Topics: Systems of linear equations, Gaussian elimination, homogeneous equations. Vector spaces and subspaces. Linear independence. Basis and dimensions. Linear transformations. Matrix representation. Image and kernel. Inner products. Length and distances. Angles and orthogonality. Orthonormal basis, orthogonal complement, orthogonal projections. Determinant and trace. Eigenvalues and eigenvectors. Spectral theorem. Singular value decomposition. Rank-k approximations. Basic notions from probability theory. Conditional probability. Bayes' theorem. Random variables. Probability distributions. Summary statistics. Joint distributions. Independent rvs. Covariance and correlation. Central limit theorems. Conjugacy and exponential family. Change of variables/inverse transform. Least squares and data fitting. Linear regression.
Prerequisites: MATH UN1101 - Calculus I (or equivalent) is recommended.
Instructor: Chen-Chih Lai
Email: cl4205 at math dot columbia dot edu
Office: 622 Mathematics Building
Office hours provide you with opportunities to ask questions about course material or mathematics in general.
Office Hours: Mon 4:10pm–5:25pm and Tue 10:10am–11:25am, or by appointment (in-person or via Zoom)
Teaching assistant(s):
Graduate TA:
Nicolás Vilches (Help room hours: Wed 9:00am–12:00pm in 406 Math)
Shanshan Gong (Tue 5:00pm–7:00pm and Wed 7:00pm–8:00pm in 406 Math)
Undergraduate TAs:
Heyuan Yao (Help room hours: Thu 10:00am–12:00pm in 406 Math);
Textbook: Mathematics for Machine Learning, by Marc Peter Deisenroth, A. Aldo Faisal, and Cheng Soon Ong.
Probability and Statistics for STEM: a course in one semester, by Emmanuel N. Barron, John G. Del Greco.
Grading: Homework (25%), Project (15%), Midterm 1 (15%), Midterm 2 (15%), Final Exam (30%).
Important websites for this course:
Lecture:
Days & Times: Mon, Wed 1:10pm–2:25pm
Room: 312 Mathematics Building
Class dates: Jan 17, 2024–Apr 29, 2024
Exam Dates:
You are encouraged to take advantage of the math Help Rooms. The schedule is available at https://www.math.columbia.edu/general-information/help-rooms.
This schedule will be updated as we go along.
| Monday | Wednesday |
|---|---|
| Jan 17: System of linear equations, Matrices and vectors | |
| Jan 22: Gaussian elimination | Jan 24: Vector spaces |
| Jan 29: Vector subspaces, Linear independence/HW1 due | Jan 31: Basis and dimension, Linear transformations |
| Feb 5: Matrix representation, Image and kernel of a linear transformation/HW2 due | Feb 7: Rank, Inner product, Length and distances |
| Feb 12: Review/HW3 due | Feb 14: Miterm 1 |
| Feb 19: Angles and orthogonality, Orthonormal basis, Orthogonal complement | Feb 21: Orthogonal projections, Determinant |
| Feb 26: Trace. Eigenvalues and eigenvectors, Spectral theorem/HW4 due | Feb 28: Eigendecomposition and diagonalization |
| Mar 4: Singular value decomposition/HW5 due | Mar 6: Rank-k approximations |
| Mar 11: No class | Mar 13: No class |
| Mar 18: Basic notions from probability theory/HW6 due | Mar 20: Conditional probability, Bayes' theorem |
| Mar 25: Review/HW7 due | Mar 27: Midterm 2 |
| Apr 1: Random variables | Apr 3: Probability distributions |
| Apr 8: Probability distributions, Summary statistics/HW8 due | Apr 10: Moment generating functions, Joint distributions |
| Apr 15: Independent rvs, Covariance and correlation/HW9 due | Apr 17: Central limit theorems, Conjugacy, Exponential family |
| Apr 22: Change of variables, Inverse transform, Least squares and data fitting, Linear regression/HW10 due | Apr 24: Project presentation |
| Apr 29: Project presentation | May 1: No class/HW11 due |
| May 6: Final Exam (9:00am–12:00pm) |
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