Mathematical Treasure: Felix Klein’s Lecture Notes on Riemann Surfaces and Hypergeometric Functions

Author(s):

Frank J. Swetz (The Pennsylvania State University)

Felix Klein (1849–1925) was one of the most influential German mathematicians of his time. Many of his students were from abroad, traveling to Germany to study under him. His lectures were carefully copied and reproduced. Here are images of Klein’s 1892 lectures on Riemann Surfaces.

Title page for handwritten copy of Klein's lecture notes on Riemann Surfaces, 1892.

Page 1 from handwritten copy of Klein's lecture notes on Riemann Surfaces, 1892.

Page 10 from handwritten copy of Klein's lecture notes on Riemann Surfaces, 1892.

A full digitization of the photostat owned by the University of California is available from HathiTrust.

Other versions added a printed title page and table of contents:

Title page for 1894 partially-printed version of Klein's lecture notes on Riemann Surfaces.

First page of table of contents for 1894 partially-printed version of Klein's lecture notes on Riemann Surfaces.

Second page of table of contents for 1894 partially-printed version of Klein's lecture notes on Riemann Surfaces.

Third page of table of contents for 1894 partially-printed version of Klein's lecture notes on Riemann Surfaces.

First page of 1894 partially-printed version of Klein's lecture notes on Riemann Surfaces.

A full digitization of the copy owned by the University of California is available from the Internet Archive.

In a similar manner, his lectures from 1894 on hypergeometric functions, were also published. They had been collected and edited by a student, Ernst Ritter (1867–1885). Ritter had completed his studies in Germany and was offered a position at Cornell University in the United States; however, in transit, he died of typhus. Felix Klein wrote his obituary.

Title page of Ueber die hypergeometrische function, 1894.

The table of contents:

First page of table of contents for Ueber die hypergeometrische function, 1894.

Second page of table of contents for Ueber die hypergeometrische function, 1894.

Third page of table of contents for Ueber die hypergeometrische function, 1894.

A full digitization of the copy owned by the University of Michigan is available in the Internet Archive.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Felix Klein’s Lecture Notes on Riemann Surfaces and Hypergeometric Functions," Convergence (April 2024)

Convergence

Tags:

Riemann Surfaces