Jarník’s notes of the lecture course Punktmengen und reelle Funktionen by P. S. Aleksandrov (Göttingen 1928). (German, English) Zbl 1247.01022

Dějiny Matematiky / History of Mathematics 43. Prague: Matfyzpress (ISBN 978-80-7378-113-2). 143 p., open access (2010).

The book under review is devoted to an archival material, Jarnik’s mathematical notebook. It was written during his studies at the University of Göttingen in the academic year 1927/1928 and contains notes to the lecture course “Punktmengen und reelle Funktionen” [Point sets and real functions] by Pavel Sergeevich Aleksandrov.
The book consists of seven chapters. Chapter 1 gives a short description of Alexandrov’s life and work as well as his pedagogical activities. In Chapter 2 the life and work of Jarnik are described. Both chapters contain many interesting footnotes bringing additional information on mathematicians and their works. Chapter 3 is devoted to the University of Göttingen and to the development of mathematical studies there. Chapter 4 provides a general account of fourteen Jarnik’s notebooks with special emphasis put on the fifth notebook containing Alexandrov’s lectures. Chapters 6 and 7 forming the heart of the book contain, resp., Aleksandrov’s lectures rewritten from Jarnik’s manuscript and detailed mathematical, historical and bibliographical comments. The book is closed by 19 illustrations (copies of some pages of Jarnik’s notebook, some portraits and pictures) and by an index of names.
The book is a valuable source to the history of mathematics as well as the history of its teaching at the University of Göttingen.
Table of contents:
Preface; Pavel Sergeevich Aleksandrov (1896–1982) (7–23); Vojtěch Jarník (1897–1970) (25–32); Mathematics in Göttingen (33–46); Jarník’s notebooks from Göttingen (47–49); Aleksandrov’s “Punktmengen und reelle Funktionen” (51–90); Summary of results and bibliographical and historical comments (91–110); Table of illustrations (113); Illustrations 133-143 ([114]–[132]); Name index ([145]–[148]).

Reviewer: Roman Murawski (Poznań)

MSC:

01A60	History of mathematics in the 20th century
01-02	Research exposition (monographs, survey articles) pertaining to history and biography
01A75	Collected or selected works; reprintings or translations of classics
01A70	Biographies, obituaries, personalia, bibliographies
26-03	History of real functions