代数几何学

自从1945年MacLane与Eilenberg提出范畴的概念和理论以来，它在数学的许多分支，例如代数几何学、拓扑学、微分几何学以及函数理论中均已有所应用。

In 1945 MacLane and Eilenberg introduced the concept and theories of categories , which have played a role in many branches of mathematics such as algebraic geometry , topology , differential geometry and functional theories .

逐步阐明格论，概述影响整数最优化的代数几何学思想，并讨论整数最优化的几何学。

Develops the theory of lattices , outlines ideas from algebraic geometry that have had an impact on integer optimization , and discusses the geometry of integer optimization .

当时我学习的课程有物理、代数、几何学、希腊语和拉丁文。

I had physics , algebra , geometry , astronomy , Greek and Latin .

定理机器证明的研究已有将近50年的历史，并已经在数理逻辑、初等代数和几何学等学科取得显著成功。

There has been a lot of success in the study of automated theorem proving during the past 50 years .

多元李代数系统在几何学、动力学系统及玄论中有着广泛的应用。

The n-Lie algebra has its wide applications in geometries , mechanics and string theories .

特别是n-李代数的导子代数，是n-李代数在几何学及相关学科应用的重要工具。

Especially , the derivation algebra of n-Lie algebras plays an important role in applications of n-Lie algebras .