* Mathematics: This was a core part of her expertise, encompassing geometry, arithmetic, and astronomy. Her work on conic sections and astronomy suggests a deep understanding of advanced mathematical concepts.
* Philosophy: She was a Neoplatonist philosopher, teaching and commenting on the works of Plato, Aristotle, and other prominent thinkers. Her education would have included extensive study of metaphysics, ethics, and logic.
* Astronomy: Closely related to mathematics, her astronomical knowledge was significant enough to contribute to the field.
* Rhetoric and Literature: As a public lecturer and teacher, she must have been highly skilled in rhetoric, the art of persuasive speaking and writing. Her education would have encompassed the classics of Greek literature.
* Possibly other sciences: Given the breadth of knowledge in the Alexandrian school, she likely had some exposure to other sciences like medicine.
It's important to note that her education was likely informal, yet highly rigorous, probably including both private tutoring and participation in the vibrant intellectual life of the Library of Alexandria and its associated schools. Her father, Theon of Alexandria, a renowned mathematician and astronomer, was undoubtedly a major influence and likely her primary instructor in many subjects. The highly intellectual atmosphere of Alexandria itself provided a unique opportunity for advanced learning, connecting her to a network of scholars and thinkers.