Course Syllabus

Lecturer: Jack Thompson, jackth@kth.se

Assistant: Andrea Minna, aminna@kth.se

Lecture Plan

Module 1 (week 44): Vector Geometry

  • Lecture 1: The concept of vectors, chapter 1.1 
  • Lecture 2: Scalar product, orthogonality and angles. Cross product. chap. 1.2, 4.3 
  • Workshop 1.
  • Lecture 3: Lines and planes in space. Orthogonal projection on a vector. chap 1.3, 7.7 
  • Workshop 2.
  • Seminar: Written exam and workshop

Module 2 (week 45): Linear systems of equations and matrices

  • Lecture 4: Linear systems of equations. Gauss elimination. chap 2.1-2.2 
  • Lecture 5: Matrix arithmetic. Chapter 3.1 
  • Workshop 3.
  • Lecture 6: Inverse matrices and their calculation. Chapter 3.2-3.3 
  • Workshop 4.
  • Seminar: Written exam and workshop.

Module 3 (week 46): Solution sets, determinants and volume

  • Lecture 7: Solution sets of linear equation systems and linear independence. chap 3.4-3.5
  • Lecture 8: Determinants. chap 4.1-4.2
  • Workshop 5.
  • Lecture 9: Cross product, areas and volumes. Chapter 4.3
  • Workshop 6.
  • Seminar: Written exam and workshop.


Module 4 (week 47): Eigenvalues, eigenvectors and linear maps

  • Lecture 10: Linear mappings and their geometry. chap 6.1-6.2
  • Lecture 11: Eigenvalues ​​and eigenvectors, chapter 4.4
  • Workshop 7.
  • Lecture 12: The kernel and the image space. Composition of linear maps. chap 6.3-6.4
  • Workshop 8.
  • Seminar: Written exam and workshop.


Module 5 (week 48): Bases, projections and the least squares method

  • Lecture 13: Bases and dimension. Zero space and column space, the dimension theorems. chap. 7.1-7.6
  • Lecture 14: Projections. The least squares method. chap 7.7-7.8
  • Workshop 9.
  • Lecture 15: Gram-Schmidt orthonormalization. Chapter 7.9 
  • Workshop 10.
  • Seminar: Written exam and workshop.


Module 6 (week 49): Diagonalization and quadratic forms

  • Lecture 16: Coordinates and change of base. Chapter 7.11
  • Lecture 17: Matrix representations of a linear map.  Diagonalization. chap 8.1-8.2, 4.4
  • Workshop 11.
  • Lecture 18: Orthogonal diagonalization and quadratic forms. chap 8.3-8.4
  • Workshop 12.
  • Seminar: Written exam and workshop.


Module 7 (week 50): Quadratic curves and abstract vector spaces

  • Lecture 19: Quadratic curves and quadratic surfaces. Chapter 8.4
  • Lecture 20: Abstract vector spaces, linear mappings. chap. 9.1, 9.3
  • Workshop 13.
  • Lecture 21: Revision/exam preparation
  • Workshop rehearsal.