Linear Algebra
Share this course
Overview
Reviews
spContent=“Linear Algebra” is a very important undergraduate mathematical course. As he said "all problems can be transformed into mathematical problems, all mathematical problems can be transformed into algebraic problems, and all algebraic problems can be transformed into equations."
—— Instructors
About this course

Linear algebra is an important component of undergraduate mathematics. The course content covers fundamental concepts of linear algebra such as solving linear system of equations, vector/matrix algebraic theory, determinant and its properties, vector space, linear transformations, orthogonality, eigenvalues, eigenvectors and applications to linear differential equations, Least squares and projections. With its strong logic, abstract feature and wide applications, linear algebra mainly discusses the linear theory and method of the finite-dimensional linear space. With the fast development of science and technology, there are many problems in Big data, Artificial Intelligence, Cloud calculation etc. concerning the fundamental matrix theory and systems of linear equations.

The famous French mathematician called Rene Descartes said “all problems can be transformed into mathematical problems, and all mathematical problems can be transformed into algebraic problems, and all algebraic problems can be transformed into equations.” Therefore, once the equation problem has been solved, all problems will be solved!

Furthermore, elementary linear algebra is a valuable introduction to mathematical abstraction and logical reasoning because the theoretical development is self-contained, consistent, and accessible to most students.

Thus, after learning this course, you will master not only matrix theory and systems of linear equations, vector space, eigenvalue etc., but also have the ability of matrix operation, matrix methods to solve some practical problems. We hope this course will help you to build the essential mathematics for the study of follow-up courses and other academic subjects, the further broadening of mathematical knowledge and the improvement of mathematical attainment.

Dear students, the main objective of this course is to develop students’ abstract thinking and to train the students’ practical ability.

Objectives

- master not only matrix theory and systems of linear equations, vector space, eigenvalue etc., but also have the ability of matrix operation, matrix methods to solve some practical problems.

- build the essential mathematics for the study of follow-up courses and other academic subjects.

- develop the further broadening of mathematical knowledge and the improvement of mathematical attainment.



Syllabus
Prerequisites

Calculus 1 and Primary Mathematics


CertificatesRequirements

为积极响应国家低碳环保政策, 2021年秋季学期开始,中国大学MOOC平台将取消纸质版的认证证书,仅提供电子版的认证证书服务,证书申请方式和流程不变。

 

电子版认证证书支持查询验证,可通过扫描证书上的二维码进行有效性查询,或者访问 https://www.icourse163.org/verify,通过证书编号进行查询。学生可在“个人中心-证书-查看证书”页面自行下载、打印电子版认证证书。

 

完成课程教学内容学习和考核,成绩达到课程考核标准的学生(每门课程的考核标准不同,详见课程内的评分标准),具备申请认证证书资格,可在证书申请开放期间(以申请页面显示的时间为准),完成在线付费申请。

 

认证证书申请注意事项:

1. 根据国家相关法律法规要求,认证证书申请时要求进行实名认证,请保证所提交的实名认证信息真实完整有效。

2. 完成实名认证并支付后,系统将自动生成并发送电子版认证证书。电子版认证证书生成后不支持退费。


References

Textbook:

Linear Algebra with Applications (9th Edition), Steven J. Leon, China Machine Press, 2012.

References:

[1] Elementary Linear Algebra (7th Edition), Ron Larson, Cengage Learning, 2012.

[2] Introduction to Linear Algebra (3rd Edition), Gilbert Strang, Wellesley-Cambridge Press, 2003.

[3] Student Guide to Linear Algebra with Applications, ISBN 0-13-600930-1.

[4] A special Web site to accompany the 8th edition: www.pearsonhighered.com/leon

[5] The collection of software tools (M-files) downloaded from the ATLAST Web site: www.umassd.edu/specialprograms/atlast