Introduction to algebra

Introduction to algebra

Modern Mathematics (algebra in English) is a sub-division of mathematics. According to its development, it can be divided into elementary algebra and advanced algebra.

Elementary Algebra is an extension of arithmetic, that is, calculation between numbers, letters, and letter expressions based on the calculation rules of numbers. solving the equation is a central issue in elementary mathematics.

There was a record about the application of the one-dimensional equation in the ayinte paparrus document, which was written about before 1700, in this document, we have used the formula method to solve the quadratic equation of the first element. however, in ancient times, arithmetic, algebra, and ry were intertwined. In Greece, for this reason, algebra became almost an accessory to geometry.

In 100 AD, the ancient Greek mathematician nickelke mark (the first century) wrote an introduction to arithmetic. For the first time, the science of mathematics was separated from ry and independent, setting an example for the establishment of pure substitute mathematics.

In the third century, the Greek mathematician fan tu (about 246-330) published the first mathematical masterpiece, including number theory and indefinite equations-arithmetic. In this book, the lost graph introduces unknown numbers and some operator numbers, which greatly simplifies the expression of algebra. however, most of the symbols of the lost graph are abbreviations of related terms. Therefore, the algebra of the later called lost graph is the abbreviation algebra.

In around 825 AD, the famous Arabic mathematician al-Hualien model (about 780-850) wrote an algebraic book named Kitab-Al Jabr w'al-Mugabala. the original title of the book was the science of restoration (or transfer) and cancellation. In around 1140, Robert translated it into Latin and translated the Arabic Al-jebra into Latin aljebra, the rest of the titles were gradually forgotten, and aljebra finally became the proprietary name of mathematics. as for the translation of aljebra Han into "math", it was in China's Qing Dynasty mathematician Li Shanlan (1811-1882) and the English man Wei liari (1815-1887) it appeared in a book translated in August 1851 by the British Edison mongan.

In China, like in the West, it has a long history to regard algebra as a science of solving equations. in the ninth chapter of arithmetic in the century, the author has a numerical solution to the quadratic equation of the first element (which is also applicable to general high-order equations) and linear equations, and applied negative numbers. in the seventh century, wang xiaotong, a mathematician in the Tang Dynasty, wrote a series of ancient computing classics as the world's first three-dimensional algebraic solutions. After the tenth century, Jia Xian (11th century) and Qin jiuyu (1202-1261) such as the "increment multiplication open method" for the numerical solution for the high-level equation, the "tianyuan" for the column of the one-dimensional high-order equation in the 11th century, and the "four-element technique" in the future, it represents a glorious page in the history of algebra.

The 16th century is a period worth mentioning in the history of algebra in the world. The root solution of cubic and four equations has been solved successively; especially the French mathematician Wei Da (1540-1603), known as the father of algebra, regards algebra as "arithmetic of Classes" to distinguish Arithmetic (arithmetic of numbers ), it also consciously introduced a batch of algebraic symbols and established the "symbol on behalf of mathematics", making it a more general and widely used mathematical division.

In the 18th century, Gauss proved the basic theorem of algebra. In the early 19th century, the Norwegian mathematician team Abel (1802-1829) proved that it was impossible to use the root formula to solve a general five-time equation; in 1832, garova (1811-1832), a number of French experts, used the idea of "group" to completely solve the possibility of using the root formula to solve the problem of algebraic equations. galova's immortal achievement is not only to solve the possibility of using the root formula to solve the algebraic equation, but more importantly, he first proposed the idea of "group. in this way, the generation mathematics is transformed from the science used as the solution to the science used to study the structure of the algebra operation, that is, the generation mathematics is pushed from the elementary algebra to the Higher Algebra, that is, the modern algebra. Therefore, galova is generally called the founder of modern algebra.