Vorlesungen Ueber die Entwicklung der Mathematik
The two volumes collected here represent what were to be the first two parts of Klein's plan to write a complete history of the mathematics of the 19th Century. This remarkable book was written by Klein during the last years of his life, a time coinciding with exciting mathematical activity and also the first World War. It is his personal view of the significant developments in mathematics in the 1800s (and early 1900s), especially those connected with the German school. This period includes the time of Klein's greatest activity and influence as a mathematician. The selection of topics reflects Klein's own interests in mathematics. The topics in the first volume include: Gauss's work in pure and applied mathematics; mathematics in France during the early decades of the 19th Century; the contributions of Mobius, Plucker and Steiner to the development of algebraic geometry; mechanics and mathematical physics in England and Germany up to the 1880s; complex analysis according to Riemann and according to Weierstrass; automorphic functions and the interplay between group theory and function theory. The second volume focuses on invariants and their applications in mathematical physics, with particular emphasis on special relativity. Both volumes were published after Klein's death. The final draft for the first volume was prepared by Courant and Neugebauer. The second volume was prepared by Courant and Cohn-Vossen.
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