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Curricular information is subject to change
Students are expected to achieve the following competence:
* Giving algebraic and geometrical representations for vectors
* Performing arithmetic with vectors;
* Using vectors to solve classical geometric problems;
* Manipulating dot and cross products, and using them to solve geometric problems;
* Solving systems of linear equations in terms of Gaussian elimination and Cramers rule;
* Performing matrix arithmetic;
* Calculating inverse of a matrix and a determinant;
* Solving eigenvalue problem for a matrix;
* Diagonalizing a matrix;
* Solving a quadratic form problem in terms of matrix diagonalization;
* Being able to identifying the rank of a matrix;
* Giving the space spanned by a number of vectors.
Teaching Plan
Week 1: Appendix: Revisit to high school mathematics: Set theory, summation and product notations, mathematical induction.
Definitions & properties of vectors.
Week 2: Definitions & properties of vectors, scalar multiplication, linear independence. Tutorial 1.
Week 3: Dot product (algebraic & geometric definitions), projection of vectors, two important inequalities, applications.
Week 4: Cross product (algebraic & geometric definitions), applications. Tutorial 2.
Week 5: Applications of vectors: equations of lines and planes, scalar triple product.
Week 6: Matrices and systems of linear equations, Gaussian elimination. Tutorial 3.
Week 7: Row echelon form, reduced echelon form, homogeneous systems.
Week 8: Revision for mid-term exam. Tutorial 4.
Week 9: Matrix algebra, elementary matrices, partitioned matrices, LU decomposition.
Week10: Determinant of a matrix, properties of determinants. Tutorial 5.
Week11: Adjoint matrix, Cramers rule.
Week12: Definitions of eigenvalue and eigenvector of a matrix. Tutorial 6.
Week13: Diagonalization of matrix.
Week14: Quadratic forms, positive and negative definite matrices, rank of matrix. Tutorial 7.
Week15: Vector spaces and subspaces spanned by vectors.
Week16: Revision for final exam.
Remarks:
1. In each odd week there are two lectures; in each even week there is one lecture and one tutorial.
2. The chapter of vector spaces is only a brief review of the theory. Interested students are encouraged to read reference textbooks, and wait for future advanced
courses on algebra theory.
| Student Effort Type | Hours |
|---|---|
| Lectures | 64 |
| Practical | 66 |
| Total | 130 |
Not applicable to this module.
| Description | Timing | Component Scale | % of Final Grade | ||
|---|---|---|---|---|---|
| Examination: Midterm Exam. 90 minutes examination, at 1/2 of the semester. |
Unspecified | No | Alternative linear conversion grade scale 40% | No | 20 |
| Continuous Assessment: Attendence recording and tutorial participation. | Throughout the Trimester | n/a | Pass/Fail Grade Scale | No | 5 |
| Assignment: Assignment. Essay based on group work + Oral presentation. 1st round: Selection based on the submitted essays. Top 15% enter into 2nd round. 2nd round: Selection based on oral defense. |
Unspecified | n/a | Graded | No | 15 |
| Examination: Quiz. 30 minutes examination, at 1/4 of the semester. |
Unspecified | No | Alternative linear conversion grade scale 40% | No | 10 |
| Examination: Final Exam. 90 minutes of examination, at the end of the semester. |
Unspecified | No | Alternative linear conversion grade scale 40% | No | 50 |
| Remediation Type | Remediation Timing |
|---|---|
| In-Module Resit | Prior to relevant Programme Exam Board |
• Group/class feedback, post-assessment
• Peer review activities
Not yet recorded.