1.hat is a determinant,how many ways to calculate it? What is a adjoint of a matrix? 3.教学内容 Section:Introdction to Deterins Class Class Froperties of determinants,exercises 4.教学方法 Nethod of lecture and questions between classes 5教学评价 Through the teaching of this chapter.students can sasterdeterminants.matrix operations and lipear transfornations 第四章V6 ctor Spa088(小四号黑体) 1.教学目标（五号宋体） 2教学重难点 Probleas: 1.What is a vector space and subspace? 2.Think of the difference between null space and column space? 3.What is the use of rank? 4.hat is the dimension of a vector space? 5.hat is the procedure fora change of basis and coordinate 3.教学内容 Section 1:Introduction to Vector Spaces Class 1:Definition of vector spaces and subspaces,properties Class 2:Definition of mll space,column space,exercises Class 3:Linearly independent sets.bases Class 7:Change of basis,exercises 4教学方法 Nethod of lecture and estios betseen classes and exercises after classes 5.教学评价 Through the teaching of this chapter,students can master vector spaces. 第五章Eigenvalues and Eigenvectors(小四号黑体) 1.教学目标（五号宋体 2.教学重难点 1.What are eigenvalues and eigenvectors? rop equ1. What is a determinant, how many ways to calculate it? 2. Think of the relations between matrix and determinant? 3. What is a adjoint of a matrix? 4. What is the use of the Cramer’s rule? 5. What are general properties for determinant calculation? 3.教学内容 Section 1: Introduction to Determinants Class 1: Definition of determinants, the expansion theorem Class 2: Properties of determinants, exercises Class 3: Cramer’s rule, exercises Class 4: More calculation on determinants 4.教学方法 Method of lecture and questions between classes. 5.教学评价 Through the teaching of this chapter, students can masterdeterminants, matrix operations and linear transformations. 第四章 Vector Spaces（小四号黑体） 1.教学目标 （五号宋体）  Learning knowledges about vector spaces. 2.教学重难点 Problems: 1. What is a vector space and subspace? 2. Think of the difference between null space and column space? 3. What is the use of rank? 4. What is the dimension of a vector space? 5. What is the procedure for a change of basis and coordinate transformation? 3.教学内容 Section 1: Introduction to Vector Spaces Class 1: Definition of vector spaces and subspaces, properties Class 2: Definition of null space, column space, exercises Class 3: Linearly independent sets, bases Section 2: Coordinate transformation Class 4: Definition of coordinate system, coordinate transformation Class 5: Dimension of a vector space, the basis theorem Class 6: Rank, the rank theorem, exercises Class 7: Change of basis, exercises 4.教学方法 Method of lecture and questions between classes and exercises after classes. 5.教学评价 Through the teaching of this chapter, students can master vector spaces. 第五章 Eigenvalues and Eigenvectors（小四号黑体） 1.教学目标 （五号宋体）  Learning knowledges about eigenvalues and eigenvectors. 2.教学重难点 Problems: 1. What are eigenvalues and eigenvectors? 2. What is the procedure to solve eigen-problems? 3. What is the condition for a matrix which can be diagonalized or not? 4. What are the properties for the characteristic equation?