代数学

The theory of group: This is one of the most oldest and richest branches of abstract algebra.

二。群论：群论是抽象代数学里发达最早而内容最丰富的一个部门。

Introduction to the fundamental theory of abstract algebra.

课程目的：介绍代数学之基本理论。

The study of the theory of semirings is one of the important topics in algebra.

半环的代数理论是代数学中的重要课题之一，许多专家学者在这一领域内做出了深入细致的研究。

It reflects the algebra in other algebraic structure of the basic idea.

它体现了代数学中研究其他代数结构的基本思路。

I want to learn some complexity theory,mathematics theory such as Computational number theory,Algorithmic Algebra,Algebraic function fields over finite fields and the group thoery.

在这半年里，我将系统地加深学习一些必要的数学知识，比如计算复杂性理论，计算性数论算法，群论，算法的代数学等等。

This article listed the main clue of the development of mathematics in the sixteenth and seventeenth century. Based on that, we analyzed the algebraic basis of calculus. The basis had an algorithmic character which could use program to calculate.

本文在列出十六、十七世纪代数学发展主线的基础上，分析了微积分产生的代数学基础，这个基础本身带有强烈的程序化的算法特征。

The next part introduces schemes and algebraic varieties, the basic language of algebraic geometry.

下一个部分实施计划和代数学的种类，代数学的几何学的BASIC语言。

Representation Theory and Higher Algebraic K-Theory is the first book to present higher algebraic K-theory of orders and group rings as well as characterize higher algebraic K-theory as Mackey functors that lead to equivariant higher algebraic K-theory and their relative generalizations.

代表理论和更高的代数学的K 理论是第一个书提出订货和组戒指的更高的代数学的K 理论，好和导致equivariant更高的代数学的K 理论和他们的有关的概括的麦基functors一样表现更高的代数学的K 的特性理论。

The research of differential structure on the algebra system, has opened up a new field for the research of algebra, and offered a new method and thinking, greatly expanded the scope of application of algebra.

代数系统上的微分结构的研究，为代数学的研究开辟了新的领域，提供了新的方法和思路，极大的扩展了代数学应用的范围。

Topics covered include: programming and computability theory based on a term-rewriting,"substitution" model of computation by Scheme programs with side-effects; computation as algebraic manipulation: Scheme evaluation as algebraic manipulation and term rewriting theory; paradoxes from self-application and introduction to formal programming semantics; undecidability of the Halting Problem for Scheme; properties of recursively enumerable sets, leading to Incompleteness Theorems for Scheme equivalences; logic for program specification and verification; and Hilbert's Tenth Problem.

其所包含的主题：程序和运算理论是基于根据算数和具有一些副作用的计划纲要的条款重写和"代入"模式之上的、关于代数学计算的算数：关于代数学计算和术语重写理论的评价方案作计划、应用程序自己和说明的自相矛盾到形式上的程序语义、关于计划Halting 问题的不可判定性、可递归可列举集合的属性、导致对于等同计划的不完整规则、对于逻辑和证明程序的规范和Hilbert的第十问题。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