The most important part to understand about Chinese mathematics is the way it differs from the Greeks. There is no axiomatic development of mathematics. Chinese mathematics, like the language, is very concise. It was based on the problems of the new and developing calendar, trade, land measurements, architecture, government records and taxes. By the fourth century of BC the counting board was very useful for agriculture reasons and schooling. Counting boards were no used by any other civilizations.
Our knowledge of Chinese mathematics is very sketchy until 1984 the Suan shu shu (a book of arithmacy) was discovered. It was written on bamboo strips. The next important book is a sixteen chapter work called Suanshu written by Du Zhong and another twenty six piece called Xu Shang by Xu Shang. It is a book about computational prescriptions.
The Egyptians had a writing system based on hieroglyphics, which are little symbols with meanings, from around 3000 BC. Some words are easy to understand like the symbol for bird is a little bird. The numbers were based on a 10 numeral system of hieroglyphics. Adding and subtracting numbers was somewhat easy, although dividing was tougher. Not much else is known about the early mathematics.
Today astronomy requires a deep understanding of math and physics. The Greeks had thought of philosophy from the time of the Thales. Although Thales if famed for his prediction of the eclipse, many doubt he had much knowledge of astronomy himself, yet he brought back some knowledge of Egyptian and maybe a little Babylonian math.
Around 700 BC astronomy was basically all to do with time-keeping. Farmers would base their planting strategies on the rising and setting of the moon. There was an early time scale based on 12 months in a year and 30 days in a month. This did not work out well because the moon rapidly changes in a 30 day period. The calendar today is based on the roan idea of 12 months in a year and a number that varies from 28-31 days in a month.