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TOCB1101 — Đại số | Chương trình đào tạo NEU

TOCB1101 — Đại số

Credits
3
Self-study hours
81
Showing intake
K68-2026

Course description

This course is designed to equip learners with the knowledge and skills in linear algebra to solve practical, computational, and mathematical problems. It covers basic concepts and methods of linear algebra, with emphasis on vector spaces, basis, transformations, and effective calculation tools for systems of linear equations, matrices, and determinants. The course aims to train thinking ability, calculation skills, and improve the ability to apply mathematical knowledge to analyze and research problems in economics, business, and engineering. The course also equips learners with the necessary knowledge, skills, and competencies to study related subjects in the training program, and continue to higher education.

The content of the course consists of 6 chapters:

Chapter 1. Systems of Linear Equation

Chapter 2. Matrix algebra

Chapter 3. Determinants and diagonalization

Chapter 4. Vector spaces

Chapter 5. Linear transformations

Chapter 6. Change of basis

Course requirements

Requirements for Final Examination

Attendance score must be at least 5 (according to University regulations).

See Appendix 2, Rubric 1 for attendance evaluation.

Requirements for Class Attendance

Students are responsible for attending all classes. In case of absence from school due to force majeure reasons, sufficient and reasonable proof must be provided. For each absence, 1 point will be deducted 1 point. Students who miss any classes more than 3 times, with or without reason, will be considered as failing to complete the course and have to re-register.

Students will be awarded points for constructive comments. These points are added to attendance points and group assignments (if any).

Individuals/groups who do not submit the group work will receive a score of 0 (zero). Late submissions will be deducted for each day of late submission.

Requirements for In-class Behaviour

The course is conducted on the principle of respecting learners and lecturers. Any behaviour that affects the teaching and learning process is strictly prohibited.

Students must come to class on time. Students who are late more than 10 minutes after class starts will not be allowed to attend the class. Do not make noise and affect others during the learning process.

Laptops and tablets are only used for the purpose of taking notes for and calculating for lectures and exercises, absolutely forbidden to use for other purposes

Lecturers

  • Le Thi Anh
  • Phung Minh Duc
  • Bui Quoc Hoan
  • Nguyen Duc Nam
  • c. Nguyễn Mai Quyên
  • c. Hoàng Văn Thắng
  • Doan Trong Tuyen
  • Tong Thanh Trung
  • Nguyen Van Quy

Teaching plan

Week 1

Lecture 1: Introduction to the course
References
Syllabus
Activities
Lecturer: + Introduce syllabus, textbooks, references; + Set learning requirements; + Instructs students to read documents. Students: + Read the Syllabus provided.
Assessment
Rubric1

Week 1

Chapter 1. Systems of Linear Equation 1.1 Solutions and Elementary Operations 1.2. Gaussian Elimination 1.3. Homogeneous Equations 1.4. An Application to Network Flow
References
[1] Chapter 1 [2] Chapter 1
Activities
Lecturer: + Deliver theory lectures; + Guide reading; + Require preview of examples, questions, exercises for Seminar 1. Students: + Read assigned materials before coming to class. + Prepare answers to questions and exercises for Seminar 1.
Assessment
Rubric1

Week 2

Seminar 1
References
[1] Chapter 1 [2] Chapter 1
Activities
Lecturer: + Attend roll call; + Guide students to answer questions and exercises; + Provide discussion situations and answer questions Students: + Read materials in advance; + Answer questions in the Seminar 1 slides; + Participate in discussions.

Learning resources

  • 1. Course Books
  • . Linear Algebra with Applications — Nicholson, W.K, Open Edition, 2023
  • 2. References
  • . Linear Algebra and its Applications — David C. Lay, Steven R. Lay & Judi J. McDonald, 5th Edition, 2016
  • 3. Other resources available at the University Library
Assessment
Rubric 1

Week 3

Lecture 2: Chapter 2. Matrix Algebra 2.1. Matrix Addition, Scalar Multiplication, and Tranposition 2.3. Equations, Matrices 2.4. Matrix Multiplication
References
[1] Chapter 2 [2] Chapter 1, 2
Activities
Lecturer: + Deliver theory lectures; + Guide reading; + Require preview of examples, questions, exercises for Seminar 2. Students: + Read assigned materials before coming to class. + Prepare answers to questions and exercises for Seminar 2.
Assessment
Rubric1

Week 4

Seminar 2
References
[1] Chapter 2 [2] Chapter 3
Activities
Lecturer: + Attend roll call; + Guide students to answer questions and exercises; + Provide discussion situations and answer questions Students: + Read materials in advance; + Answer questions in the Seminar 2 slides; + Participate in discussions.
Assessment
Rubric 1

Week 5

Lecture 3: Chapter 2. (continued) 2.4. Matrix Inverses 2.5. Elementary Matrices 2.7. LU-Factorization
References
[1] Chapter 2 [2] Chapter 5
Activities
Lecturer: + Deliver theory lectures; + Guide reading; + Require preview of examples, questions, exercises for Seminar 3. Students: + Read assigned materials before coming to class. + Prepare answers to questions and exercises for Seminar 3.
Assessment
Rubric 1

