Muslim Mathematicians

(1) Abd al-Hamīd ibn Turk
Abd al-Hamīd ibn Turk (fl. 830), known also as ‘Abd al-Hamīd ibn Wase ibn Turk Jili was a ninth century Muslim mathematician. Not much is known about his biography. The two records of him, one by the Persian Ibn Nadim and the other by al-Qifti are not identical. However al-Qifi mentions his name as Abd al-Hamīd ibn Wase ibn Turk Jili. Jili means from Gilan.
He wrote a work on algebra of which only a chapter called "Logical Necessities in Mixed Equations", on the solution of quadratic equations, has survived.
He authored a manuscript entitled Logical Necessities in Mixed Equations, which is very similar to al-Khwarzimi's Al-Jabr and was published at around the same time as, or even possibly earlier than, Al-Jabr. The manuscript gives the exact same geometric demonstration as is found in Al-Jabr, and in one case the same example as found in Al-Jabr, and even goes beyond Al-Jabr by giving a geometric proof that if the determinant is negative then the quadratic equation has no solution. The similarity between these two works has led some historians to conclude that algebra may have been well developed by the time of al-Khwarizmi and 'Abd al-Hamid.

(2) Abū al-Hasan ibn Alī al-Qalasādī
Abū al-Hasan ibn ‘Alī al-Qalaṣādī (1412 in Baza, Spain – 1486 in Beja, Tunisia) was an Arab Muslim mathematician and an Islamic scholar specializing in Islamic inheritance jurisprudence. He is known for being one of the most influential voices in algebraic notation since antiquity and for taking "the first steps toward the introduction of algebraic symbolism." He wrote numerous books on arithmetic and algebra, including al-Tabsira fi'lm al-hisab (Arabic: التبصير في علم الحساب‎ "Clarification of the science of arithmetic").

Symbolic algebra
In Islamic mathematics, al-Qalasadi made the first attempt at creating an algebraic notation since Ibn al-Banna two centuries earlier, who was himself the first to make such an attempt since Diophantus and Brahmagupta in ancient times. The notations of his predecessors, however, lacked symbols for mathematical operations. Al-Qalasadi's algebraic notation was the first to have symbols for these functions and was thus "the first steps toward the introduction of algebraic symbolism." He represented mathematical symbols using characters from the Arabic alphabet, where:
• wa means "and" for addition (+)
• illa means "less" for subtraction (-)
• fi means "times" for multiplication (*)
• ala means "over" for division (/)
• j represents jadah meaning "root"
• sh represents shay meaning "thing" for a variable (x)
• m represents mal for a square (x2)
• k represents kab for a cube (x3)
• l represents yadilu for equality (=)

(3) Abū Kāmil Shujā ibn Aslam
Abū Kāmil Shujāʿ ibn Aslam ibn Muḥammad ibn Shujā (c. 850 – c. 930) Abu Kamil (Arabic: ابو كامل‎) for short, was an Egyptian Muslim mathematician during the Islamic Golden Age. He has also been called al-Hasib al-Misri—literally, "the Egyptian calculator."
Unlike the many polymaths of this era—notably al-Khwarizmi, al-Kindi, Ibn al-Haytham (Alhacen in the West), al-Biruni, Ibn Sina (Avicenna), and Ibn Rushd (Averroes)—Abu Kamil was a specialist. His field was algebra.
His mathematical techniques were later adopted by Fibonacci, thus allowing Abu Kamil an important role in introducing algebra to Europe.

Works
His Book on rare things in the art of calculation treated systems of equations whose solutions are whole numbers or fractions and also combinatorics. This work led to later research into the real numbers, solutions of polynomials, and finding roots by later scientists of the age such as al-Karaji and Ibn Yaḥyā al-Maghribī al-Samawʾal. His work The Book of Precious Things in the Art of Reckoning contains general methods for solving linear equations.
He was also the first to treat irrational numbers as algebraic objects. He was the first to accept irrational numbers (often in the form of a square root, cube root or fourth root) as solutions to quadratic equations or as coefficients in an equation. He was also the first to solve three non-linear simultaneous equations with three unknown variables.