Summary

Background history and geography of Greek civilization. In particular, we need to understand the place of Greek culture in the genealogy of Western civilization. There are profound differences in the ways that Greeks organized their culture in comparison to the ancient cultures of Egypt and Mesipotamia.  Also, the 'Greece' that is important for history of mathematics is different in many ways from the usual conceptions of 'Greece'.  
Look at maps from Historical Atlas.
Introduction to Greek mathematics and comparison with ANE and Egypt.
The Classical Ideal.
Early Greek mathematics.
Problems of interpretation and evidence.
Pythagorean number theory: special types of numbers; figurate numbers; theory of means.
Incommensurability; anthyphareisis.
Music and mathematics.

Links

Introduction to Greek civilization

Reading

B.L. van der Waerden, Science Awakening, 92-102.
'Pythagoras of Samos,' DSB.
D.M. Burton History of Mathematics, Sections 3.2 and 3.3.
A. Jones, 'Greek Mathematics to AD 300', in I. Grattan-Guinness, Companion Encyclopedia of the History and Philosophy of Mathematics, 46-57.