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.
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.
半群的研究在代数学的理论研究中占有很重要的地位。 其中格林关系在半群理论的研究中有着重要的意义。
The research of semigroup plays an important role in the research of the theory of algebra, and the Green's equivalences are especially significant in the study of semigroups.
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.
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.
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.
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.
代数表示论是上世纪七十年代初兴起的代数学的一个新的分支，它的基本内容是研究环与代数的结构。
Algebra representation theory is a new algebraic branch arising in 1970s whose researches mainly focuses on rings and algebraic structures.
离散数学是近几十年来产生的一门新课程，它是现代数学的一个重要分支，是计算机科学中专业基础理论的核心课程。
Discrete mathematics is a summary of recent decades, generated a new course, it is an important modern branch of mathematics, computer science professionals in the basic theory of the core curriculum.
在教学过程中特别强调结合具体的例子来理解代数学的数学思想和思维方法，注意介绍最新的科研成果以开阔同学的视野。
In the course we introduce the core concepts and ideals through a detailed study of some important examples. We also introduce some recent progress on algebraic researches.
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.
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.
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.
从复变函数理论出发，利用辐角原理、最大模原理、最小模原理给出代数学基本定理的几种新的证明方法。
This paper uses several methods of complex functions theorey to prove fundamental theorem of algebra by argument principle, maximum modulus principle and minimum modulus principle.
本文综合运用概率论、代数学、逻辑函数频谱理论等方面的知识，对多输出函数的有关性质与构造进行了研究。
Using the theories of probability, algebra and spectral theory comprehensively, the dissertation investigates the properties and constructions of multi-output functions.
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.
从复变函数理论出发，利用辐角原理、最大模原理、最小模原理给出代数学基本定理的几种新的证明方法。
The minimum modulus principle is proved by using the preserving field theorem, and the span of minimum modulus point is discussed.
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.
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.
数学公式的演变对现代数学教学具有极其重要的指导意义，对如何更好地开展素质教育提供了学术上可应用的实例和实施的指导方向。
The evolution of the maths formulas has the directive significance to the modern maths teaching, it offers applicable academic cases and directions on how to develop the quality education properly.
学习的情境理论是现代教育理论中的主流，而现代数学教育研究中也对“情境”给予了充分的重视。
The learning's situated theories are the mainstream of the modern education theories, and much importance has been attached to the "situated"by modern mathematics education research.
十九世纪的代数学知识体系庞大，它包含置换群、矩阵、代数数论、代数几何等多个分支。
In the nineteenth century, the system of algebraic knowledge is enormous, which contains the permutation group, matrix, algebraic number theory, algebraic geometry and other branches.
“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.
“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.
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