Arithmetic, Induction, and the Algebra of Polynomials : Al-Samaw'āl and his "Splendid Book of Algebra"
| dc.contributor.author | Bajri, Sanaa Ahmed E. | en |
| dc.date.accessioned | 2012-02-29T01:44:24Z | |
| dc.date.available | 2012-02-29T01:44:24Z | |
| dc.date.issued | 2011 | en |
| dc.description.abstract | Al-Samaw'āl (with the complete name Al-Samaw'āl Ibn Yahyā Al-Maghribī), born around 1130 in Baghdad, Iraq, is best known in the History of Mathematics for his seminal work the Al-Bāhir fī Al-Jabr (literally The Splendid Book of Algebra) which he composed at the prodigious age of nineteen. In this work, following the Euclidean tradition, Al-Samaw'āl put together and advanced many key algebraic rules formulated by his predecessors, notably Al-Khwārizmi, Ibn Turk, Ibn Qurra, Al-Kūhī, Al-Uqlīdīsī, Abū'l-Wafā, Al-Karajī, Ibn Aslam, Al-Sijzī, Ibn Al-Haytham, Qustā Ibn Lūqā, and Al-Harīrī. Al-Bāhir is a large work and consists of four sections. Section one provides an account of operations on polynomials in one unknown with rational coefficients, section two deals essentially with second-degree equations, indeterminate analysis, and summations, section three concerns irrational quantities, and section four presents the application of algebraic principles to a number of problems. In this thesis, we give close attention to book four from the second section in which Al-Samaw'āl discusses mathematical relations which amount to the binomial theorem and the Pascal triangle and lays out a table of binomial coefficients and demonstrates how to generalise the entries in the table for any desired value. Our main contribution is a complete translation of the Arabic text, the first time this has been done in a European language. We will then provide a detailed mathematical commentary and offer a careful analysis of the status and impact of this work in the History of Mathematics, paying due attention to the historical context in which it was produced. | en |
| dc.identifier.uri | http://hdl.handle.net/10092/6344 | |
| dc.identifier.uri | http://dx.doi.org/10.26021/9047 | |
| dc.language.iso | en | |
| dc.publisher | University of Canterbury. Mathematics and Statistics | en |
| dc.relation.isreferencedby | NZCU | en |
| dc.rights | Copyright Sanaa Ahmed E. Bajri | en |
| dc.rights.uri | https://canterbury.libguides.com/rights/theses | en |
| dc.title | Arithmetic, Induction, and the Algebra of Polynomials : Al-Samaw'āl and his "Splendid Book of Algebra" | en |
| dc.type | Theses / Dissertations | |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | University of Canterbury | en |
| thesis.degree.level | Masters | en |
| thesis.degree.name | Master of Science | en |
| uc.bibnumber | 1750089 | en |
| uc.college | Faculty of Science | en |
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