Linear Algebra, Part 1

This is the course web page for the course Linear Algebra, Part 1.

What you will get from this course: Completing this course will provide you with a solid understanding of the fundamental concepts of linear algebra and skill in performing basic operations of linear algebra. You will also have the opportunity to practice these skills throughout the course, and to get feedback on your practice so that you will know what you have to work on to improve. You will learn how to apply what you have learned to solve important practical problems. You will gain in mathematical maturity, and you will be better able to cope with abstractions. This course will help you to prepare for the fast pace of university courses.

Linear algebra is considered to be the hardest mathematics course for first-year university students in mathematics, science, and engineering programs. It has even been hard for future mathematicians! The problem is that for virtually all students this is their first encounter with abstract mathematics, and it hits hard. I remember my own difficulties with abstract mathematics when I was in my first two years of university. For almost all students, coping with abstractions at a young age is a real challenge. This course helps to bridge the yawning abyss between concrete mathematics and abstract mathematics, by bringing you along step by step. By grappling with all the key concepts in gradual steps of increasing difficulty, you will be well-prepared to flourish in first-year linear algebra courses that are typically taught in very abstract ways.

Syllabus

  • Coordinate systems in two and three dimensions
  • Equations of a line
  • Parametric equations and their physical interpretation
  • Vectors
  • Scalar products of vectors and some applications
  • Cross product of vectors and some applications
  • Using vectors in Euclidean geometry
  • Solving systems of linear equations
  • Solving systems of linear equations using matrix notation
  • Complex numbers
  • Vector spaces
  • Linear transformations
  • Eigenvalues and eigenvectors
  • Applications in physics and engineering

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