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*Curricular information is subject to change*

Learning Outcomes:

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 Cramer’s 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, Cramer’s 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 Hours:

Student Effort Type | Hours |
---|---|

Lectures | 64 |

Practical | 66 |

Total | 130 |

Approaches to Teaching and Learning:

Lecturing (face-to-face teaching) + tutorials + group project on open questions + oral defense in full English + close-book examinations.

Lecturing (face-to-face teaching) + tutorials + group project on open questions + oral defense in full English + close-book examinations.

Requirements, Exclusions and Recommendations

Not applicable to this module.

Module Requisites and Incompatibles

This module is delivered overseas and is not available to students based at the UCD Belfield or UCD Blackrock campuses

Remediation Type | Remediation Timing |
---|---|

In-Module Resit | Prior to relevant Programme Exam Board |

Feedback Strategy/Strategies

• Group/class feedback, post-assessment

• Peer review activities

How will my Feedback be Delivered?

This is about the component of Assignment. For the final total score of this course, it will be released by the UCD administrative department.

Name | Role |
---|---|

Enchang Sun | Tutor |

Wenying Wu | Tutor |