Linear Algebra

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

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