Doblhofer, Ernst, Voices in Stone (Paladin, 1973; orig. edn. 1957). Not especially mathematical, but a good account of the decipherment of hieroglyphs and cuneiform texts if you want to follow that up.
Flegg, Graham, Numbers (Penguin, 1984; orig. edn. 1983). A book packed with much more information about numbers and their history than we have time for during the course.
Friberg, Jöran, ‘Methods and Traditions of Babylonian Mathematics’, Historia Mathematics 8 (1981) pp. 277–318. The most recent, full discussion of Plimpton 322, a little more advanced than ours, and what we can learn about how and why Babylonians used mathematics.
MacKie, Euan, Science and Society in Prehistoric Britain (Elek, 1977). A useful and scholarly attempt to see what picture emerges from the results of archaeological and other recent research.
Menninger, Karl, Number Words and Number Symbols (MIT Press, 1969; orig. edn. 1958). More full detail of the history of numbers, particularly attentive to linguistic evidence.
Neugebauer, Otto, The Exact Sciences in Antiquity (Dover, 1969; orig. edn. 1949).A highly readable account by one of the most eminent of modern historians of the period, van der Waerden, B. L., Science Awakening I (Oxford University Press, 1961). A full and carefully considered account of what is known of ancient mathematics, with much more detail about Egyptian and Babylonian problems than we have been able to cover.