Detailed definition of algebra:
Algebra is a branch of mathematics. Traditional algebra uses expressions with characters to perform arithmetic operations, and characters represent unknowns or undetermined numbers. If division is not included, every expression is a rational coefficient polynomial. For example:1/2xy+1/4z-3x+2/3 An algebraic equation expresses conditions imposed on variables by making polynomials equal to zero.
If there is only one variable, then what satisfies this equation will be a real number or a complex number-its root. Algebraic number is the root of the equation. Galois theory, algebraic number theory, is one of the most satisfactory branches of mathematics. Galois, who established this theory, died in a duel at the age of 2 1.
Algebraic traceability:
"Algebra", as a proprietary mathematical term, represents a branch of mathematics. It was officially used in China, and it was first used in 1859.
That year, Li, a mathematician in Qing Dynasty, and Leali, an Englishman, translated a book written by Di Yaogan, an Englishman. The name of the translation is algebra. Of course, the contents and methods of algebra have long been produced in ancient China. For example, there are equation problems in "Nine Chapters of Arithmetic".
Composition of algebra:
Elementary algebra:
Elementary Algebra Operation In ancient times, when a large number of solutions to various quantitative problems were accumulated in arithmetic, in order to find a systematic and more general method to solve various quantitative relations, elementary algebra centered on the principle of solving algebraic equations was produced.
Advanced algebra:
Advanced algebra is a general term for the development of algebra to an advanced stage, including many branches. Higher algebra offered by universities generally includes linear algebra and polynomial algebra.
On the basis of elementary algebra, advanced algebra further expands the research object and introduces many new concepts and quantities which are completely different from usual ones, such as set, vector and vector space. These quantities have operational characteristics similar to numbers, but the research methods and operational methods are more complicated.