book also describes the personality quirks of the members, and has some commentary on the contents of the various texts of Bourbaki.It doesn't explain technical details like why Bourbaki chose to define integrals the way they did.
If you didn't major in math, this book probably won't interest you. ... Read more

Product Description
This is the softcover reprint of the English translation of 1974 (available from Springer since 1989) of the first 3 chapters of Bourbaki's 'Algèbre'. It gives a thorough exposition of the fundamentals of general, linear and multilinear algebra. The first chapter introduces the basic objects: groups, actions, rings, fields. The second chapter studies the properties of modules and linear maps, especially with respect to the tensor product and duality constructions. The third chapter investigates algebras, in particular tensor algebras. Determinants, norms, traces and derivations are also studied. ... Read more

Customer Reviews (1)

Bourbaki - The Bible of Modern Math
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. ... Read more

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From the reviews of the French edition

"This is a rich and useful volume. The material it treats has relevance well beyond the theory of Lie groups and algebras, ranging from the geometry of regular polytopes and paving problems to current work on finite simple groups having a (B,N)-pair structure, or "Tits systems". A historical note provides a survey of the contexts in which groups generated by reflections have arisen. A brief introduction includes almost the only other mention of Lie groups and algebras to be found in the volume. Thus the presentation here is really quite independent of Lie theory. The choice of such an approach makes for an elegant, self-contained treatment of some highly interesting mathematics, which can be read with profit and with relative ease by a very wide circle of readers (and with delight by many, if the reviewer is at all representative)." (G.B. Seligman in MathReviews)

Product Description
This is a softcover reprint of the English translation of 1987 of the second edition of Bourbaki's Espaces Vectoriels Topologiques (1981). This second edition is a brand new book and completely supersedes the original version of nearly 30 years ago. But a lot of the material has been rearranged, rewritten, or replaced by a more up-to-date exposition, and a good deal of new material has been incorporated in this book, all reflecting the progress made in the field during the last three decades. ... Read more

Product Description

This is a softcover reprint of the English translation of 1990 of the revised and expanded version of Bourbaki's textbook, Algèbre, Chapters 4 to 7 (1981).

The English translation of the new and expanded version of Bourbaki's Algèbre, Chapters 4 to 7 completes Algebra, 1 to 3, by establishing the theories of commutative fields and modules over a principal ideal domain. Chapter 4 deals with polynomials, rational fractions and power series. A section on symmetric tensors and polynomial mappings between modules, and a final one on symmetric functions, have been added. Chapter 5 has been entirely rewritten. After the basic theory of extensions (prime fields, algebraic, algebraically closed, radical extension), separable algebraic extensions are investigated, giving way to a section on Galois theory. Galois theory is in turn applied to finite fields and abelian extensions. The chapter then proceeds to the study of general non-algebraic extensions which cannot usually be found in textbooks: p-bases, transcendental extensions, separability criterions, regular extensions. Chapter 6 treats ordered groups and fields and based on it is Chapter 7: modules over a p.i.d. studies of torsion modules, free modules, finite type modules, with applications to abelian groups and endomorphisms of vector spaces. Sections on semi-simple endomorphisms and Jordan decomposition have been added.

Chapter IV: Polynomials and Rational Fractions

Chapter V: Commutative Fields

Chapter VI: Ordered Groups and Fields

Chapter VII: Modules Over Principal Ideal Domains

... Read more

Customer Reviews (1)

The BEST of The BEST New Math Bible
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 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. ... Read more

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Les Éléments de mathématique de Nicolas Bourbaki ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements.

Ce dixième chapitre du Livre d Algèbre, deuxième Livre du traité, pose les bases du calcul homologique.

Ce volume est a été publié en 1980.

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At the age of 68, distinguished Princeton science professor Max Weiss is bribed into taking an early retirement. He takes an ingenious revenge in the form of "Doctor Diana Skordylis"--a pseudonym for a partnership among Weiss and three aging colleagues. Their soaring success is unanticipated and professional jealousy soon threatens Diana Skordylis's life. "A beautifully ingenious, funny, brilliantly inteligent and moving tale of very human scientists. A splendid novel."--Iris Murdoch. ... Read more

Customer Reviews (3)

Excellent premise, but not as well crafted as "Cantor's Dilemma"
Djerassi is once again to be commended for writing an entertaining novel to educate the general public about the forces that really drive scientists as individuals, and the world of scientific research in general.If the public is to make intelligent decisions about how to fund, teach, and promote science, then this kind of insight into the (sometimes messy) realities of the research world is a must.For this purpose, a well-told story is worth a hundred dry, factual reports.

