### Linear Algebra I (B)

Course Code: B11001Y-B01

Course Name: Linear Algebra I (B)

Credits: 4.0

Pre-requisite: Not required

Lecture Time: 80 hrs

Instructors:

Course Description

This course is a required basic course for all undergraduates in all majors. It is required that students should master the introductory knowledge and methods of linear algebra as well as the relevant basic knowledge of algebra. This course is divided into three types which are type A (Mathematical), type B (Science and Technology), and type C (Engineering). These three types have the same basic content (see the teaching content and class hours). However, the specific calculation and applications are paid more attention in type C; there is more theoretical analysis in type B; while the foundation for type A is rigorous theoretical proof.

Type A is suitable for those students who will continue to study mathematics, physics, computer and other subjects. Type B is suitable for those students who will study any majors other than mathematics in the future. Type C is suitable for those students who will study any majors other than mathematics, physics and computer in the future.

Through this course, students should meet the following basic requirements: Master the introductory knowledge of linear algebra as well as the relevant basic concepts and basic methods of algebra; Have a preliminary understanding and way of thinking in linear algebra that lays foundation for linear algebra II and other courses.

Topics and Schedule

1.            Origin of algebra (16 hrs)

1.1.   Simply talk about algebra and initial linear equation

1.2.   Low order determinant

1.3.   Sets and mapping

1.4. Equivalence relation and quotient mapping

1.5. Replacement

1.6. Divisibility

1.7. Induction (in the discussing course of exercise)

2.            Matrix (10 hrs)

2.1.   Row and column vector space

2.2.   Rank of a matrix

2.3.   Linear mapping and multiplication of matrix

3.            Determinant (14 hrs)

3.1.   Determinants, structure and basic properties

3.2.   Further properties of determinants

3.3.   Applications of determinants

3.4.   Axiomatic structure of determinants

4.            Group, ring, domain (12 hrs)

4.1.   A set with algebraic operations

4.2.   Group

4.3.   Ring and domain

5.            Polynomial (12 hrs)

5.1.   Polynomial ring

5.2.   Factorization of polynomial rings

5.3.   Roots of a polynomial

5.4. Symmetric polynomial

Teaching methods

1. Two times a week and 80 minutes each time for teaching, the format is 50 minutes for classroom teaching, 10 minutes for rest and 30 minutes for classroom teaching.

2. One time a week and 100 minutes each time for exercises and discussion.

The assessment will include the class routine performance, the mid-term examination and the final examination, which will count for 30%, 30% and 40% each. The class routine performance includes homework, classroom discipline, attendance, discussion and so on. The mid-term and the final examination are close-book examinations.

Textbook

Kostrikin, Introduction to Algebra, the first volume

References

[1]   Shirov, Introduction to the Linear Space (second edition), Higher Education Press

[2]   D. C. Lay, Linear Algebra and its Applications, Machinery Industry Press

[3]   Apostol. T. M , Linear Algebra and its Applications, People's Posts and Telecommunications Press

[4]   Axler. S, We Should Learn Linear Algebra Like This, People's Posts and Telecommunications Press