A branch of mathematics, which will arithmetic relations can be described and used on behalf of the number of letter symbols, variables, or other mathematical entities to explore (such as vector and matrix), the letter symbols are combined, and especially in accordance with the designated law form equation of the situation next
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No. 2
见“ 代数学 ”。
No. 3
Algebra is the study of numbers and algebra theory and methods of the text, more precisely, is the study of real and complex, as well as branches of mathematics in their coefficients of the polynomial algebra theory and methods. Elementary algebra is the promotion and development of more ancient arithmetic. In ancient times, when accumulated a lot of arithmetic, the number of questions on a variety of solution after, in order to seek a systematic, more general approach to address the relationship between the number of problem arises with the principles of solution of the equation for the center elementary algebra problem. By arithmetic to algebra evolution, which is not in doubt. As for what's algebra generated by this discipline, it is not easy to say clearly. For example, if you think "algebra" refers to the solution bx + k = 0 with the notation techniques such equations. So, this "algebra" in the sixteenth century to develop. If we are not asking for algebraic notation concise as they are now, then produce algebra can be traced back to an earlier era. Westerners will be the third century BC ancient Greek mathematician Diophantus seen as the originator of algebra. In China, algebra problems to express in words appearing on the earlier of the. "Algebra" as a mathematical terms, the official representative of a branch of mathematics used in China, was first developed in 1859. That year, the Qing Dynasty and the British 韦列亚 math at home Shanlan force co-translated English Di Gan wrote it in a book, the name translation is called the "algebra." Of course, the content and methods of algebra, ancient China already produces, such as "Nine Chapters on Arithmetic" in the equation of the problem there. Elementary algebra is central to solving equations, which has long been regarded as scientific understanding of algebra, equations mathematicians also the main focus in the research equation. Its research methods are highly computational. To discuss the equation, the first problem encountered is how the composition of the actual number of algebraic relationships and then list the equation based on the same amount of relationships. So an important part of elementary algebra is algebra. Due to the number of different things in the relationship, forming a substantially Zhengshi elementary algebra, fractions and algebraic radical of these three categories. Is the incarnation of algebraic numbers, and thus in algebra, they can be four operations, subject to the basic laws of arithmetic, but can also be a power of two new operators and prescribing. This operation is usually called six algebra to distinguish contains only four arithmetic operations. In the process of the emergence and development of elementary algebra, the solution of the equation through research, but also to promote the further development of the concept of number, will discuss the concept of arithmetic integer and fractional rational expansion of the range, so that the number includes positive and negative integers, positive and negative scores and zero. This is another important part of elementary algebra, is the expansion of the number of concepts. With rational, elementary algebra to solve the problem greatly expanded. However, some equations in the rational range is still no solution. Thus, the concept in a number of expansion to the real number, which in turn further expansion into the complex. So the range is not within the complex there is still no solution equation must also be extended to the complex re-do? Mathematicians say: no. This is the algebra of a famous theorem - Fundamental Theorem of Algebra. This theorem simply the n equation has n roots. December 15, 1742 letter to the Swiss mathematician Leonhard Euler had done explicitly stated, and later another mathematician, Germany gives a rigorous proof of Gauss in 1799. Analyzed the contents of the above together, the components of the basic content of elementary algebra is: Three kinds number - rational numbers, irrational numbers, complex numbers Three kinds of style - Zhengshi, fractional, radical Central element of the equation - Zhengshi equation, Fenshifangcheng, radical equations and systems. Substantially equivalent to the content of elementary algebra content of modern high school algebra courses _set_, but not identical. For example, strictly speaking, the concept of the number of permutations and combinations to be included in the content of arithmetic; function is to analyze the content of mathematics; inequality solution method to solve the equation a little bit like, but inequality as a method of estimating the value of, essentially within the scope of the analysis of mathematics; coordinate method is the study of analytic geometry ....... These are just a scheduling method for forming history. Elementary algebra is the continuation and extension of arithmetic, elementary algebra research object is to solve arithmetic and algebraic equations. Features algebra is only a limited number of operations. All together there are ten total elementary algebra rules. This is the point of learning algebra need to understand and master's. This ten rules are: Five basic operations law: Addition commutative, associative law of addition, multiplication commutative, associative multiplication, distributive; Two basic properties of the equation: both sides of the equation with a number, the equation unchanged; both sides of the equation is multiplied by a non-zero number, the equation unchanged; Three exponential law: the same base power multiplied by the sum of the base index unchanged; Index of power equal to the base index unchanged want to take; plot of power equal to a power of the plot. Elementary algebra to further the development of the two, one is more a study of unknowns equations; on the other hand is the study of the higher number of high-order equation unknown. At this time, elementary algebra, algebra by the direction toward the development of advanced algebra. (1) ab = 0, a = b (2) a + b = 0, a =-b, b =-a (3) a * b = 0, a = 0 or b = 0
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Encyclopedia
Algebra I Algebra I Chuan geb;. Gung e6pa] A branch l) mathematics (see algebra (al Lo bra ". the word Can be used to form compound words, such as homological algebra (h omologicalal Luo - bra), commutative algebra (commutative al Lo bra), Linear Algebra (Linear al Lo bra), multiple, linear algebra (multilinear al Shao - bra) and topological algebra (toPOlogical al Lo bra). 2) special circumstances operator ring (o potassium rator ring): the domain of body Or the algebra (sometimes as linear algebra or vector exchanged rings on behalf of the Number). Associative algebra (formerly known as "super-complex system" (hypercom mouth ex sys- tems) and non-associative algebra is algebra this sense. 3) algebra (universal al Lo bra) synonyms. Include such Public double e algebra (Boolean al Lo bra), a number of the Yuan Dynasty (unary al Luo - bra), etc. so some of the algebra.
advanced algebra