Course Description

Advanced Algebra is one of professional basic courses in mathematics major. It contains the polynomial theory and the theory of linear algebra. It is suitable for freshman of mmighthemmightics in our university. In this course we will study Determinant, Matrix, Vector space and Euclidean space. Throughout the course, we will instruct students in ability of abstract thinking and logical reasoning. And it is the antecedent course of other subsequent selective courses.

Course Learning Outcomes

The student learning outcomes are what student would be able to know and to do on the completion of this course. In details are:

1.Explain the properties of determinant and matrix, the structure of solution.

2.Understand Vector space, Euclidean space.

3.Analyse and manipulate simple versions of these forms.

4.To use simple mathematical models to calculate the result of changes in the advanced algebra.

5.Use the standard models to interpret and analyse real problems in advanced algebra.

Relationship to Other Courses

Pre-requisites : High school math

Textbook and Reading Lists

The textbook for this course is:

Wang Efang, Shi Shengming(2003), “Advanced Algebra”, 5th edition. Higher Education Press.

Course Assessment

Item	Title	Due Date	Value
1	Home work	Every week	10%
2	Questions in class	Randomly selected weeks	10%
3	Test in class	Week 10	10%
4	Final exam	Exam period	70%

Course Schedule

Week	Topic	Text
Week 4	Determinant: The definition and properties of determinant, N order determinant, Cramer’s Rule	Chapter 1
Week 5	National Day
Week 6-7	MatrixⅠ: The definition and properties of matrix Matrix calculations, Inverse matrix	Chapter 2
Week 8-9	Matrix Ⅱ: Rank of matrix, Symmetric matrix,Quadratic form, Positive definite matrix	Chapter 3
Week 10-12	Vector space: Linear correlation, Subspace, Spatial isomorphism Basis and dimension of vector space	Chapter 5
Week 13-14	System of linear equations: Elementary transformation, The structure of solution, Eigenvalues and eigenvector	Chapter 6
Week 15-16	Linear transforms: The calculation of linear transform, Invariant subspace, Eigenvalues and eigenvector	Chapter 7
Week 17	Euclidean space: Metric matrix, Orthogonal basis, Orthogonal matrix, Orthogonal transformation	Chapter 8
Week 18	Review
19	Final exam