Recognized for its cultural significance, this work contributes to the foundational knowledge of civilization. Scholars have highlighted its importance, ensuring that it remains a valuable resource for understanding historical and societal contexts.
Die Betrachtung der acht Kapitel fokussiert sich auf deren spezifische Ziele und die zugrunde liegende Fragestellung. Der Autor legt besonderen Wert auf den Einheitskreis und dessen mathematische Bedeutung. In der Einleitung wird der Kreis I x I thematisiert, um die Grundlagen für die folgenden Erklärungen zu schaffen. Die Struktur und die Herangehensweise des Buches bieten eine tiefgehende Analyse der Konzepte, die im weiteren Verlauf behandelt werden.
Presents an account of the theory of algebraic numbers and ideals leading up to Dedekind's theorem that every ideal of an algebraic number field is the unique product of prime ideals. This work studies Landau's generalization of the prime number theorem that was conjectured by Gauss and proven by Hadamard and Vallee Poussin in 1896.
After completing his famous Foundations of Analysis, Landau turned his attention to this book on calculus. The approach is that of an unrepentant analyst, with an emphasis on functions rather than on geometric or physical applications. The book is another example of Landau's formidable skill as an expositor. It is a masterpiece of rigor and clarity. And what a book it is! The marks of Landau's thoroughness and elegance, and of his undoubted authority, impress themselves on the reader at every turn, from the opening of the preface ... to the closing of the final chapter. It is a book that all analysts ... should possess ... to see how a master of his craft like Landau presented the calculus when he was at the height of his power and reputation. --Mathematical Gazette