But solving model problem can not be done without mathematics.

解决模型问题又往往离不开数学语言。

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The research in the issuing scope of national debts cannot do without mathematics thinking modes and mathematics methods, such as qualitative analysis and quantitative analysis.

国债发行规模的研究离不开数学思维方式和数学方法，如定性分析与定量分析；

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A serious study of physics is impossible without some knowledge of mathematics.

没有一点数学知识是不能开展严谨的物理学研究的。

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However, most of the task can be accomplished without any knowledge of mathematics and computers.

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To teach cleaners and nightwatchmen advanced mathematics (such as adding up without a calculator) seemed pretty wasteful, and apt to breed discontent.

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As it becomes clear that students cannot thrive in a broad range of subjects without first learning the fundamentals, NCLB is focused squarely on the educational building blocks of reading and mathematics.

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