The premise of "The Bourbaki Gambit" is excellent.(The title of the book comes from the pseudonymous mathematician Nicolas Bourbaki, although only one character in the book is a mathematician.)An older and highly successful biochemist, feeling that he has been prematurely put out to pasture, seeks revenge by recruiting three other like-minded colleagues to form a pseudonymous and anonymous collaboration.Their goal?To expose the ageist prejudices of the scientific world by publishing outstanding research under a pen name and then, after the kudos roll in, to reveal their true identities.The plan seems perfect---until paradoxically, they become victims of their own success.

In a world where people are living increasingly long and healthy lives, and where collaboration is becoming increasingly important even in traditionally "solitary" fields (as I write this, the renowned mathematician Tim Gowers is experimenting on his blog with "Polymath," a large-scale pseudonymous---but not anonymous---wiki-style collaborative research entity), the premise of "The Bourbaki Gambit" is extremely relevant.Scientists themselves (and not just the general public) would do well to grapple more directly and openly with the problems and issues that are highlighted in this book.

I must confess, however, that I found "The Bourbaki Gambit" to be less well-written than Djerassi's more famous book, "Cantor's Dilemma."One gets the feeling that the author overindulged himself by inserting a lot of trivia about his favorite hobbies and pet interests.These details can be interesting if you happen to share the same interests---for example, even though I am a mathematician and know about Hy Bass, I did not know that he contributed to Bourbaki---but too often they fail to enliven the characters or plot, or contribute to the underlying social commentary, and thus they cause the book to drag.The characters in "Cantor's Dilemma" are more believable, three-dimensional, and likable.So if you have never read Djerassi before, I recommend you start with "Cantor's Dilemma."

By the way, the characters' main scientific discovery in the book is in fact a real piece of science, and the true story of its discovery is quite fascinating in its own right.Be sure to check it out after finishing Djerassi's book.

Issues in science and mathathics: age, gender and originality
The collective Individual of the French mathematicalcommunity Nicolas Bourbaki is the inspiration for four people in biochemistry: they form the collective individual Diana Skordylis and publish research papers under that name. What breaks up the association is not failure, but success.
The book is slow and almost too literary, but the character development is better than many faster or more interesting novels.
Had they developed a biotoxinor a weapon of some kind, it might have
had spies and intrigue that would
have gained the book a wider audience.
Insteadit became a polemic against sex and age discrimination in the
scientific and educational community.
The fact that one gets paid more for getting more published under an individual name and that individuals can't get published without some recognized sponsorship makes the systemsystem somewhat secure
from raging originality and not all an open form. It is not at all clear why older successful people would be threatened by being retired
so that younger people can get at least a chance
should be much of an issue:
a more important issue is the voices who are never heard or even allowed to speak or publish their work or ideas.

Djerassi did not win a nobel prize.
This excellent book explored the collaborative process of science in the framework of an interesting story. It is a must read for scientists who should learn lessons from this book.It should be noted however that theauthor is not a nobel prize winner as the first review would have usbelieve. ... Read more

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Formes sesquilinéaires et formes quadratiques.

Les Éléments de mathématique de Nicolas BOURBAKI ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements.

Ce neuvième chapitre du Livre d Algèbre, deuxième Livre du traité, est consacré aux formes quadratiques, symplectiques ou hermitiennes et aux groupes associés.

Il contient également une note historique.

Ce volume est une réimpression de l édition de 1959.

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Les Éléments de mathématique de Nicolas Bourbaki ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements.

Ce volume du Livre d Algèbre commutative, septième Livre du traité, est la continuation des chapitres antérieurs. Il introduit notamment les notions de profondeur et de lissité, fondamentales en géometrie algébrique. Il se termine par l introduction des modules dualisants et de la dualité de Grothendieck.

Ce volume est paru en 1998.