课程号：

MS196002

课程名：

模与线性代数

英文课程名：

Modules and Linear Algebra

开课单位：

数学与统计学院

授课教师：

Sergio Estrada

责任教师：

李欢欢

助理教师：

杨丹丹

学分/学时：

1/16

选课年级：

2016级（大三）

选课专业：

全校

教师简介（中英文）：

Sergio Estrada教授，男，1976年9月15日出生。2003年3月毕业于西班牙阿尔默大学，获数学博士学位，现为西班牙穆尔西亚大学数学系副教授。曾应邀到麻省理工学院和肯塔基大学合作研究，主要研究方向为同调代数、表示论和模型范畴。美国数学会和zbMATH评论员;“Khayyam Journal of Mathematics”及 “Hacettepe Journal of Mathematics and Statistics”等杂志编委。已在Advance in. Math，J. Lond. Math. Soc.，Journal of Algebra，J. Pure App. Algebra，Comm. in Algebra等国际期刊上发表SCI论文50多篇。（Professor Sergio Estrada, male, born on September 15, 1976. He got his Ph. D. in Mathematics at the University of Almería in Spain in March 2003, and is now a Full time Associate Professor at the department of Mathematics, University of Murcia. Hewas invited to visit the University of Kentucky and the Massachusetts Institute of Technology to work in the topics: homological algebra, representation theory and model theory. He has been acted as a reviewer for AMS Math Reviews and Zentralblatt; he is a member of the Editorial Board of the "Khayyam Journal of Mathematics"and "Hacettepe Journal of Mathematics and Statistics". More than 50 papers have been published in "Advance in. Math", "J. Lond. Math. Soc.", "Journal of Algebra", "J. Pure App. Algebra", "Comm. in Algebra" and other international journals.）

课程简介（中英文）：

线性代数不仅是数学方向的专业课，同时也是其它工科方向的必修课，其着重于用代数的方法解决和研究矩阵、行列式、线性方程组、二次型等相关问题。若从更高的层度来看，线性空间就是特殊的模范畴。《模与线性代数》这门课程，主要从模论的角度出发，介绍环与模的一些基本概念、模的直和分解以及模的相关理论在群和矩阵中的一些应用。该课程将从更高的维度出发，使学者对线性代数中的理论有更深刻的理解。(Linear algebra is not only a specialized course in mathematics, but also a compulsory course in other engineering fields. It focuses on solving and studying related problems such as matrix, determinant, linear equation system and quadratic form by algebraic methods. If viewed from a higher level, linear space is a special category of modules. This course, mainly introduces some basic concepts of rings and modules, direct sum decompositions of modules and some applications of related theories of modules in groups and matrices from the viewpoint of module theory. This course will start from a higher level, so that the students will have a deeper understanding of the theories in linear algebra.)

先修课程：

线性代数、抽象（近世）代数