### Designing a Course in Ancient Mathematical Astronomy

During Fall 2009, I designed a new course at SUNY Oneonta with the title *Ancient Mathematical Astronomy*. The course was based on my academic expertise and the idea of incorporating design and construction of objects into my teaching.* Ancient Mathematical Astronomy* is a 300-level course that provides an introduction to and a survey of the history of the astral sciences from ancient Mesopotamia to Copernicus. Beginning with astronomical records kept by Mesopotamian priests, the course traces the history and development of astronomy with an emphasis on the role of both mathematics and observation in the formation of astronomical theories and models. As an important part of the course, the students, divided into groups, are asked to research and design an astronomical instrument of their choice. The parts for the instruments are constructed by Allen Anderson, after which the instruments are assembled by the students. The instruments should ideally be tested by simple observations, though the feasibility of this step depends on the instrument in question, time available, and the weather.

##### Course objectives

By incorporating the practical component of instrument construction into the course, I seek to root mathematical theory in practical application with the aim of providing my students with a solid understanding of how the models of mathematical astronomy work. The idea is that the course should provide an attractive elective for our Mathematics majors that draws on both the history of mathematics and applied mathematics. In fact, one of the justifications for adding *Ancient Mathematical Astronomy* as a permanent course was that it would provide an elective with a focus on applied mathematics, an underrepresented branch of mathematics in my department.

The main lesson that I want my students to take away from the course is knowledge of the history and development of the astral sciences and their role in world intellectual history. More specifically, I want the students to understand and appreciate the role played by mathematics in the formation of astronomical theories and models, and, more generally, in the formation of theories and models in the sciences. Another aspect that I seek to emphasize is awareness of natural phenomena that were hugely important to our ancestors in the past, but which now mostly pass unnoticed due to the use of modern technology.

##### Course prerequisites

Prerequisites are an important consideration for any new course, and I gave serious thought to the prerequisites for *Ancient Mathematical Astronomy*. On the one hand, I did not want the course to be too restricted; on the other hand, I wanted to have mature students with sufficient mathematical skills to handle the difficult material of the course. After some reflection on the matter, I decided to make *Ancient Mathematical Astronomy* a 300-level course and require that students enrolling in it must have passed either *Calculus II* or *Discrete Mathematical Structures* with a grade of C or better (the latter course introduces students to mathematical proof at SUNY Oneonta). I felt that completion of either of these courses would ensure that a student possessed sufficient mathematical maturity and capability. The reason for requiring only one of the courses and not both, which is generally the case for higher-level mathematics courses at SUNY Oneonta, is that I did not want to exclude Physics and Astronomy majors or minors, who are required to take *Calculus II* but only rarely take *Discrete Mathematical Structures.* (The Department of Physics and Astronomy at SUNY Oneonta offers a major in Physics and minors in Physics and Astronomy.) At the same time, I did not want Mathematics majors who had taken *Discrete Mathematical Structures* but not yet *Calculus II* to have to wait to take the course, which is offered infrequently.

##### Course modules

SUNY Oneonta operates with a semester system, each of the two semesters per year being 15 weeks long, including a week for finals. Regular classes meet three times per week for 50 minutes per meeting.

The theoretical parts of the course are divided into six modules:

*Introduction to ancient astronomy* (approx. 3 weeks), which makes students familiar with ancient astronomy and cosmological models, and introduces them to various astronomical instruments.
*The birth of mathematical astronomy* (approx. 2 weeks), the focus of which is the formation of ancient Mesopotamian astronomy, including a discussion of how belief in astral omens led to careful observational records.
*Ancient Greek and Hellenistic astronomy* (approx. 3 weeks), which explores the formation of Greek geometrical models of the heavens, starting with early Greek astronomy and ending with Ptolemy and the *Almagest.*
*Indian astronomy* (approx. 2 weeks), which explores classical Indian astronomy, though pre-classical Indian astronomy is also discussed.
*Islamic astronomy* (approx. 2 weeks), which explores the history and development of astronomy in the Islamic world.
*Astronomy in Medieval and Renaissance Europe* (approx. 2 weeks), which examines the reception of astronomy from the east in Europe and the development it took there.

The mathematical content of the course includes numerical models of planetary motion from ancient Mesopotamia, geometric models of planetary motion from ancient Greece and other cultures, spherical geometry, and spherical trigonometry. These topics are by no means simple, and it requires maturity and dedication on the part of the students to master them.

##### Course textbook

For the course textbook I decided on James Evans' excellent *The History and Practice of Ancient Astronomy* (Oxford University Press, 1998). It is a book that I have benefited from in my own studies and research, and one that I felt would be sufficiently accessible to the students in the course. In fact, the students who have taken the course have expressed to me that they enjoyed the textbook, which they found informative and helpful.