Mathematics in the medieval Islamic world

Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics (Euclid, Archimedes, Apollonius) and Indian mathematics (Aryabhata, Brahmagupta). Important progress was made, such as full development of the decimal place-value system to include decimal fractions, the first systematised study of algebra, and advances in geometry and trigonometry. Arabic works played an important role in the transmission of mathematics to Europe during the 10th—12th centuries. The study of algebra, the name of which is derived from the Arabic word meaning completion or "reunion of broken parts", flourished during the Islamic golden age. Muhammad ibn Musa al-Khwarizmi, a Persian scholar in the House of Wisdom in Baghdad was the founder of algebra, is along with the Greek mathematician Diophantus, known as the father of algebra. In his book The Compendious Book on Calculation by Completion and Balancing, Al-Khwarizmi deals with ways to solve for the positive roots of first and second-degree (linear and quadratic) polynomial equations. He introduces the method of reduction, and unlike Diophantus, also gives general solutions for the equations he deals with. Al-Khwarizmi's algebra was rhetorical, which means that the equations were written out in full sentences. This was unlike the algebraic work of Diophantus, which was syncopated, meaning that some symbolism is used. The transition to symbolic algebra, where only symbols are used, can be seen in the work of Ibn al-Banna' al-Marrakushi and Abū al-Ḥasan ibn ʿAlī al-Qalaṣādī. On the work done by Al-Khwarizmi, J. J. O'Connor and Edmund F. Robertson said: "Perhaps one of the most significant advances made by Arabic mathematics began at this time with the work of al-Khwarizmi, namely the beginnings of algebra. It is important to understand just how significant this new idea was. It was a revolutionary move away from the Greek concept of mathematics which was essentially geometry.

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (2)

Related concepts (17)

Related courses (4)

Related lectures (29)

MATH-110(a): Advanced linear algebra I

L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire et de démontrer rigoureusement les résultats principaux de ce sujet.

MATH-124: Geometry for architects I

Ce cours entend exposer les fondements de la géométrie à un triple titre : 1/ de technique mathématique essentielle au processus de conception du projet, 2/ d'objet privilégié des logiciels de concept

MATH-240: Statistics

Ce cours donne une introduction au traitement mathématique de la théorie de l'inférence statistique en utilisant la notion de vraisemblance comme un thème central.

In any sport or human endeavor, coaches regularly state “play to your strengths.” One might not guess that a land-locked, mountainous country like Switzerland would have strengths that would give them a chance at winning the oldest, most competitive sailin ...

2009

Robust 3D Dynamic Triangulations for Collision Detection in DEM Simulations of Granular Materials

Thomas Liebling, Jean-Albert Ferrez

Computer simulations of granular materials based on the distinct element method (DEM) are now commonly used in the design and optimization of industrial processes. One of the leading mathematical approach to DEM uses dynamic triangulations for detecting co ...

2002

Latin translations of the 12th century were spurred by a major search by European scholars for new learning unavailable in western Europe at the time; their search led them to areas of southern Europe, particularly in central Spain and Sicily, which recently had come under Christian rule following their reconquest in the late 11th century. These areas had been under Muslim rule for a considerable time, and still had substantial Arabic-speaking populations to support their search.

Algebra () is the study of variables and the rules for manipulating these variables in formulas; it is a unifying thread of almost all of mathematics. Elementary algebra deals with the manipulation of variables (commonly represented by Roman letters) as if they were numbers and is therefore essential in all applications of mathematics. Abstract algebra is the name given, mostly in education, to the study of algebraic structures such as groups, rings, and fields.

Islam (ˈɪslɑːm; ۘالِإسْلَام, al-ʾIslām ʔɪsˈlæːm, ) is an Abrahamic monotheistic religion centered on the Quran and the teachings of Muhammad. Adherents of Islam, called Muslims, number approximately 2 billion globally and are the world's second-largest religious population after Christians. Muslims believe that Islam is the complete and universal version of a primordial faith that was revealed many times through earlier prophets such as Adam (believed to be the first man), Ibrahim, Moses, and Isa (Jesus), among others.

Covers the definition and operations of polynomials, including addition and multiplication, degree, coefficients, and their role in algebraic systems.

Delves into powers and roots, emphasizing irrational equations and the disjunction of cases.

Covers the concepts of mixed product, cross product, homo coordinates, and general conics.