Nicolas Bourbaki je kolektivní pseudonym, pod kterým skupina matematiků vytvořila sérii knih prezentujících moderní pokročilou matematiku. Jejich cílem bylo založit veškerou matematiku na teorii množin, přičemž dbali na rigoróznost a obecnost. Práce skupiny vedla k objevu několika konceptů a terminologií, které se dodnes diskutují a ovlivňují matematickou komunitu.
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.
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).
This softcover reprint of Bourbaki's "Groupes et Algèbres de Lie" covers Chapters 7 to 9, focusing on semi-simple Lie algebras and compact Lie groups. Topics include Cartan subalgebras, root systems, finite-dimensional modules, and representation theory, making it a comprehensive resource on Lie groups and algebras.
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.
This is the sixth and last of the books that form the core of the Bourbaki series, comprising chapters 1-6 in English translation. One striking feature is its exposition of abstract harmonic analysis and the structure of locally compact Abelian groups. This English edition corrects misprints, updates references, and revises the definition of the concept of measurable equivalence relations.
This is a softcover reprint of the 1987 English translation of the second edition of Bourbaki's Espaces Vectoriels Topologiques. Much 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, reflecting decades of progress in the field.
Exploring the complexities of societal integration, this book delves into the challenges and triumphs of diverse communities coming together. It highlights personal stories that illustrate the impact of cultural exchange and the importance of empathy in fostering understanding. Through a blend of research and narrative, the author examines historical contexts and contemporary issues, offering insights into how integration shapes identities and promotes social cohesion. The work serves as both a call to action and a reflection on the human experience in a multicultural world.
The book presents an English translation of the final French edition of Bourbaki's work, renowned for its rigorous approach to mathematics. It emphasizes the importance of formalism and abstraction in mathematical theory, showcasing Bourbaki's influential contributions to the field. The text is structured to enhance understanding of complex concepts, making it a valuable resource for both students and professionals seeking to deepen their mathematical knowledge.
Exploring the complexities of cultural integration, this book delves into the challenges and triumphs faced by individuals navigating diverse identities. It examines personal stories and societal dynamics, highlighting the emotional and psychological impacts of merging different backgrounds. Through insightful analysis, the narrative addresses themes of belonging, identity, and the quest for acceptance in a multicultural world. Readers are invited to reflect on their own experiences and the broader implications of integration in contemporary society.
The English translation presents a thoroughly revised version of the eighth chapter from the 1958 edition of Algebra, part of the foundational work Elements of Mathematics. It offers updated insights and interpretations, making complex mathematical concepts more accessible to modern readers. This edition aims to enhance understanding and appreciation of algebra's principles and applications.