Linear Algebra
Week 1: February 1-5, 2021
Assignment 1 Out
Topics:
- Course logistics
- Vectors
- Systems of linear equations as matrices
- Adding and multiplying matrices
- Matrix transpose and symmetry
- Particular and general solution
- Transformations
- Row echelon form
- Gaussian elimination
Readings and Supplementary Material:
Week 2: February 8-12, 2021
Assignment 1 Due 6pm ET Friday 12 Feb 2021
Assignment 2 Out
Topics:
- Computing the inverse
- Overconstrained and underconstrained systems
- Applications
- Brief tour of more advanced methods: Jacobi, Gauss-Seidel, Krylov subspaces
- Groups
- Vector spaces
- Vector subspaces
- Linear independence
- Rank
- Basis sets
Readings and Supplementary Material:
Week 3: February 15-19, 2021
Assignment 2 Due 6pm ET Friday 19 Feb 2021
Assignment 3 Out
Topics:
- Linear maps
- Change of basis
- Image and kernel
- Vector norms
- Inner products
- Positive definite matrices
- Orthogonal vectors
- Orthogonal bases
- Orthogonal complement
- Orthogonal projections
Readings and Supplementary Material:
Week 4: February 22-26, 2021
Assignment 3 Due 6pm ET Friday 26 Feb 2021
Assignment 4 Out
Topics:
- Gram-Schmidt orthogonalization
- Determinant and trace
- Eigenvalues and eigenvectors
- Eigenvalue decomposition
- Cholesky factorization
Readings and Supplementary Material:
Week 5: March 1-5, 2021
Assignment 4 Due 6pm ET Friday 5 March 2021
Assignment 5 Out
Topics:
- SVD intuition
- SVD computation
- Approximation of matrices
- Applications of SVD
- QR factorization
- LU factorization
Readings and Supplementary Material:
Week 6: March 8-12, 2021
- Catchup and review
- MIDTERM
- No precept
Probability
Week 7: March 17-19, 2021 (short week)
Assignment 5 Due 6pm ET Friday 19 March 2021
Assignment 6 Out
Topics:
- Random variables
- Probability density functions
- Probability mass functions
- Some useful distributions
Readings and Supplementary Material:
Week 8: March 22-26, 2021
Assignment 7 Out
Topics:
- Joint probability
- Independence and dependence
- Covariance
- Conditional independence
Readings and Supplementary Material:
Week 9: March 29 - April 2, 2021
Assignment 7 Due 6pm ET Friday 2 April 2021
Assignment 8 Out
Videos:
- Basic inequalities and limit theorems
- Transforming random variables
- Univariate Gaussian distribution
- Multivariate Gaussian distribution
- Pseudo-random numbers
- Inverse transform sampling
Readings and Supplementary Material:
Week 10: April 5-9, 2021
Assignment 8 Due 6pm ET Friday 9 April 2021
Assignment 9 Out
Topics:
- Integrals as expectations
- Proving unbiasedness
- Variance of Monte Carlo estimators
- Rejection sampling
- Importance sampling
- Information theory
Readings and Supplementary Material: