Dr. Xiaomin Zhang: Mathematics Department, School of Science, Ningbo University
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Mathematical English 1: Mathematics, Equation and Ratio
trigonometry and algebra, in which only the constants were considered. The rapid development of industry in 17th century promoted the progress of economics and technology and required dealing with variable with variable quantities. The leap from constants to variable quantities brought about two new branches of mathematics -- analytic geometry and calculus, which belong to the higher mathematics. Now there are many branches in higher mathematics, among which are mathematical analysis, higher algebra, differential equations, function theory and so on. Mathematicians study concepts and propositions. Axioms, postulates, definitions and theorems are all propositions. Notations are a special and powerful tool of mathematics and are used to express conceptions and propositions very often. Formulas figures and charts are full of different symbols. Some of the best know symbols of mathematics are the Arabic numerals 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, and signs of addition “+”,
Dr. Xiaomin Zhang: Mathematics Department, School of Science, Ningbo Universitylish 1: Mathematics, Equation and Ratio
Notations
mathematical analysis The area of mathematics generally taken to include those topics that involve the use of limiting process. Thus differential calculus and integral calculus certainly come under this heading. Besides these, there are other topics, such as the summation of infinite series, which involve infinite processes of this sort. The term analysis has also come to be used to indicate a rather more rigorous approach to the topics of calculus, and to the foundations of the real number system. logical deductions The logico-deductive method, a system of inference where conclusions (new knowledge) follow from premises (old knowledge) through the application of sound arguments.
induction The process of deriving general principles from particular facts or instances.
axioms, postulates The basic assumptions underlying a given body of deductive knowledge. They are accepted without demonstration. All
Dr. Xiaomin Zhang: Mathematics Department, School of Science, Ningbo University
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Mathematical English 1: Mathematics, Equation and Ratio
other assertions (theorems, if we are talking about mathematics) must be proven with the aid of the basic assumptions. Axiom , in classical terminology, referred to a self-evident assumption common to many branches of science. At the foundation of the various sciences lay certain basic hypotheses that had to be accepted without proof. Such a hypothesis was termed a postulate . The postulates of each science were different. Their validity had to be established by means of real-world experience. The classical approach is well illustrated by Euclid's elements, where we see a list of axioms and postulates. A1 Things which are equal to the same thing are also equal to one another.
Mathematical English 1: Mathematics, Equation and Ratio
Mathematical English
Dr. Xiaomin Zhang Email: zhangxiaomin@
Dr. Xiaomin Zhang: Mathematics Department, School of Science, Ningbo University
A2 If equals be added to equals, the wholes are equal. A3 If equals be subtracted from equals, the remainders are equal. A4 Things which coincide with one another are equal to one another. A5 The whole is greater than the part. Dr. Xiaomin Zhang: Mathematics Department, School of Science, Ningbo University
Dr. Xiaomin Zhang: Mathematics Department, School of Science, Ningbo University
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Mathematical English 1: Mathematics, Equation and Ratio
subtraction “−”, multiplication “×”, division “÷” and equality “=”. The conclusions in mathematics are obtained mainly by logical deductions and computations. For a long period of the history of mathematics, the centric place of mathematics was occupied by the logical deductions. Now, since electronic computers are developed promptly and used widely, the role of computation becomes more and more important. In our times, computation is not only used to deal with a lot of information and data, but also to carry out some work that merely could be done earlier by logical deductions, for example, the proof of most of geometrical theorems.
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Mathematical English 1: Mathematics, Equation and Ratio