当我告诉一群表现出无助行为的学生说，是缺乏努力导致了他们数学上的错误，他们就学会了在问题变得棘手时继续尝试。
When I told a group of school children who displayed helpless behavior that a lack of effort led to their mistakes in math, they learned to keep trying when the problems got tough.
数学上的虚假性存在于夸张的推理中。
The falseness of the maths lies in an exaggerated inference.
即使在美国，很多人仍然把教育的“性别差异”与女孩儿在数学上的落后表现联系起来。
Even in the United States, many people still associate the educational "gender gap" with girls left behind in math.
我知道复杂性有三到四种数学上的定义，但没有哪种可以大体上解答我刚刚提出的这类问题。
I am aware of three or four mathematical definitions for complexity, none of them broadly useful in answering the type of questions I just asked.
它所基于的理念是数学上的“trap - door”函数，它可以沿着一个方向轻松地进行计算，但是很难从相反的方向进行计算。
It's based on the idea of mathematical "trap-door" functions, which are easy to compute in one direction but very difficult to compute in the reverse direction.
其表现表明：在2005年的一个全国性的考试中，Cidadeolimpica在葡语和数学上的分数低于城市、州和国家的平均水平。
Its performance shows it: in a national exam administered in 2005 Cidade olimpica's scores in Portuguese and maths were below average for city, state and country.
数学上的分形（fractals）是一种非常复杂的几何形状，这正是医生所要关注的，它是协助医生区分健康的细胞形态和癌变的一个重要特征。
The mathematics of fractals – very complex geometric shapes – is just what the doctor ordered, helping to capture the difference between the shape of a healthy cell and a cancerous one.
爱因斯坦将其称为宇宙常数，并略带厌恶地将它加入他的理论，因为如果没有宇宙常数，它的理论在数学上优美极了。
Einstein called the something the cosmological constant and added it to his theory with some distaste, because the work had been so mathematically beautiful without it.
这在数学上是不可能的。
SSL协议基于公钥密码，加密密钥成对地出现在公钥密码中，它们是在数学上是相关的，但无法由一个推知另一个。
The SSL protocol is based on public-key cryptography where encryption keys come in pairs that are mathematically related, but one cannot be deduced from knowing the other.
数学上等同于有超过七百五十亿种可能的排列。
The math equates to just over 75 billion possible permutations.
多亏了你的帮助，我在数学上不断取得进步。
Thanks to your help, I have made continuous progress in math.
任何一种没有奇点的宇宙模型都将解决广义相对论中困扰着科学家们的奇点问题，因为奇点在数学上是无法定义的。
Any kind of singularity-free Universe would solve the singularity problem that has bothered scientists about general relativity, since a singularity cannot be mathematically defined.
根据一个数学上设计更为客观的新生活质量指数，美国的生活质量位列全球第二。
The US comes second in a new quality of life index designed to be mathematically objective.
虽然吉萨的巨型金字塔在数学上非常惊人，它的建设还是超不出当时天文学家、学者与建筑师的聪明才干。
Whilst the Great Pyramid at Giza is mathematically astounding, its construction was not beyond the ingenious astronomers, scholars and architects of the time.
他们究竟是如何从数学上得出这个结论的呢？
这个模型产生了两种所谓犯罪热点的类型，在数学上被归类于超临界的(不稳定的系统)和亚临界的(稳定的系统)。
The model produced two types of so-called criminal "hot spots," which are mathematically referred to as supercritical (which is an unstable system) and subcritical (which is a stable system.)
这是因为散列可以将输入值转化为新的值，而这些新值不能从数学上逆向生成原始值。
This is because hashing an input value converts it into a new value that is mathematically impossible to undo to produce the original value.
这个问题可以在数学上进行分解，如图1a所示，一个用户在应用中使用单独凭证的单对单模型可以被表示成
The problem can be broken down mathematically. As Figure 1a shows, the one-to-one model of a user having individual credentials in an app can be represented as
我们的老师给了我们许多数学上有帮助的书。
他在数学上创立的“二进位制”奠定了现代控制论和计算机原理的基础。
His binary notation in mathematics laid the foundation for modern cybernetics and computer theory.
在英格兰(OECD不再将其列在前十位)，一个三等的，甚至是刚及格的学士学位，再加上在英语和数学上基本合格就足够了。
In England (which the OECD no longer ranks in the top ten), a third-class or even a pass bachelor's degree will suffice, along with the most basic qualifications in English and maths.
然而，威斯康星医学院的著名色视觉专家杰·奈茨说，单从数学上解释，其差别会令人震惊。
But mathematics alone suggests the difference would be astounding, said Jay Neitz, a renowned color vision researcher at the Medical College of Wisconsin.
多亏了你的鼓励，我在数学上不断地取得进步，最终决定在大学里学习数学。
Thanks to your encouragement, I made continuous progress in math, and finally made up my mind to study it in the university.
这是我们远远落后的地方。我们的技术竞争力，将取决于我们在数学和科学上取得多大的成绩。
That's an area where we've really fallen far behind, and our technological competitiveness is going to depend on how well we do in math and science.
在某个时候，这种冲击将会发生，数学上这是必然的。
At some point, such a shock will come. Mathematically it must.
他断言，在理解冗长且完全抽象的一系列观点方面，他的能力非常有限，因此他深信自己在数学上永远不会成功。
He asserted that his power to follow a long and purely abstract train of thought was very limited, for which reason he felt certain that he never could have succeeded with mathematics.
如果2006到2009年的成绩增长在2012年下一届PISA测试中重现，实现数学和科学上增长25分的目标将远远提前。
If the gains from 2006 to 2009 are duplicated when the PISA is next given in 2012, the goal of making 25-point gains in math and science will be met far ahead of schedule.
如果2006到2009年的成绩增长在2012年下一届PISA测试中重现，实现数学和科学上增长25分的目标将远远提前。
If the gains from 2006 to 2009 are duplicated when the PISA is next given in 2012, the goal of making 25-point gains in math and science will be met far ahead of schedule.
应用推荐