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Students should use
ODTUClass
There will be a total of 42 one hour units in the course. Each week, three units will be taught.
The contents of each unit are listed below, where the section numbers refer to the course textbook by L. Smith.
Note: This schedule may be modified/reorganized as the class progresses.
Week 1:
Sep.2327 
0  Introduction to the Course 
1 
Chapter 2. Vector Spaces §2.1: Axioms for Vector Spaces. 

2 
§2.2: Cartesian (or Euclidean) Spaces. §2.3: Some Rules for Vector Algebra. 

Week 2:
Sep.30Oct.4 
3 
Chapter 3. Examples of Vector Spaces §3.1: Three Basic Examples. 
4 
§3.2: Further Examples of Vector Spaces. 

5 
Chapter 4. Subspaces §4.1: Basic Properties of Vector Subspaces. 

Week 3:
Oct.711 
6 
§4.2: Examples of Subspaces. 
7 
Chapter 5. Linear Independence and Dependence §5.1: Basic Definitions and Examples. 

8 
§5.2: Properties of Independent and Dependent Sets. 

Week 4:
Oct.2125 
9 
Chapter 6. FiniteDimensional Vector Spaces and Bases §6.1: FiniteDimensional Vector Spaces. 
10 
§6.2: Properties of Bases. 

11 
§6.3: Using Bases. 

Week 5:
Oct.28Nov.1 
Holiday: Tuesday, 29 October  
12 
Chapter 7. The Elements of Vector Spaces: A Summing Up §7.1: Numerical Examples. 

Midterm 1 at 17:40 on Thursday, 31 October (boo!)  
Week 6:
Nov.48 
13 
Chapter 8. Linear Transformations §8.1: Definition of Linear Transformations. 
14 
§8.2: Examples of Linear Transformations. 

15 
§8.3: Properties of Linear Transformations. 

Week 7:
Nov.1115 
16 
§8.4: Images and Kernels of Linear Transformations. 
17 
§8.5: Some Fundamental Constructions. 

18 
§8.6: Isomorphism of Vector Spaces. 

Holiday: Friday, 15 November  
Week 8:
Nov.1822 
19 
Chapter 9. Linear Transformations: Examples and Applications §9.1: Numerical Examples. 
20 
Chapter 10. Linear Transformations and Matrices §10.1: Linear Transformations and Matrices in R^{2}. 

21 
§10.2: Some Numerical Examples. 

Week 9:
Nov.2529 
22 
§10.3: Matrices and Their Algebra. 
23 
§10.4: Special Types of Matrices. 

24 
Chapter 11. Representing Linear Transformations by Matrices §11.1: Representing a Linear Transformation by a Matrix. 

Week 10:
Dec.26 
25 
§11.2: Basic Theorems. 
26 
§11.3: Change of Bases. 

27 
Chapter 12. More on Representing Linear Transformations by Matrices §12.1: Projections. §12.2: Nilpotent Transformations. §12.3: Cyclic Transformations. 

Midterm 2 at 17:40 on Thursday, 5 December  
Week 11:
Dec.913 
28 
Chapter 13. Systems of Linear Equations §13.1: Existence Theorems. 
29 
§13.2: Reduction to Echelon Form. 

30 
§13.2: Reduction to Echelon Form (cont). 

Week 12:
Dec.1620 
31 
Chapter 14. The Elements of Eigenvalue and Eigenvector Theory §14.1: The Rank of an Endomorphism. 
32 
§14.2: Eigenvalues and Eigenvectors. 

33 
§14.3: Determinants. 

Week 13:
Dec.2327 
34 
§14.4: The Characteristic Polynomial. 
35 
§14.5: Diagonalization Theorems. 

36 
§17.3: Jordan Form (parts of). 

Week 14:
Dec.30Jan.3 
37 
Chapter 15. Inner Product Spaces §15.1: Scalar Products. 
Holiday: Wednesday, 1 January  
38 
§15.2: Inner Product Spaces. 

39 
§15.3: Isometries. 

Week 15:
Jan.610 
40 
Additional Topics and Applications §15.4: The Riesz Representation Theorem. 
41 
Chapter 16. The Spectral Theorem and Quadratic Forms §16.1: SelfAdjoint Transformations. 

42 
§16.2: The Spectral Theorem. 

FINAL EXAM 9:00 on Friday, 24 January 