这在数学上是不可能的。
他经常在数学上帮助我。
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.
这就是为什么它在物理、历史和数学上都得了高分。
研究表明，男孩通常比女孩在科学上表现更好，但他们在数学上几乎没有差别。
The study shows that boys generally did better than girls in science, but there was little difference between them in maths.
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.
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.
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.
由于他的粗心大意，他在数学上丢了3分。
祖不仅在数学上很成功，而且在天文学上也很成功。
再一次，数学上有点复杂，但是很实用。
Again, a little more complicated mathematically but more practical in real use.
从数学上说，此时这是零。
And what this is just telling us mathematically is, when that happens this is zero.
你能在数学上帮助我吗？
他们究竟是如何从数学上得出这个结论的呢？
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.
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.
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.
我们的老师给了我们许多数学上有帮助的书。
在数学上，它是一个参数，用于确定一个算法的函数输出。
Mathematically, it is a parameter which determines the functional output of an algorithm.
在PISA评分系统中，上海在数学上得到了600分。
In the PISA scoring system, Shanghai scored six hundred in math.
斯蒂格勒博士和米勒博士都注意到了另一个差异，特别是在数学上。
Another difference, particularly in math instruction, stood out to both Dr. Stigler and Miller.
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.
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.
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.
Bonnet认识到树枝和树叶具有一种螺旋布局模式，在数学上可以用分数来表达。
Bonnet saw that tree branches and leaves had a mathematical spiral pattern that could be shown as a fraction.
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.
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.
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.
如果经验观测与模型不符，无论这个模型概念上多么精致或者数学上多么简洁，它必然被抛弃或被修正。
If empirical observation is incompatible with a model, the model must be trashed or amended, even if it is conceptually beautiful or mathematically convenient.
如果经验观测与模型不符，无论这个模型概念上多么精致或者数学上多么简洁，它必然被抛弃或被修正。
If empirical observation is incompatible with a model, the model must be trashed or amended, even if it is conceptually beautiful or mathematically convenient.
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