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Mathematics

Linear Algebra, Part I

Learn the foundations of linear algebra through a balance of mathematical rigor and intuitive understanding.

Instructor Dr. Waleed A. Yousef Adjunct Professor, University of Victoria, Canada
A blue vector lattice transformed into a parallelepiped

01

Course overview

Learn the foundations of linear algebra through a balance of mathematical rigor and intuitive understanding.

02

What you will learn

This course is part I of a series of courses. It offers a rigorous introduction to linear algebra, guided by the foundational textbook by Gilbert Strang. Designed for students with a keen interest in mathematics and its applications, the course focuses on the core concepts presented in the first four chapters of Strang's book, while enhancing the learning experience with a comprehensive set of lecture notes that include all necessary proofs, which go beyond what is provided in the textbook.

The course emphasizes a balanced approach, combining mathematical rigor with intuitive understanding. Key topics include systems of linear equations, vector spaces, and orthogonality. Students will not only master the theoretical aspects of these subjects but also develop a strong intuition for their practical applications in various fields.

03

Lecture syllabus

Video titles and durations as published on Arabsera. The advertised lecture total may differ from the number of video entries, which can include introductions, tutorials, and split sessions.

Video titles and durations 30
  1. 01 Linear Algebra and Applications: "Data Science" in particular
  2. 02 Sec. 1.0 Introduction to Vectors (back to school)
  3. 03 Sec. 1.1 angle, length, dot product (back to school)
  4. 04 Sec. 1.2 Abstraction and extension to high dimensions
  5. 05 Sec. 2.1 Linear Equations (column and row pictures)
  6. 06 Sec. 2.2 The idea of elimination
  7. 07 Sec. 2.3 Rules of matrix operations (a)
  8. 08 Sec. 2.3 Rules of matrix operations (b): understanding matrix multiplication
  9. 09 Sec. 2.3 Rules of matrix operations (c)
  10. 10 Sec. 2.3 Rules of matrix operations (d): application to graph theory
  11. 11 Sec. 2.3 Rules of matrix operations (e): quadratic forms
  12. 12 Sec. 2.4 Elimination Using Matrices (a)
  13. 13 Sec. 2.4 Elimination Using Matrices (b): block elimination
  14. 14 Sec. 2.5 Inverse Matrices (a)
  15. 15 Sec. 2.5 Inverse Matrices (b): special matrices
  16. 16 Sec. 2.5 Inverse Matrices (c): inverse by Gauss-Jordan elimination
  17. 17 Sec. 2.5 Inverse Matrices (d): pivots, solution, left, right, inverse, uniqueness
  18. 18 Sec. 2.6 LU Factorization (a): is Gauss-elimination
  19. 19 Sec. 2.6 LU Factorization (b): properties of L
  20. 20 Sec. 2.6 LU Factorization (c): properties of L
  21. 21 Remarks on Computations (a): scientific computing
  22. 22 Remarks on Computations (b): complexity of algorithms
  23. 23 Remarks on Computations (c): rounding-off analysis and hardware
  24. 24 Sec. 3.1 Vector Spaces (a)
  25. 25 Sec. 3.1 Vector Spaces (b): subspaces
  26. 26 Sec. 3.1 Vector Spaces (c): column space
  27. 27 Sec. 3.2 Null Space (a): definition and examples
  28. 28 Sec. 3.2 Null Space (b): more examples
  29. 29 Sec. 3.2 Null Space (c): data science
  30. 30 Sec. 3.2 Null Space (d): Gauss elimination algorithm revisited and detailed

04

Teaching support (check your plan)

  • Discussion groups
  • TA-human texting for Q&A
  • TA-GPT (coming soon)

05

Textbook

Strang, G., 2016. Introduction to Linear Algebra, 5th Edition.

06

Certificate

Awarded after passing a brief sample exam, which you may attempt multiple times.