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Combining Strands of Many Colors: Episodes from Medieval Islam for the Mathematics Classroom - About the Author / References / Additional Resources

Randy K. Schwartz (Schoolcraft College)

About the Author

Randy K. Schwartz holds degrees in mathematics from Dartmouth College and the University of Michigan. He is a Professor of Mathematics at Schoolcraft College, a community college in Livonia, Michigan, where he has taught since 1984. At Schoolcraft, his teaching focuses on preparing students for careers in engineering, science, health care, and business. Prof. Schwartz is a member of the Commission on the History of Science and Technology in Islamic Societies (CHSTIS), and has participated in several international conferences on the history of Arab mathematics. In 2000, he was awarded the Democracy in Higher Education Prize (National Education Association) for his essay, “Unity in Multiplicity: Lessons from the Alhambra,” an argument for a multicultural approach in mathematics education.


Berggren, J. Lennart. Episodes in the Mathematics of Medieval Islam. New York: Springer-Verlag, 1986.

Chabert, Jean-Luc (ed.). A History of Algorithms: From the Pebble to the Microchip. New York: Springer-Verlag, 1999.

Edwards, A. W. F. Pascal’s Arithmetical Triangle. London: Charles Griffin & Company, 1987.

Farès, Nicolas. “Le Calcul du Maximum et la ‘Dérivée’ Selon Sharaf al-Din al-Tusi.” Arabic Sciences and Philosophy: A Historical Journal 5 (1995): 219-237.

Houzel, Christian. “Sharaf al-Din al-Tusi et le Polygône de Newton.” Arabic Sciences and Philosophy: A Historical Journal 5 (1995): 239-262.

Joseph, George Gheverghese. “Foundations of Eurocentrism in Mathematics.” Race & Class 28 (1987): 13-28.

Joseph, George Gheverghese. The Crest of the Peacock: Non-European Roots of Mathematics, Second edition. Princeton: Princeton University Press, 2000.

Katz, Victor J. “Ideas of Calculus in Islam and India.” Mathematics Magazine 68:3 (June 1995), pp. 163-74.

Katz, Victor J. “Combinatorics and Induction in Medieval Hebrew and Islamic Mathematics.” In Vita Mathematica, edited by Ronald Calinger, pp. 99-106. Washington, D.C.: Mathematical Association of America, 1996.

Katz, Victor J. A History of Mathematics: An Introduction, Third edition. Boston: Addison-Wesley, 2009.

Kline, Morris. Mathematical Thought from Ancient to Modern Times. New York: Oxford University Press, 1972.

Lamrabet, Driss. Introduction à l’Histoire des Mathématiques Maghrebines. Rabat, Morocco: Imprimerie El maârif Al Jadida, 1994.

Lesser, Lawrence M. “Reunion of Broken Parts: Experiencing Diversity in Algebra.” Mathematics Teacher 93 (January 2000): 62-67.

Niman, John, and Jane Norman. “Mathematics and Islamic Art.” American Mathematical Monthly 85 (June-July 1978): 489-490.

Özdural, Alpay. “Mathematics and Arts: Connections between Theory and Practice in the Medieval Islamic World.” Historia Mathematica 27 (2000): 171-201.

Rashed, Roshdi. The Development of Arabic Mathematics: Between Arithmetic and Algebra. Dordrecht, Netherlands: Kluwer Academic Publishers, 1994.

Rosen, Frederic (ed.). The Algebra of Mohammed ben Musa [al-Khuwarizmi]. London: Oriental Translation Fund, 1831.

Schwartz, Randy K. “Unity in Multiplicity: Lessons from the Alhambra.” Thought and Action 17 (Summer 2001): 63-75. Available at

Schwartz, Randy K. “Adapting the Medieval ‘Rule of Double False Position’ to the Modern Classroom.” In Amy Shell-Gellasch and Richard Jardine (eds.), Mathematical Time Capsules. Mathematical Association of America, forthcoming.

Shen Kangshen, John N. Crossley, and Anthony W.-C. Lun. The Nine Chapters on the Mathematical Art: Companion and Commentary. Oxford: Oxford University Press, 1999.

Sigler, Laurence E. (ed.). Fibonacci’s Liber Abaci: A Translation into Modern English of Leonardo Pisano’s Book of Calculation. New York: Springer-Verlag, 2002.

Van Brummelen, Glen. The Mathematics of the Heavens and the Earth: The Early History of Trigonometry. Princeton: Princeton University Press, 2009.

Additional Resources on Mathematics in the Medieval Middle East

Abdeljaouad, Mahdi. “Quelques Éléments d’Histoire de l’Analyse Combinatoire.” Journées Nationales 2003 de l’Association Tunisienne des Sciences Mathématiques. Available at

Berggren, J. Lennart. “History of Mathematics in the Islamic World: The Present State of the Art.” Middle East Studies Association Bulletin 19 (1985): pp. 9-33.

Berggren, J. Lennart. “Mathematics and Her Sisters in Medieval Islam: A Selective Review of Work Done from 1985 to 1995.” Historia Mathematica 24 (1997): pp. 407-440.

Covington, Richard. "Rediscovering Arabic Science." Originally published in Saudi Aramco World (May/June 2007): pp. 2-16. Available at

Djebbar, Ahmed. Enseignement et Recherche Mathématiques dans le Maghreb des XIIIème - XIVème siècles, doctoral thesis. Orsay, France: Université de Paris-Sud (Publications Mathématiques d’Orsay no. 81-02), 1981.

Djebbar, Ahmed. Mathematics in the Medieval Maghrib: General Survey on Mathematical Activities in North Africa. Available at

Langermann, Y. Tzvi, and Shai Simonson. “The Hebrew Mathematical Tradition.” In Mathematics Across Cultures: A History of Non-Western Mathematics, ed. by Helaine Selin, pp. 167-188. Dordrecht, Netherlands: Kluwer Academic Publishers, 2000.

Oaks, Jeff. “Bibliography by Topic of the Mathematical Sciences in the Medieval Islamic World.” Available at

Rashed, Roshdi, ed. Encyclopedia of the History of Arabic Science, three volumes. New York: Routledge, 1996, 2000. Volume 2, “Mathematics and the Physical Sciences.”

Al-Samaw’al ben Yahyâ, Al-Bahir en Algèbre. Trans. by Salah Ahmad and Roshdi Rashed. Damascus: Univ. of Damascaus, 1972.

Sesiano, Jacques. “Islamic Mathematics.” In Mathematics Across Cultures: A History of Non-Western Mathematics, ed. by Helaine Selin, pp. 137-165. Dordrecht, Netherlands: Kluwer Academic Publishers, 2000.

Smith, John D. “The Remarkable Ibn al-Haytham.” The Mathematical Gazette 76 (March 1992), pp. 189-198.

Randy K. Schwartz (Schoolcraft College), "Combining Strands of Many Colors: Episodes from Medieval Islam for the Mathematics Classroom - About the Author / References / Additional Resources," Convergence (November 2010), DOI:10.4169/loci003546