当代数学的论证过程往往错综复杂，需要用上很多不同的步骤、成分和符号。
A typical argument in modern mathematics is often quite intricate, requiring many different steps, ingredients, and notation.
代数学,据约翰·德比夏尔所说,可以追溯到古巴比伦人留在楔形文字石碑上的简单的代数问题.
THE roots of algebra, asJohn Derbyshire tells us, go back to the ancient world: the Babylonians leftcuneiform tablets showing simple algebraic problems.
函数逼近论是现代数学的一个重要分支。
The approximation theory of functions is one of the important branches of modern mathematics.
“四元术”是中国古代数学最杰出的成就之一。
"Siyuanshu" was one of the most distinguished achievements in the ancient mathematics in China.
滤子在现代数学中占有重要的位置。
函数逼近论在现代数学是一个重要的分支。
Approximation theory of functions is an important branch in modern mathematics.
我在中学就学过代数学。
它体现了代数学中研究其他代数结构的基本思路。
It reflects the algebra in other algebraic structure of the basic idea.
我始终没有真正地领会代数学在几何学上的应用。
I have never got so far as to understand properly the application of algebra to geometry.
前者源于希腊，后者则贯穿整个中国古代数学。
The former has its root in Greece and the latter runs through the whole mathematical history of ancient China.
卷整体上是迷人并且令人激动的当代数学的概述。
The volume as a whole is a fascinating and exciting overview of contemporary mathematics.
盈不足方法是古代数学中一项具有一般性的重要方法。
The method of excess and deficiency that had general applications was important in ancient mathematics.
Q F环的研究已成为近期国际代数学界研究的热点。
Now the study of QF rings has been a hotspot in international algebraic world.
“大众数学”教育是现代数学教学改革的一个重要方向。
Mass mathematics education is a reforming direction of modem mathematics teaching reform.
在断裂问题的理论研究中经常用到近代数学的理论和方法。
The theory and method of modern mathematics are used in the theoretical research for fracture problem usually.
目前，非线性泛函分析已经成为现代数学中的一个重要分支。
At present, nonlinear functional analysis has been one of the most important branch of learning in modern mathematics.
在中学数学教学中实施心理教育是当代数学教学的重要发展趋势。
It is the important trend to put Psychological teaching into contemporary mathematical teaching, especially for junior student.
大体而言，他的理论基于以下几种学科：古代数学、几何学、占数学和占星学。
In general, his theories are based on the followings: ancient mathematics, geometry, numerology and astrology.
从实际工程出发，以现代数学理论为依托，研究了随机结构系统的特征值问题。
The eigenvalue problem is studied for random structure system from the view point of practical engineering on the background of modern mathematics theories.
他的主要研究方向以及贡献是在与数论、代数学以及密码学有关的计算机算法上面。
Shoup's main research interests and contributions are computer algorithms relating to number theory, algebra, and cryptography.
由于集值算子在现代数学的广泛应用，本文还研讨了关于集值算子方程解的存在性；
Due to the wide applications of setvalued operators in modern mathematics, the solvability of the setvalued operator equations are studied.
从内容上说，这部著作把十九世纪所产生的纷繁芜杂的代数学内容有机地组织在一起。
With regard to the content, this book organized a huge body of knowledge of algebra produced in the nineteenth century.
算法对于数学教育也有着重要的作用，同时也是中国古代数学的重要思想和主要特征。
Algorithm also has an important role in the mathematical education, and represents the important thoughts and main characteristics of the Chinese ancient mathematics.
近代数学的一些学科，如代数结构理论与泛函分析可以在矩阵论中寻找到它们的根源。
Some subjects of modern mathematics, such as the algebraic structure theory and functional analysis, would be found in the Matrix theory.
根据当代科学技术向力学提出的问题，简要综述了现代力学所涉及的现代数学领域和方法。
According to the problems that the modern science and technology put before mechanics, we have briefly reviewed the domain of the modern mathematics and methods related to the modern mechanics.
根据当代科学技术向力学提出的问题，简要综述了现代力学所涉及的现代数学领域和方法。
According to the problems that the modern science and technology put before mechanics, we have briefly reviewed the domain of the modern mathematics and methods related to the modern mechanics.
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