Numbers and Beyond numbers: GC-Queen of the Sciences: A History of Mathematics lecture #7-12

Very important Lesson learned

1. logarithm invented to facilitate multiplication calculation
2. Inertia

7 Chinese Mathematics—Advances in Computation

The Zhoubi Suanjing (Chinese: 周髀算經; Wade–Giles: Chou Pi Suan Ching) is one of the oldest Chinese mathematical texts. "Zhou" refers to the ancient Zhou dynasty (1046–256 BCE); "Bi" means thigh and according to the book, it refers to the gnomon of the sundial. The book is dedicated to astronomical observation and calculation. "Suan Jing" or "classic of arithmetics" were appended in later time to honor the achievement of the book in mathematics.

This book dates from the period of the Zhou dynasty, yet its compilation and addition of materials continued into the Han dynasty (202 BCE–220 CE). It is an anonymous collection of 246 problems encountered by the Duke of Zhou and his astronomer and mathematician, Shang Gao. Each question has stated their numerical answer and corresponding arithmetic algorithm.

The Nine Chapters on the Mathematical Art (九章算術) is a Chinese mathematics book, composed by several generations of scholars from the 10th–2nd century BCE, its latest stage being from the 2nd century CE. This book is one of the earliest surviving mathematical texts from China, the first being Suan shu shu (202 BCE – 186 BCE) and Zhoubi Suanjing (compiled throughout the Han until the late 2nd century CE). Extend place value to 0.1, 0.01. Negative numbers did not recognize as numbers but as an intermediate step.

Around A. D 1000, the Chinese would begin to use zero a placeholder

Liu Hui 劉徽 c. 225- c. 295

Haidao Suanjing (海島算經; The Sea Island Mathematical Manual) was written by the Chinese mathematician Liu Hui of the Three Kingdoms era (220–280) as an extension of chapter 9 of The Nine Chapters on the Mathematical Art. During the Tang Dynasty, this appendix was taken out from The Nine Chapters on the Mathematical Art as a separate book, titled Haidao suanjing (Sea Island Mathematical Manual), named after problem No 1 "Looking at a sea island." In the time of the early Tang dynasty, Haidao Suanjing was selected into one of The Ten Computational Canons as the official mathematical texts for imperial examinations in mathematics.

Zu's pi is accurate to a degree of less than 3 parts in 10 millions.

Sunzi Suanjing (孙子算经; lit. 'The Mathematical Classic of Master Sun/Master Sun's Mathematical Manual') was a mathematical treatise written during 3rd to 5th centuries AD which was listed as one of the Ten Computational Canons during the Tang dynasty. The specific identity of its author Sunzi (lit. "Master Sun") is still unknown but he lived much later than his namesake Sun Tzu, author of The Art of War. From the textual evidence in the book, some scholars concluded that the work was completed during the Southern and Northern Dynasties. Besides describing arithmetic methods and investigating Diophantine equations, the treatise touches upon astronomy and attempts to develop a calendar.

Li Chunfeng (李淳風) (602–670). Shibu Suanjing (十部算经) in 656. These were ten mathematical manuals submitted to the emperor.

Jia Xian (賈憲 ca. 1010–1070) was a Chinese mathematician from Kaifeng of the Song Jia was a palace eunuch of the Left Duty Group.

Li Ye (李冶 1192–1279), born Li Zhi (李治), courtesy name Li Jingzhai published and improved the tian yuan shu method for solving polynomial equations of one variable. Along with the 4th-century Chinese astronomer Yu Xi, Li Ye proposed the idea of a spherical Earth instead of a flat one before the advances of European science in the 17th century. his work, Ceyuan haijing (測圓海鏡, Sea mirror of circle measurements, Mirror like the Ocean, Reflectign the Heaven of Calculation of Circles (written 1248)

Qin Jiushao ( 秦九韶; ca. 1202–1261) courtesy name Daogu (道古)

Zhu Shijie (=朱世傑; pinyin: Zhū Shìjié; Wade–Giles: , 1249–1314), courtesy name Hanqing (漢卿), pseudonym Songting (松庭), . He was a Chinese mathematician during the Yuan Dynasty. Zhu was born close to today's Beijing. Two of his mathematical works have survived. Introduction to Computational Studies (算學啓蒙 Suan hsüeh Ch'i-mong), and Jade Mirror of the Four Unknowns. Siyuan yujian (四元玉鉴), also referred to as Jade Mirror of the Four Origins,is a 1303 mathematical monograph by Yuan dynasty mathematician Zhu Shijie. Zhu advanced Chinese algebra with this Magnum opus.The book consists of an introduction and three books, with a total of 288 problems.

Chinese mathematicians disappears after 13th century.

8 Islamic Mathematics—The Creation of Algebra

Al-Kwarizmi' name is also the origin of algorithm, which is used in mathematics to mean a procedure with clearly prescribed steps. The equal sign "=" was not invented until the 16th century in western Europe.

9 Italian Algebraists Solve the Cubic