数学是研究纯量之科学。
模糊数学是研究和处理模糊性现象的数学。
Fuzzy mathematics is the mathematics researching and treating with fuzziness phenomena.
数学是研究现实生活中数量关系和空间形式的数学。
Mathematics is the study of quantitative relationship between real life and space form of math.
数学是研究现实世界的空间形式和数量关系的科学。
Mathematics is the science of space form and the quantity relation that studies modern world.
数学是研究，数量，结构，空间，变化，和相关主题的模式和形式。
Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form.
组合数学是研究离散对象的科学，正因为有了以组合数学为基础的组合算法，才使人感到计算机好像是有思维的。
It is the combinatorial algorithms which based on a science of studying discrete objects, Combinatorics, that make people feel that computer may have its own thought.
没有一点数学知识是不能开展严谨的物理学研究的。
A serious study of physics is impossible without some knowledge of mathematics.
心理学家苏珊·莱文是芝加哥大学研究幼儿数学发展的专家。她发现，在2岁至4岁之间玩拼图的孩子在后来会发展出更好的空间能力。
Psychologist Susan Levine, an expert on mathematics development in young children the University of Chicago, found children who play with puzzles between the age of 2 and 4 later develop better spatial skills.
他的专长是博弈论，一个研究人们如何进行谈判的数学分支。
His specialism is game theory, a branch of maths that studies how people negotiate with each other.
那种建模的方法是怎么进化来的？很显然的，这里有很强的数学研究背景，但是怎么把它转化成一种实用的东西呢？
How did that approach to modeling evolve? Obviously, there's this strong mathematical research background. But what's the process like of translating that theory into something that's usable?
另一项研究表明舞蹈家和编舞指导的离婚率是43%，与之相对比的是数学家，离婚率只有19%。
Another study claims that dancers and choreographers face a 43 per cent chance of getting divorced compared to 19 per cent among mathematicians.
因此，人类学中的“文化”的概念，就像数学中“集”的概念一样，是一个抽象概念，它使得大量的具体研究和认识成为可能。
Thus，the anthropological concept of “culture” ，like the concept of “set” in mathematics，is an abstract concept which makes possible immense amounts of concrete research and understanding。
其中一个例子是来自50个国家的94年和99年数学与科学研究(TIMSS)数据的趋势分析。
One of many examples is an analysis of 1994 and 1999 Trends in Mathematics and Science Study (TIMSS) data from 50 countries.
佐治亚梅森大学(George Mason University)的一个终身数学教授，并且是四个孩子的母亲，不太同意这个研究的发现。
Rebecca Goldin a tenured math professor at George Mason University, and a mother of four, is not sure about all the findings of the study.
他们从卡内基·梅隆大学招募了141名大学生，参加表面上是关于数学技能的研究。
They recruited 141 undergraduates from Carnegie Mellon University to participate in a study ostensibly about math skills.
但令人吃惊的是，数学模型表明，相对于过去研究得出的90%的结论，这些病例中只有38%可以归结为遗产因素。
But surprisingly, mathematical modeling suggested that only 38 percent of the cases could be attributed to genetic factors, compared with the 90 percent suggested by previous studies.
精算师应用数学，统计学，和金融理论研究不确定的未来事件，尤其是和保险和养老金领域的问题。
Actuaries use mathematics, statistics and financial theory to study uncertain future events, especially those of concern to insurance and pension programs.
注：这些是在数学领域中有大量文献记载的概念，经过充分的研究和严格的定义。
Note: these are well documented concepts in mathematics that have been well studied and rigorously defined.
顺便提一下，某种意义上来讲，这就是拓扑学的起点，拓扑学是研究区域形状的一个数学分支。
And by the way, I mean, this is also somehow the starting point of topology, which is the branch of math that studies the shapes of regions.
如果数学是对纯理念王国的感知的话，那么研究数学就需要让自己的大脑以某种方式抵达现实世界之外的某地。
If mathematics is the perception of this realm of pure ideas, then doing mathematics requires our brains to somehow reach beyond the physical world.
马毅是微软亚洲研究院视觉计算组的主任研究员。他的研究兴趣在于视觉认知背后的数学原理以及对视觉数据的理解。
Ma, research manager of the visual Computing Group at Microsoft research Asia, is interested in the mathematical principles behind the processing and understanding of visual data.
最近一项研究显示，相较于认真听课的人，有更多人是在不知不觉中学会数学概念的。
There's more to picking up math concepts than paying attention in class, according to recent research.
尤其通过中间和侧面前额皮质大脑活动，研究者能判断志愿者做数学题时是决定将两个数字相加还是相减。
Specifically, the researchers determined whether a volunteer decided to add or subtract two numbers in a math exercise from patterns of brain activity in the medial and lateral prefrontal cortex.
数学是我的研究领域。
数学家们都偏好于玩一些游戏，尤其是一种特殊的游戏，他们观察并研究人们如何去选择个人的行为方式并获得最大度的收益回报。
MATHEMATICIANS like to play games. In particular, they like to play games that examine how people pick ways of behaving that will maximise returns.
如此震动心灵的故事，解释了为什么这本薄薄的小书恰是对某些著作的一剂对症解药，因为多数学者研究档案后往往拿出令人望而却步的成果。
Such moving stories explain why this slim book is just the right antidote to the often daunting studies most scholars produce after working in the archives.
该研究小组是采用光学的方法，而不是数学方法，——采用数学方法的话是不可能达到这样的速率的。 ——他们把不同时间到达的光分成不同的路径，在检测器上再把他们合并起来。
The team does this optically - rather than mathematically, which at these data rates would be impossible - by splitting the incoming beam into different paths that arrive at different times.
该研究小组是采用光学的方法，而不是数学方法，——采用数学方法的话是不可能达到这样的速率的。 ——他们把不同时间到达的光分成不同的路径，在检测器上再把他们合并起来。
The team does this optically - rather than mathematically, which at these data rates would be impossible - by splitting the incoming beam into different paths that arrive at different times.
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