Princeton University, Spring 2021

Contact: cos302-s21@lists.cs.princeton.eduCourse Google Calendar

Prof. Ryan Adams (OH: Mon/Wed 1-3pm) Zoom

TA: Joshua Aduol (OH: TBD)

TA: Jad Rahme (OH: TBD)

TA: Geoffrey Roeder (OH: TBD)

- 22 January 2021: Precept P05 (Fri 1:30-2:20pm) is cancelled.

Assignment 1 Out

- 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

- [required] MML 2.0-2.2
- [required] MML 2.3
- [optional] 3Blue1Brown video on vectors

Week 2: February 8-12, 2021

Assignment 1 **Due 6pm ET Friday** 12 Feb 2021

Assignment 2 Out

- 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

- [required] MML 2.3
- [required] MML 2.4
- [required] MML 2.5-2.6
- [optional] 3Blue1Brown video on basis vectors

Week 3: February 15-19, 2021

Assignment 2 **Due 6pm ET Friday** 19 Feb 2021

Assignment 3 Out

- Linear maps
- Change of basis
- Image and kernel
- Vector norms
- Inner products
- Positive definite matrices
- Orthogonal vectors
- Orthogonal bases
- Orthogonal complement
- Orthogonal projections

- [required] MML 2.7-2.8
- [required] MML 3.0-3.3
- [required] MML 3.4-3.8
- [optional] 3Blue1Brown video on change of basis
- [optional] 3Blue1Brown video on linear transformations

Week 4: February 22-26, 2021

Assignment 3 **Due 6pm ET Friday** 26 Feb 2021

Assignment 4 Out

- Gram-Schmidt orthogonalization
- Determinant and trace
- Eigenvalues and eigenvectors
- Eigenvalue decomposition
- Cholesky factorization

- [required] MML 3.8-3.9
- [required] MML 4.0-4.2
- [required] MML 4.3-4.4
- [optional] 3Blue1Brown video on determinants
- [optional] 3Blue1Brown video on eigenvectors and eigenvalues

Week 5: March 1-5, 2021

Assignment 4 **Due 6pm ET Friday** 5 March 2021

Assignment 5 Out

- SVD intuition
- SVD computation
- Approximation of matrices
- Applications of SVD
- QR factorization
- LU factorization

- [required] MML 4.5
- [required] MML 4.6-4.7

Week 6: March 8-12, 2021

- Catchup and review
- MIDTERM
- No precept

Assignment 5 **Due 6pm ET Friday** 19 March 2021

Assignment 6 Out

- Random variables
- Probability density functions
- Probability mass functions
- Some useful distributions

- [required] MML 6.0-6.2

Week 8: March 22-26, 2021

Assignment 7 Out

- Joint probability
- Independence and dependence
- Covariance
- Conditional independence

- [required] MML 6.3-6.4

Week 9: March 29 - April 2, 2021

Assignment 7 **Due 6pm ET Friday** 2 April 2021

Assignment 8 Out

- Basic inequalities and limit theorems
- Transforming random variables
- Univariate Gaussian distribution
- Multivariate Gaussian distribution
- Pseudo-random numbers
- Inverse transform sampling

- [required] MML 6.7

Week 10: April 5-9, 2021

Assignment 8 **Due 6pm ET Friday** 9 April 2021

Assignment 9 Out

- Integrals as expectations
- Proving unbiasedness
- Variance of Monte Carlo estimators
- Rejection sampling
- Importance sampling
- Information theory

- [required] MML 6.5

Assignment 9 **Due 6pm ET Friday** 16 April 2021
Assignment 10 Out

- Differentiation basics
- Partial derivatives
- Best affine approximation
- Gradient and steepest ascent
- Differentiation with respect to vectors and matrices
- Useful identities

- [required] MML 5.0-5.1
- [required] MML 5.2-5.5
- [optional] MML 5.6-5.8

Assignment 10 **Due 6pm ET Friday** 23 April 2021

- Optimization basics
- Constrained optimization
- Lagrange multipliers
- Convex optimization
- Linear programming

- [required] MML 7.0-7.1
- [required] MML 7.2
- [required] MML 7.3

- Assignments: 60% (lowest dropped)
- Midterm Exam: 20%
- Final Exam: 20%

**Does this course count towards****the SML certificate as a "Foundations of ML"?**No it does not. This is not a machine learning course in of itself. This course is intended to help you get the background to take machine learning and other courses that require continuous mathematics.**Does this course count towards the COS applications track?**No.**Can I take this concurrently with MAT 202?**Yes.**Are undergraduates and graduate students graded the same way?**Everyone's assignments and exams are graded with the same rubric, but the final grades will be curved separately.**Are precepts required?**No, but you should attend precept.**Why don't you do late days?**It introduces substantial additional bureaucracy and bookkeeping. I would rather that energy be spent working with students and making the course better.**What is Metacademy?**Metacademy is an exciting online tool developed by Roger Grosse and Colorado Reed for helping you to develop personalized instruction. It's meant to help you manage what you know about different topics and develop an individualized curriculum to learn a new subject.