1. The beginning of the Greek philosophy and mathematics.

2. The discovery of incommensurability and its consequences.

3. The first crisis of mathematics. The way out of this crisis.

4. The famous problems of Greek antiquity. Squaring of the circle, trisection the angle, duplication of the cube.

5. "Nonclassical" solving of clasical problems. Hippokrates, Hippias, Archytas, Menaechmus, Dinostratus.

6. The problems with infinity. Zeno of Elea and his arguments about motion. Theodorus of Cyrene and Theaetetus, Eudoxus and his method of exhaustion.

7. Eudoxus, theory of proportion.

8. Socrates, Plato, Aristotle.

9. Archimedes, his life, work and activities.

10. Eratosthenes and his work. Apollonius, Claudius Ptolemy.

11. Diophantus of Alexandria and his Arithmetica. Pappus and his Mathematical Collection.

This course is devoted to ancient Greek mathematics.