What level are the books 'Elements de Mathematiques' by Bourbaki?

  • Context: Foundations 
  • Thread starter Thread starter fxdung
  • Start date Start date
  • Tags Tags
    Books
Click For Summary
SUMMARY

The books 'Elements de Mathematiques' by Bourbaki are not classified as undergraduate or graduate level; they serve more as an encyclopedic reference within an axiomatic framework. Readers are advised to approach these texts with caution, as they do not function effectively as traditional textbooks for learning mathematics. Instead, they represent a culmination of mathematical concepts rather than a guide to the creative process of mathematics. For those interested in studying Bourbaki, starting with specific subjects such as abstract algebra is recommended, and prior reading of 'Undergraduate Algebra' by Lang may enhance comprehension.

PREREQUISITES
  • Familiarity with axiomatic mathematics
  • Basic understanding of abstract algebra
  • Knowledge of mathematical rigor and proof techniques
  • Experience with self-directed study in advanced mathematics
NEXT STEPS
  • Read 'Undergraduate Algebra' by Serge Lang to build foundational knowledge before tackling Bourbaki.
  • Explore the first three chapters of Bourbaki's Algebra for insights into abstract algebra.
  • Investigate the 'Treatise on Analysis' by Dieudonné for a complementary perspective on analysis.
  • Research the differences between traditional textbooks and encyclopedic mathematical texts.
USEFUL FOR

This discussion is beneficial for mathematics students, educators, and self-learners interested in advanced mathematical concepts, particularly those considering the works of Bourbaki and Dieudonné.

fxdung
Messages
387
Reaction score
23
What level(undergraduate or graduate) are the books Elements de Mathematiques by Bourbaki?Is good if I read it?If I like to read(undergraduate) then I must read following which order?(Eg first I must read book The Set theory).By the way,what about The Treatise on analysis by Dieudonne?
 
Last edited:
Physics news on Phys.org
Best is try to read and see for yourself if it is good for you or not. As to the level, I would say, no, they are neither undergrad nor grad level. Same for the Treatise, you can think of it as the analysis text Bourbaki never wrote. I personaly wouldn't recommend to study from those books.
 
I think one should consider them not as textbooks at all. It's more like an encyclopedia which puts math into an axiomatic framework. It's so-to-say the "final result" of a finished "mathematical edifice". I don't think that one can learn, how math is really done as a creative process.
 
I think because it is rigorous,it might be easy to read for self studying?
 
  • Haha
Likes   Reactions: vanhees71 and Demystifier
I do not find them easy to read, but that's just me. How about you choose a subject and pick up a volume of Bourbaki on this matter? Tell us what the subject is and also what your impression of the style is.
 
  • Like
Likes   Reactions: vanhees71
I will begin abstract algebra, so I choose Algebra chapter 1-3 by Bourbaki. I do not like Fraleigh, because it seems to me not very rigorous(is that correct?)
 
Alright, then come back here with your honest opinion on Bourbaki's Algebra.
 
  • Like
Likes   Reactions: vanhees71 and Demystifier
Is it good to read Undergraduate Algebra by Lang before reading Bourbaki(self studying)? Is the Lang's book easy to read?
 

Similar threads

  • · Replies 15 ·
Replies
15
Views
7K
  • · Replies 8 ·
Replies
8
Views
691
  • · Replies 5 ·
Replies
5
Views
4K
  • · Replies 3 ·
Replies
3
Views
5K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
25
Views
6K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 5 ·
Replies
5
Views
4K