A Study On The Mathematical Works Of Zhang Dunren

Zhang Dunren(1754-1834),was bom in Yangcheng City,Jiangxi province,and his another name was Guyu.He was a famous Sinologist and mathematician in the middle of Qing Dynasty.He has served as a magistrate in Nangong,Jiangxi,Gao'an,Luling and other places.He has also served as a magistrate of Tonggu,Chuansha,Jiangning,Yangzhou,Nanchang and Ji'an.When he was old,he went to Jinling for the aged because he was seriously ill.His mathematical works included Qiu Yi Suan Su(????),Kai Fang Bu Ji(????)and Ji Gu Suan Jing Xi Cao(??????).In the years of Zhang Dunren's life,mathematicians attached great importance to the study o f ancient mathematics,he himself also attached great importance to the latest developments in ac ademia,and often discussed mathematics with his friends at that time.Some obscure and inco mprehensible parts of his ancient mathematical works were analyzed in a deep and simpl e way.He has made great contributions to the development of traditional mathematics in the aspects of "Da Yan Zong Shu Shu(?????)" and "Kai Fang Shu(???)",whic h is also the main content of this paper.Chapter 1 introduces Zhang Dunren's life based on some original documents and research documents.Chapter 2 embodies the characteristics of its algorithm step by step through analyzing Zhang Dunren's understanding of "Da Yan Zong Shu Shu(?????)”.This chapter mainly analyzes the contents of Qiu Yi Suan Shu(????)in detail and summarizes its characteristics by selecting typical topics as examples from the middle volume and the next volume.Chapter 3 focuses on the discussion of the first volume of Kai Fang Bu Ji(????),the second to eighth volumes mainly record the specific equation of the process,this chapter will select typical topics to be interpreted in detail,trying to use the current symbolic mathematics to explain Zhang Dunren's contributions to the"Kai Fang Shu(???)”.Chapter 4 selects some classical topics from the Book of Ancient calculation to explain Zha ng Dunren's interpretation of the book Ji Gu Suan Jing Xi Cao(??????),which is more convenient than Wang Xiaotong's original works.At the end of this paper,Zhang Dunren's mathematical achievements are summarized and e valuated objectively based on the above analysis and research.I think that Zhang Dunren has co ntributed to the interpretation and dissemination of the quintessence of estimation,but he has fail ed to surpass the level of ancient books as a whole.