SrVishi said:I was wondering what is considered the better of the two.
examples of errors?micromass said:Lang has very nice key insights, but much of his text is confusing and the book is riddled with errors.
bolbteppa said:Bourbaki's algebra is IMO the best book on the subject, even just understanding why group representation theory is at the end of the (untranslated!) chapter 8 was just so immensely illuminating and I couldn't find that answered anywhere else, but use Dummit and Foote as well and complete DF while taking in Bourbaki over time, it is a bit insane.
bacte2013 said:Is English-translation version not as insightful as original? Strangely, I cannot find Chapter 8 as English-version contains Chap. 1 through 7.
bolbteppa said:I think only chapters 1 to 7 are translated, there's a new (French) algebraic topology too. Also the manifolds book is not translated :(
Lang and Bourbaki were two influential mathematicians who had different approaches to teaching and studying algebra. Lang's approach was more traditional and focused on teaching concrete examples and techniques, while Bourbaki's approach was more abstract and focused on the underlying structures and concepts of algebra.
This ultimately depends on the individual learner and their preferences. Some may find Lang's approach more intuitive and easier to grasp, while others may prefer Bourbaki's more rigorous and abstract approach. It is recommended to try both approaches and see which one works best for you.
One key difference is that Lang's textbooks are more comprehensive and cover a wider range of topics, while Bourbaki's textbooks are more concise and focused on the fundamental concepts of algebra. Additionally, Lang's textbooks often include more exercises and examples, while Bourbaki's textbooks have a more theoretical and proof-based approach.
Both approaches are still used in modern mathematics, but Bourbaki's approach has had a greater influence and is more commonly used in research and graduate-level courses. Lang's approach is still popular for undergraduate courses and for those who prefer a more concrete and applied approach to algebra.
Yes, many students and mathematicians use both textbooks together as a complementary approach to learning algebra. By using both perspectives, one can gain a deeper understanding and appreciation for the subject. However, it is not necessary to use both textbooks and one can still learn algebra effectively by using either one.