To expand search, see The Islamic World. Laterally related topics: The Hindu-Arabic Numerals, Th\^abit ibn Qurra, Omar Khayyam (abu-l-Fath Omar ibn Ibrahim Khayyam), Nasir al-Din al-Tusi, and Abu Kamil (b. 850).
The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and in the connections between mathematics and other disciplines. The notes in these pages are intended as much to evoke ideas as to indicate what the books and articles are about. They are not intended as reviews. However, some items have been reviewed in Mathematical Reviews, published by The American Mathematical Society. When the mathematical review (MR) number and reviewer are known to the author of these pages, they are given as part of the bibliographic citation. Subscribing institutions can access the more recent MR reviews online through MathSciNet.
Arndt, A. B. Al-Khwarizmi. Mathematics Teacher 76 (1983), 668--70.
An introduction to the work of al Khwarizmi. Focuses on his algebra, the Al-Kitab Al-jabr wa'l muqabalah and its influence on the West. Reprinted in Swetz, Frank J., From Five Fingers to Infinity.
Høyrup, Jens. Sub-scientific mathematics: observations on a pre-modern phenomenon. Hist. of Sci. 28 (1990), no. 79, part 1, 63--87. (Reviewer: David Singmaster.) SC: 01A10 (01A05 01A12 01A80), MR: 91j:01007.
Høyrup makes a distinction between scientific and subscientific mathematics. These fields correspond somewhat to pure and applied mathematics. However, by using this new terminology, the author hopes to avoid suggesting that "subscientific" mathematics is always derived from "scientific" mathematics in the way that "applied" mathematics is derived from "pure" mathematics. Høyrup discusses the distinction between scientific and subscientific mathematics and also their various kinds of relationships. His examples are drawn from Greece, Egypt, India, the Islamic World (with references to the Silk route), and from the Carolingian Propositiones ad acuendos jevenes. (The latter is traditionally associated with Alcuin.) Høyrup touches on relevant work by the mathematicians Hero, Diophantus, and al Khwarizmi. Surveying is discussed as a particularly important type of subscientific mathematics. Closely related topics: Applied Mathematics (General), Greece, Ancient Egypt, India, The Islamic World, Alcuin, Heron, Diophantus, and Surveying.
Pazwah, Hormoz; Mavrigian, Gus. The Contributions of Karaji---Successor to al-Khwarizmi. Mathematics Teacher 79 (1986), 538--41.
An introduction to the work of al Karaji (often known as al Karkhi). Includes a little on arithmetic, algebra, geometry, and surveying. Reprinted in Swetz, Frank J., From Five Fingers to Infinity.