代数学

But the group theory is in the algebra is most ancient one of richest branches, is the modern algebra foundation.

而群论是代数学中最古老最丰富的分支之一，是近世代数的基础。

Relation appeas in higher algebra.

关系是在高等代数学中才出现的概念。

The main contents are modules on rings,representations of groups and character theory, categories, and homological algebra.

它为数学系各方向的研究生，提供基本的现代代数学的思想、方法、和工具。

Providing new insights into classical results and opening avenues for further applications, the book then uses representation-theoretic techniques-especially induction theory-to examine equivariant higher algebraic K-theory, their relative generalizations, and equivariant homology theories for discrete group actions.

提供更进一步的应用的新对古典结果和开的大街了解，书然后使用代表理论技术特别是就职理论检查equivariant高代数学K 理论，他们有关概括，和equivariant 相同理论适合分离的组行动。

Key words: algebra; Drazin inverse; block matrices; index; rank

关键 词：代数学；Drazin逆；分块矩阵；指数；秩

Using the theories of probability, algebra, cryptography, Information theory and "Hybrid technique" and "Reduction theory" as tools, and basing on the notion of computational indistinguishability, properties and constructions of DES-model permutations are studied in this dissertation and some useful conclusions are given.

本文综合运用概率论、代数学、密码学、信息论等相关学科的知识及"混合技巧"和"归约论证"思想，以计算不可分辨性为基础，研究了DES型置换的性质和构造，得到较为实用的结果。

But , when we changeour trainofthought , we can find that sometimes using mathematical Analysis is a better solution to the linear algebraic problems.In thispaper, use the propertyofcontinuous function andimproper integralof infinite interval and to solve some matrix and quadratic form problems.Algebraic ideas andmethodstosolvemathematical analysisproblems are indicated by several specific examples. Close contactof differentmathematical analysis fields is shown.

该文探讨运用数学分析的有关知识（如：函数连续性、无穷区间的广义积分）和方法解决高等代数中的某些复杂、繁琐的问题；通过具体的实例，阐述高等代数的思想和方法在解决数学分析问题中的作用，揭示不同的数学领域之间的密切联系，例如：二次型与正交变换是代数学的基本内容，其用途十分广泛，而重积分的计算往往存在技术性的困难，若利用"二次型"与"正交变换"的有关理论去解决某些重积分的计算问题是颇有功效的。

The course is a comprehensive introduction to the theory, algorithms and applications of integer optimization and is organized in four parts: formulations and relaxations, algebra and geometry of integer optimization, algorithms for integer optimization, and extensions of integer optimization.

本课程对整数最优化的理论、算法和应用做了全面的介绍。课程分为四部分：公式和松弛、整数最优化的代数学和几何学、整数最优化的算法，以及整数最优化的拓展。

Moreover, by discussing the role of geometrical proof in Ars Magna and Cardano's attitude on irrational number, negative number and imaginary number, the paper points out that the role of geometry in Renaissance algebra had been tending weaker.

同时，通过考察几何证明在《大术》中所起的作用以及卡尔达诺对无理数、负数和虚数的处理，指出在文艺复兴时几何在代数学中的作用己逐渐减弱。

Matrix algebra is an important research area of algebra.

矩阵代数是代数学的一个重要研究领域，它在计算机、图论、经济、工程、控制等许多方面都有应用。

Finally, according to market conditions and market products this article paper analyzes the trends in the development of camera technology, and designs a color night vision camera.

最后根据市场情况和市面上产品的情况分析了摄像机技术的发展趋势，并设计了一款彩色夜视摄像机。

Only person height weeds and the fierce looks stone idles were there.

只有半人深的荒草和龇牙咧嘴的神像。