In comparison to the Egyptian mathematics, the Sumerian period (3rd dynasty of Ur in Mesopotamia) was much more sophisticated. The Sumers developed a placed-valued sexagesimal system, which differs from the currently world-wide used decimal system only by the base of 60 instead of 10. Thus, for instance, the number 59 would be written as a single Sumerian digit, while the number 61 would be written as two Sumerian digits used for 1, i.e. as 11=1\cdot 60^1+1\cdot 60^0.
Sumerians used clay tablets with numerical notation. Their unique symbols are shown below.
(from Wikimedia, uploaded by Josell7)
The earliest texts contain tables with symbols for 1, 60 and 60^2 as well as \frac {1}{60} and \frac {1}{60^2} and also contain examples of calculations connected with administrative tasks like cattle breeding, or taxes.
The sexagesimal placed-valued system was superior in comparison to the Egyptian number system, however, it still had some ambiguities. In particular, for a long time, the Sumers did not have a symbol for 0. Moreover, the same symbols of numbers could mean different numbers, depending on the context. For instance, 11 could mean 1\cdot 60^1+1\cdot 60^0 or 1\cdot 60^0+1\cdot 60^{-1}.
The remnants of the sexagesimal system can be found in the modern measurements of angles (360^\circ), or of time (60 minutes, 60 seconds).
