Information and Resources for the Final Project

Read these articles about giving a good math talk: Article 1, Article 2, Article 3, Article 4.

First choose your partner (you can work in groups of size 2 or 3) and a topic in history of mathematics in the Islamic World. The topic should include significant amount of mathematics.

Important Note: Please do not choose a topic without looking at resources first. Therefore, get the books (order them from Ohio link if necessary) well in advance of the first deadline.

Timeline and Deadlines for the Project

Proposal: Let me know, in writing, what topic you choose by Friday November 15. You should submit, in writing, your choice of the topic, the group members, what you plan to cover in the presentation and the paper, and main sources you want to use. Also state whether you want to give a talk or poster for the presentation part. If you are doing a topic that we covered in class, make sure you go above and beyond what we did in class and explain how. 1-2 pages would be sufficient for the proposal (one proposal per group).

Outline: Next, you submit an outline of your paper by Wednesday, December 4 (3-4 pages). The more you include, the better (one paper per group).

Presentation: You will give a class presentation (15-20 minutes) during the last week of classes. Then you will give your presentation at NICC on Saturday December 14.

Final Paper: The final paper is due at the official final exam date for this course which is 6:30 pm, Thursday December 19. (You can submit it earlier!) There is no fixed length for the final paper but keep in mind that it is a subtantial paper and must include non-trivial amount of mathematical material. It should be no less than 6-7 pages (1 or 1.5 spaced). One paper per group. Please do citations properly and avoid plagiarism. Your paper will be checked for potential plagisarism issues.

Here are some possible topics to give you an idea and get you started but this is not an exhaustive list. You may choose another topic with the approval of the instructor.

• Check out the links given on the main course web page including the documentaries.
• Lives and works of Islamic mathematicians that are available in Complete Dictionary of Scientific Biography (available as an electronic source through Kenyon). Take a look at this page and this too..
• These articles have many pointers and sources: Forgotten Brilliance, Math in Muslim Heritage, Contributions of Muslims to Math
• Many possible ideas and sources at this page, and more generally here.
• Many suitable topics in the book "The development of Arabic mathematics: between arithmetic and algebra", Roshdi Rashed (translated by A. F. W. Armstrong), Kluwer, 1994. (available at course reserve)
• Combinatorics in Islamic Mathematics. Look at the relevant chapters in
  • The Mathematics of Egypt, Mesopotamia, China, India and Islam, A Sourcebook, Victor J. Katz editor, Princeton U Press, 2007
  • A History of Mathematics: An Introduction, 2nd ed, Victor J. Katz, Addison-Wesley 1998
  • The development of Arabic mathematics: between arithmetic and algebra, Roshdi Rashed (translated by A. F. W. Armstrong), Kluwer, 1994
• Mathematics in Islamic Art and Architecture. You can start by reading these 3 articles: Article1 Article 2 Article 3. Also look at this page and see the books below.
• Islamic Geometric Patterns (notice that there are several books listed at the bottom of the page)
• Geometry Needed by Craftsmen
• Geometry of Artisans,The Mathematics of Egypt, Mesopotamia, China, India and Islam, A Sourcebook, Victor J. Katz editor, Princeton U Press, 2007
• Algebra in the Islamic World: Beginning and Developments (see the books below)
• Ideas of Calculus in Islam and India. Look at these two articles: Paper1, Paper2
• Cryptanalysis of al-Kindi. A starting point is here.
• Al Hazen Problem. Can start by looking at these two articles: Article1, Article 2.
• Ibn al-Haytham and Wilson's Theorem, in "the development of Arabic mathematics: between arithmetic and algebra", Roshdi Rashed (translated by A. F. W. Armstrong), Kluwer, 1994
• Ibn al-Haytham and Perfect Numbers, in "the development of Arabic mathematics: between arithmetic and algebra", Roshdi Rashed (translated by A. F. W. Armstrong), Kluwer, 1994
• Ibn al-Haytam's treatise on the volume of a sphere.
• Ibn al-Haytham and Ideas of Calculus in his measurement of a paraboloid. Check out this paper, and the two books: The Mathematics of Egypt, Mesopotamia, China, India and Islam, A Sourcebook, Victor J. Katz editor, Princeton U Press, 2007; Calculus and Its Origins, by D. Perkins, MAA, 2012.
• Construction of a Perfect Compass and other geometrical instruments, The Mathematics of Egypt, Mesopotamia, China, India and Islam, A Sourcebook, Victor J. Katz editor, Princeton U Press, 2007
• Algebra and Linguistics: Combinatorial Analysis in Arabic Science, in "the development of Arabic mathematics: between arithmetic and algebra"
• Numerical Equations, in "the development of Arabic mathematics: between arithmetic and algebra"
• Numerical Analysis and extraction of nth roots, our tetxbook and "the development of Arabic mathematics: between arithmetic and algebra"
• Number Theory in Islamic Mathematics, "the development of Arabic mathematics: between arithmetic and algebra"
• Thabit b. Qurra (his life and contributions to mathematics), A History of algebra : from al-Khwarizmi to Emmy Noether, B.L. van der Waerden
• Spherical Geometry and Trigonometry in Islam (Chapter 6 in our textbook)
• V. Robert's paper on connections between Copernicus and Ibn al-Shatir.
• Astronomy and Astrology in the Medieval Islamic World
• Muslim daily prayers and mathematics required to determine them, In synchrony with the heavens : studies in astronomical timekeeping and instrumentation in medieval Islamic civilization, by David A. King, 2004.
• Look at the Exercises and Bibliography at the end of each chapter of the textbook to get more ideas for possible project topics.

