查询词典 constructive mathematics

The early twentieth century saw great advances in mathematics and also in mathematical logic and the foundations of mathematics.

20世纪初看到了数学的伟大进步，并在数理逻辑和数学基础。

This paper proves strictly the soundness of a formula of the logarithm function of a complex variable and points out the wrong conclusion concerning it in《Engineering Mathematics-Functions of a Complex Variable》compiled by the Mathematics Teaching and Research Section of Xi an Jiaotong University.

本文严格证明了关于复变量对数函数的一个公式的正确性，同时指出了西安交通大学数学教研室编写的《工程数学———复变函数》一书中有关结论的错误。

In the development of digital contents of mathematics, it is mainly to adopt the concepts of iteration and vision to combine dynamic geometry software GSP (The Geometer's Sketchpad) with its characteristic of dynamics, to use the concepts of iteration, specialization and generalization to develop digital contents of mathematics.

在数位内容的研发方面，主要是以递回及视觉化的概念，在动态几何软体GSP The Geometer's Sketchpad ）上，结合其动态呈现的特性，运用「递回」、及「特殊化与一般化」的概念，研发数学数位内容。

I from as follows 5 go to design teaching method, effort practice, brave reform, promote student of overall development:let the student is in the reality scenario experience and comprehension mathematics, development its space idea;encouragement student independence thinking, leading student independence investigate, cooperation exchanges;in the teaching process adoption of the method should make student thoroughly from each aspect comprehension, encouragement work°out problem strategy of diversification;in the teaching process should availably usage indirect method;in the teaching process should progressively the development student's mathematics speech.

我从如下五个方面去设计教法，努力实践，大胆革新，促进学生的全面发展：让学生在现实情境中体验和理解数学，发展其空间观念；鼓励学生独立思考，引导学生自主探索，合作交流；教学过程中采用的方法应使学生深入地从各个方面理解，鼓励解决问题策略的多样化；教学过程中应有效地使用间接法；教学过程中应积极地发展学生的数学言语。

Industrial revolution ; mathematics ; computer ; artificial intelligence ; headwork mechanization ; mathematics mechanization ; deduction ; algorithm

工业革命；数学；计算机；人工智能；脑力劳动机械化；数学机械化；推理；算法

" "Mathematics is ordinarily considered as producing precise and dependable results; but in the stock market the more elaborate and abstruse the mathematics the more uncertain and speculative are the conclusions we draw there from … Whenever calculus is brought in, or higher algebra, you could take it as a warning that the operator was trying to substitute theory for experience, and usually also to give to speculation the deceptive guise of investment.

格雷厄姆对数学在投资中的作用认为数学一般被认为是能產生精确和可信赖的结果。但是在股票市场，所用的数学越复杂深奥，其从中得出的结果也就越不确定，越具有投机性。一旦引入了微积分或者高等代数，你可以把这看作是一个警告，这意味著使用数学者是在用理论代替经验。通常这给了投机欺骗性的偽装，变得好像是投资一样。

Higher Mathematics in derivative is a very important concept, is to study an important tool for mathematical problem, while derivative areas in mathematics also have a very wide range of use.

论文摘要翻译，谢谢摘要：导数在高等数学中是一个很重要的概念，是研究数学问题的重要工具，同时导数在数学领域外也有着非常广泛的运用。

After analyzed the result of experimentation, I found out the mathematics model between the speed of liquid and the variable of resistance.according to the minus- resistance characteristic, I brought forward a new way of hydrometry, found corresponding mathematics model of hydrometry, designed a metrical system and brought forward some advice of about this system, found some significative conclusion.

分析实验数据，验证了液体流速与其电阻变化量之间的数学模型。依据负阻特性，提出了一种新的流量测量方法，建立了相应的流量测量数学模型，并设计了一套对应的测量系统，提出了该系统的设计要点，得到了一些有意义的结论。

So to analyze in the aspect of description, it is useful to delouse the fount how inarticulateness comes into being; Based on the economic relationship and from the viewpoint of the pursuit of aim, the object of studying, the original creation of aesthetics, as well as the articulate knowledge and inarticulate knowledge, Polanyi distinguished the acquisitive way of science and technology. The development model of personal Knowledge can be generalized as the enthusiasm of seeking knowledge; Polanyi revealed how personal factors of mathematician cut across logical chasm, and gained mathematics findings in math" s activities. Thus he proved mathematics was also activity-needed techniques as natural science; Last evaluating the theory of "Personal Knowledge systematically, it can reveal its realistic significance and limitation.

波兰尼把认知结构区分为可言传知识与不可言传知识，与20世纪以来西方哲学的中心课题转向语言学的研究一致，所以从言述的角度出发，有助于了解不可言传性如何形成的根源；波兰尼以经济关系为立足点，从科学与技术的目的追求、研究对象、美的原创性，以及从可言传知识与默会知识的角度对两者的获取途径做了区分；其个人知识发展模式可以概括为：求知热情→启发性热情→说服性热情……；波兰尼揭示出数学家的个人因素是如何在数学活动中跨越逻辑鸿沟，取得数学发现的，从而证明数学同自然科学一样，也是一项需要技能的活动；最后对"个人知识"理论作一系统的评价，揭示"个人知识"理论的现实意义和局限性。

Using differential calculus knowledge to testify inequality, Calculus of higher mathematics is the core and calculus method of higher mathematics is typical of the whole mathematical method, the method is introduced for calculus ideas to solve the problem of finding an inequation, to make way for obtaining inequalities can be simple, the application of differential mid-value theorem and Taylor formula illustrate some of the inequality proof method.

运用微分学知识证明不等式；微积分是高等数学的核心，微积分思想方法是高等数学乃至整个数学的典型方法，微积分思想方法的引入为解决不等式证明的难题找到了突破，用来解不等式可使解题思路变得简单，文章应用微分中值定理及泰勒公式举例说明了部分不等式的证明方法。

Finally, the Knight strung a line between two of the monoliths and tied the horses up there.

最后，骑士们在两颗巨石之间拉了一条绳子，将他们的座骑绑在上面。

T7zN/hyS0 The island lies south by east from here.

那个岛位于此地的正南偏东方向。