1. Prerequisites and notational differences
2. Determinant in 2 and 3 dimensions
3. Determinants in $n$ dimensions
4. Cofactor expansion along rows
5. Determinant of upper triangular matrices
6. More facts about determinants
7. Bases and coordinate systems
8. Subspaces, linear dependence, basis, and dimension
9. Row space, column space, nullspace (kernel)
10. Orthonormal bases
11. Linear maps I
12. Linear maps and matrices
13. Least squares approximation
14. Eigenvalues and eigenvectors
15. Differential equations
16. Probability
17. Expectation and random variables
18. Continuous probability and normal distribution
19. Normal distribution
20. Central Limit Theorem and Binomial approximation
21. Student's $t$ distribution
22. Hypothesis testing
23. Paul the octopus
24. Algebra of events --- omitted
25. Syllabus for May 2022 exam