Some Useful Books and Other Sources for the Project (can get ideas for possible projects from these sources too)

• Complete Dictionary of Scientific Biography (available as an electronic source through Kenyon),: Charles Scribner's Sons, 2008. 27 vols (searching for names can be tricky!)
• The Mathematics of Egypt, Mesopotamia, China, India and Islam, A Sourcebook, Victor J. Katz editor, Princeton U Press, 2007 (in course reserve)
• The development of arabic mathematics: between arithmetic and algebra, R. Rashed, Kluwer 1994 (in course reserve)
• A History of Mathematics: An Introduction, 2nd ed, Victor J. Katz, Addison-Wesley 1998
• A History of algebra : from al-Khwarizmi to Emmy Noether, B.L. van der Waerden
• Introduction to the history of science, George Sarton, 1975
• Arabic Mathematical Sciences, R. Lorch, Variorum 1995
• An Episodic History of Mathematics, Steven G. Krants, MAA publication 2010
• Calculus and Its Origins, by D. Perkins, MAA publication, 2012.
• 1001 Inventions: Muslim Heritage in Our World, Salim T S Al-Hassani, 2nd ed, 2007, Foundation for Science Technology and Civilisation (UK)
• Studies in the Islamic Exact Sciences, E.S. Kennedy, colleagues, and former students, American University of Beirut, 1983
• In synchrony with the heavens : studies in astronomical timekeeping and instrumentation in medieval Islamic civilization, by David A. King,Leiden ; Boston : Brill, 2004.
• Al-Khwarizmi : the beginnings of algebra, edited, with translation and commentary, by Roshdi Rashed, SAQI, 2009.
• The Algebra of Mohammed ben Musa (transl. by F. Rosen), London: 1831. Another edition Honolulu, HI : University Press of the Pacific, 2003
• The Algebra of Abu Kamil: Kitab fi al-Jabr wa'l-muqabala, University of Wisconsin Press, 1966. Also check out this article.
• The Algebra of Omar Khayyam, by Daoud S. Kasir, Teachers College Columbia University, 1931
• Algebra wa Al-Muqabala of Omar Khayyam, translated by Roshdi Khalil, Garnet Publishing, 2008.
• Pathfinders: The Golden Age of Arabic Science, J. Al-Khalili, Allen Lane, 2010
• Arabic mathematical sciences : instruments, texts, transmission, R. Lorch, Variorum, 1996
• Science in medieval Islam : an illustrated introduction, Howard R. Turner, U of Texas Press, 1999.
• Islamic Geometric Patterns, R. Broug, Thames& Hudson, 2008.
• Islamic art and geometric design [kit]; activities for learning, the Metropolitan Museum of Art,New York, N.Y. : Metropolitan Museum of Art, c2004
• Islamic design : a genius for geometry, D. Sutton, Walker & Co, 2007
• Islamic art and architecture : the system of geometric design, Issam El-Said, Reading, UK, 1993.
• al-Biruni-Instruction in the Elements of the Art of Astrology
• Astronomy and Astrology in the Medieval Islamic World, by E. S. Kennedy, Variorum, 1998 (available at Kenyon library)
• The Muslim Heritage web site
• A History of Islamic Science
• Bibliography of Mathematics in Medieval Islamic Civilization
• Bibliography by Topic of the Mathematical Sciences in Medieval Islamic World
• Mathematics in Medieval Islam
• A Digital Library