The history of ancient Chinese mathematics and its applications has been greatly stimulated in the past few decades by remarkable archaeological discoveries of texts from the pre-Qin and later periods that for the first time have made it possible to study in detail mathematical material from the time at which it was written. By examining the recent Warring States, Qin and Han bamboo mathematical texts currently being conserved and studied at Tsinghua University and Peking University in Beijing, the Yuelu Academy in Changsha, and the Hubei Museum in Wuhan, it is possible to shed new light on the history of early mathematical thought and its applications in ancient China. Attention will also be focused on the development of techniques and justifications given for the problems that were a growing part of the corpus that eventually culminated in the comprehensive Nine Chapters on the Art of Mathematics.