This page is for archival purposes only!
Students should use
ODTU-Class
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.
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Week 1:
Oct.5-9 |
0 | Introduction to the Course |
| 1 |
Chapter 2. Vector Spaces §2.1: Axioms for Vector Spaces. |
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| 2 |
§2.2: Cartesian (or Euclidean) Spaces. §2.3: Some Rules for Vector Algebra. |
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Week 2:
Oct.12-16 |
3 |
Chapter 3. Examples of Vector Spaces §3.1: Three Basic Examples. |
| 4 |
§3.2: Further Examples of Vector Spaces. |
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| 5 |
Chapter 4. Subspaces §4.1: Basic Properties of Vector Subspaces. |
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Week 3:
Oct.19-23 |
6 |
§4.2: Examples of Subspaces. |
| 7 |
Chapter 5. Linear Independence and Dependence §5.1: Basic Definitions and Examples. |
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| 8 |
§5.2: Properties of Independent and Dependent Sets. |
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| Make-Up: Thursday lecture on Saturday, October 24 | ||
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Week 4:
Oct.26-30 |
9 |
Chapter 6. Finite-Dimensional Vector Spaces and Bases §6.1: Finite-Dimensional Vector Spaces. |
| 10 |
§6.2: Properties of Bases. |
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| 11 |
§6.3: Using Bases. |
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| Holiday: Thursday, October 29 | ||
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Week 5:
Nov.2-6 |
12 |
Chapter 7. The Elements of Vector Spaces: A Summing Up §7.1: Numerical Examples. |
| 13 |
Chapter 8. Linear Transformations §8.1: Definition of Linear Transformations. |
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| 14 |
§8.2: Examples of Linear Transformations. |
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Week 6:
Nov.9-13 |
15 |
§8.3: Properties of Linear Transformations. |
| 16 |
§8.4: Images and Kernels of Linear Transformations. |
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| 17 |
§8.5: Some Fundamental Constructions. |
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Week 7:
Nov.16-20 |
18 |
§8.6: Isomorphism of Vector Spaces. |
| 19 |
Chapter 9. Linear Transformations: Examples and Applications §9.1: Numerical Examples. |
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| 20 |
Chapter 10. Linear Transformations and Matrices §10.1: Linear Transformations and Matrices in R2. |
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Week 8:
Nov.23-27 |
21 |
§10.2: Some Numerical Examples. |
| 22 |
§10.3: Matrices and Their Algebra. |
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| 23 |
§10.4: Special Types of Matrices. |
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Week 9:
Nov.30-Dec.4 |
24 |
Chapter 11. Representing Linear Transformations by Matrices §11.1: Representing a Linear Transformation by a Matrix. |
| 25 |
§11.2: Basic Theorems. |
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| 26 |
§11.3: Change of Bases. |
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Week 10:
Dec.7-11 |
27 |
Chapter 12. More on Representing Linear Transformations by Matrices §12.1: Projections. §12.2: Nilpotent Transformations. §12.3: Cyclic Transformations. |
| 28 |
Chapter 13. Systems of Linear Equations §13.1: Existence Theorems. |
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| 29 |
§13.2: Reduction to Echelon Form. |
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Week 11:
Dec.14-18 |
30 |
§13.2: Reduction to Echelon Form (cont). |
| 31 |
Chapter 14. The Elements of Eigenvalue and Eigenvector Theory §14.1: The Rank of an Endomorphism. |
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| 32 |
§14.2: Eigenvalues and Eigenvectors. |
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| Make-Up: Wednesday lecture on Saturday, December 19 | ||
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Week 12:
Dec.21-25 |
33 |
§14.3: Determinants. |
| 34 |
§14.4: The Characteristic Polynomial. |
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| 35 |
§14.5: Diagonalization Theorems. |
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| Holiday: Wednesday, December 23 Make-Up: Friday lecture on Saturday, December 26 |
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Week 13:
Dec.28-Jan.1 |
36 |
§17.3: Jordan Form (parts of). |
| 37 |
Chapter 15. Inner Product Spaces §15.1: Scalar Products. |
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| 38 |
§15.2: Inner Product Spaces. |
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| Holiday: Friday, January 1 | ||
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Week 14:
Jan.4-8 |
39 |
§15.3: Isometries. |
| 40 |
Additional Topics and Applications §15.4: The Riesz Representation Theorem. |
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| 41 |
Chapter 16. The Spectral Theorem and Quadratic Forms §16.1: Self-Adjoint Transformations. |
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| FINAL EXAMS January 11 -- January 23 | ||