It is possible to provide a basic (though only partial) outline of what was taught at Ottoman madrasas. Students would study from the books of (sarf), syntax (nahiv) and logic (mantik) and then hadith and commentary on the Qur'an (tefsîr). Other subjects studied included mathematical sciences and philosophy (hikmet) and jurisprudence (fikih).
This short article is taken from the full article which is available here as a PDF file
From the start of their education to the very end a student at an Ottoman madrasa would be required to read a large number of books in a number of different fields of study. There are differences with regard to the subjects a student would study at the various madrasas from century to century, up until the founding of the Dârü’l-hilâfeti’l-aliyye Madrasas during the Second Constitutional period. It is possible to follow these changes by examining the education of Tasköprizâde Ahmed b. Isâmeddin who lived in the sixteenth century and the classes he later gave as a teacher as well as by examining the education of Kâtib Chelebi in the seventeenth century. In addition, one is able to obtain detailed information about the subject from a little-known source about madrasa education titled Kevâkib-i Seb’a (Seven Planets) written in the eighteenth century (1742) at the request of the French ambassador to Istanbul, Marquis de Villanueva. It is also possible to learn something about madrasa education and methods of instruction for that century from a book by the Italian Abbot Toderini titled De La Littérature des Turcs. For the nineteenth century it is possible to get quite a clear picture and conduct a detailed examination of the nature of madrasa education from the autobiography of Ahmed Cevdet Pasha.
It appears that the textbooks used for instruction at madrasas were, in the first instance, prepared so as to provide every Muslim individual with the knowledge required for religious and worldly matters. Clearly, the most fundamental goal of madrasa education was to ensure that Muslims be brought up as knowledgeable and morally correct individuals.
The legal code (kanûnnâme) pertaining to education prepared during the reign of Suleyman the Magnificent indicates that it is necessary to understand the mystery of creation, to establish a state which operates in an orderly fashion and to reveal the realities of the world in order to ensure the perpetuity of order in the world and the well-being of humanity, and that in order for all of these things to be realized it is essential that one must comprehend the universe created by God as well as learning the teachings of the prophets. To the extent that it can be clearly determined from the code written in the dense style used for official documents during that period, the views of Ottoman administrators with regard to education indicate that the purpose of education in the first instance involves the pursuit of science and wisdom (hikmet) and then an explication of virtue, talent, religion and the serîat, in that order, as well as the development of human faculties and capacities. The sultan was held personally responsible for ensuring that all of this was carried out.
During the course of their education, the books a student would read were ordered as follows. The first three were morphology (sarf), syntax (nahiv) and logic (mantik). The last two were hadith and commentary on the Qur’an (tefsîr). In between the first three studies and the last two, subjects such as elocution (âdâb-i bahs), preaching (vaaz), rhetoric (belâgat), study of philosophical theology (kelâm), philosophy (hikmet), jurisprudence (fikih), inheritance (ferâiz), tenets of faith (akaid) and legal theory and methodology (usûl-i fikih) were pursued. There would occasionally be differences in the presentation and ordering with respect to these studies.
Kevâkib-i Seb’a provides us with very valuable information about the manner in which students proceeded with their lessons. The work tells us that students had five classes a week and that each class consisted of a few lines (satir), which were examined. Further, it informs us that they studied eight or nine hours for each lesson the day before it was given, that on the following day each student would read passages from the text to the teacher in turn and that after the teacher presented his interpretation each student would present his perspective on the subject to the teacher and they would engage in a discussion. After having thoroughly analysed and researched the lesson, the students would return to their rooms and continue studying until they were once again in the presence of their teacher at the next day’s lesson.
Mathematical sciences such as arithmetic, geometry, algebra and astronomy and natural sciences such as classical physics were taught in Ottoman madrasas. Most of the autobiographies examined indicate that these sciences were studied after divine philosophy (hikmet) and prior to the most esteemed subject of Commentary on the Qur’an (tefsîr). Kevâkib-i Seb’a indicates, however, that these subjects were dealt with in a less formal manner in the Qur’anic theology (kelâm) class in the process of discussing such books as Serh al-Mevâkif and Serh al-Makasid:
“As much as books such as Serh al-Mevâkif and Serh al-Makasid pertain to theology (kelâm) they contain all of the auxiliary sciences, divine philosophy, astronomy, geometry and arithmetic. Geometry and arithmetic are easily apprehend able subjects, and because they do not require much deep thought are not studied as separate subjects. They are taken up along with the above-mentioned sciences. There is a book titled Eskâl-i Te’sis in geometry at the iktisar level that they would read. Following that, they would read Euclid with its proofs at the istiksa level. For arithmetic at the iktisar level there is Bahâiyye, which they would read. Subsequently, they would report on Ramazan Efendi and Culli, which were close to the iktisad level. Because astronomy involves the use of the imaginative powers and supposition and is therefore more difficult than geometry, they study that later as a separate subject. It is offered at the appropriate level. It is common knowledge that scholars do not weary of the temperament of students and always give Tuesdays and Fridays off from classes in order to encourage them in their studies. Students use those two days for the preparation of materials they need and during the summertime they go off on trips and picnics. Even there they do not remain idle, but undertake discussions of arithmetic, geometry, astrolabes, land surveying, Indian, Coptic and Ethiopian arithmetic, parmak hisâbi (abacus), mechanics and other such sciences which do not require independent lessons. During the winter, they engage in conversation, devote themselves to solving puzzles (muammâ) and riddles, to mukadarat (measuring and comparing), to history, poetry, prosody and to classical dîvân poetry. Some of them are occupied with the occult sciences, but the teachers do not allow them to follow such pursuits because such subjects occupy too much of their time”.
From De la Littérature des Turcs written by Toderini, who was resident in Istanbul between October 1781 and May 1786, we learn that there were teachers instructing young children in geometry and that some time was allocated between rhetoric and philosophy lessons for this area of mathematics. He says that he visited the Vâlide Madrasa twice and that he observed the students had assembled to listen to their geometry lesson and that they were using an Arabic translation of Euclid.
 C. Izgi, Osmanli Medreselerinde Ilim, 1 (Riyazî Ilimler), 69-77.