A history of algebra. From al-Khwārizmī to Emmy Noether. (English) Zbl 0569.01001

Van der Waerden, B. L.

Berlin etc.: Springer-Verlag. XI, 271 p. DM 98.00 (1985).

The author deals with the history of algebra from al-Khwārizmī to Emmy Noether, i.e. the historical development of algebric equations, groups and algebras is the central theme of this book. Chapters of special interest are those on algebra in Italy, on Gauss, Galois, Hamilton and Emmy Noether. The author divides his book into fourteen chapters. They are as follows: 1) Three Muslim authors (al-Khwārizmī, Tabit ben Qurra, Omar Khayyam); 2) Algebra in Italy; 3) From Viète to Descartes; 4) The predecessors of Galois; 5) Carl Friedrich Gauss; 6) Evariste Galois; 7) Camille Jordan; 8) Early group theory; 9) Lie groups and Lie algebras; 10) The discovery of algebras; 11) The structure of algebras; 12) Group characters; 13) The representations of finite groups and algebras; 14) Representation of Lie groups and Lie algebras. This book is a classic study on the history of modern algebra.

Reviewer: P.K.Majumdar

MSC:

01A05	General histories, source books
01-02	Research exposition (monographs, survey articles) pertaining to history and biography
12-03	History of field theory
13-03	History of commutative algebra

Keywords:

Lie groups; abstract groups; Gauss; Galois; Hamilton