Week 6

Seminar 3
References
[1] Chapter 2 [2] Chapter 5
Activities
Lecturer: + Attend roll call; + Guide students to answer questions and exercises; + Provide discussion situations and answer questions Students: + Read materials in advance; + Answer questions in the Seminar 3 slides; + Participate in discussions.
Assessment
Rubric 1

Week 7

Lecture 4: Chapter 3. Determinants and Diagonalization 3.1. The Cofactor Expansion 3.2. Determinants and Matrix Inverses
References
[1] Chapter 3 [2] Chapter 3
Activities
Lecturer: + Deliver theory lectures; + Guide reading; + Require preview of examples, questions, exercises for Seminar 4. Students: + Read assigned materials before coming to class. + Prepare answers to questions and exercises for Seminar 4.
Assessment
Rubric 1

Week 8

Seminar 4
References
[1] Chapter 3 [2] Chapter 3
Activities
Lecturer: + Attend roll call; + Guide students to answer questions and exercises; + Provide discussion situations and answer questions Students: + Read materials in advance; + Answer questions in the Seminar 2 slides; + Participate in discussions.
Assessment
Rubric 1

Week 8

Midterm1
References
[1] Chapters 1 - 3
Activities
Test and evaluate students through multiple choice test/essay
Assessment
Rubric 2

Week 9

Lecture 5: Chapter 4. Vector Spaces 4.1. Examples and Basic Porperties 4.2. Subspaces and Spanning Sets 4.3. Linear Independence and Dimension
References
[1] Chapter 6 [2] Chapter 4
Activities
Lecturer: + Deliver theory lectures; + Guide reading; + Require preview of examples, questions, exercises for Seminar 5. Students: + Read assigned materials before coming to class. + Prepare answers to questions and exercises for Seminar 5.
Assessment
Rubric 1

Week 10

Seminar 5
References
[1] Chapter 6 [2] Chapter 4
Activities
Lecturer: + Attend roll call; + Guide students to answer questions and exercises; + Provide discussion situations and answer questions Students: + Read materials in advance; + Answer questions in the Seminar 5 slides; + Participate in discussions.
Assessment
Rubric 1

Week 11

Lecture 6: Chapter 4. (continued) 4.4. Finite Dimensional Spaces 4.5. Rank of a Matrix 4.6. Similarity and Diagonalization
References
[1] Chapters 6, 5 [2] Chapters 4, 5
Activities
Lecturer: + Deliver theory lectures; + Guide reading; + Require preview of examples, questions, exercises for Seminar 6. Students: + Read assigned materials before coming to class. + Prepare answers to questions and exercises for Seminar 6.
Assessment
Rubric 1

Week 12

Seminar 6
References
[1] Chapters 6, 5 [2] Chapters 4, 5
Activities
Lecturer: + Deliver theory lectures; + Guide reading; + Require preview of examples, questions, exercises for Seminar 6. Students: + Read assigned materials before coming to class. + Prepare answers to questions and exercises for Seminar 6.

Week 13

Lecture 7: Chapter 5. Linear Transformations 5.1. Examples and Elementary Properties 5.2. Kernel and Image of a Linear Transformation 5.3. Isomorphisms and Composition 5.4. More on Linear Recurrences
References
[1] Chapter 7 [2] Chapter 3, 4, 5
Activities
Lecturer: + Deliver theory lectures; + Guide reading; + Require preview of examples, questions, exercises for Seminar 7. Students: + Read assigned materials before coming to class. + Prepare answers to questions and exercises for Seminar 7.
Assessment
Rubric 1

Week 14

Midterm 2 Assessment
References
[1] Chapters 4-6
Activities
Test and evaluate students through multiple choice test/essay.
Assessment
Rubric 2

Week 14

Seminar 7
References
[1] Chapter 7 [2] Chapter 3, 4, 5
Activities
Lecturer: + Attend roll call; + Guide students to answer questions and exercises; + Provide discussion situations and answer questions Students: + Read materials in advance; + Answer questions in the Seminar 7 slides; + Participate in discussions.
Assessment
Rubric 1

Week 15

Lecture 8: Chapter 6. Change of Basis 6.1. The Matrix of a Linear Transformation 6.2. Operators and Similarity
References
[1] Chapter 9 [2] Chapter 3, 4,5
Activities
Lecturer: + Attend roll call; + Guide students to answer questions and exercises; + Provide discussion situations and answer questions Students: + Read materials in advance; + Answer questions in the Seminar 7 slides; + Participate in discussions.
Assessment
Rubric 1

Week 15

Review
References
[1] Chapters 1-6
Activities
Lecturer: + Announce the results of the process assessment + Troubleshooting + Summary of the main content of the course + Study guide and final exam Students ask questions and discuss
Assessment
Rubric 1
[1] Chapters 1 - 6
References
Essay (only one format)
Activities
See Appendix 1 (Exam Matrix)
Assessment
Rubric 2