# COS 302 - Mathematics for Numerical Computing and Machine Learning

### Fall 2020

 Course home Outline and Lectures Assignments

### Schedule

Date Topic Readings Videos Assignments
Mon, Aug 31 Course introduction Slides Class recording Questionnaire
Wed, Sep 2 Vectors, matrices, linear systems MML 2.0-2.2; Slides: More on vectors 3Blue1Brown videos: 1, 2, 3, 4;
More on vectors;
Q&A

Precept Getting set up with Overleaf, Colab Python tutorial sec. 1-5,
NumPy tutorial ("The Basics" section),
Python/NumPy Tutorial (optional - from Stanford CS231n),
Color, Audio, Face notebooks (optional - click on "Open with Google Colaboratory")
Overleaf basics; Colab basics
Mon, Sep 7 Solving linear systems MML 2.3; Slides: Numerical analysis, Linear Systems, Optional: Strassen's method Numerical analysis, Linear Systems,
Optional: Strassen's Method;
Q&A

Wed, Sep 9 Groups and vector spaces MML 2.4-2.6; Slides: Linear Independence, Bases, Rank Linear Independence, Bases, Rank;
3Blue1Brown videos: 1, 2;
Q&A

Precept Basis concepts Slides: Groups, Vector Spaces, and Gaussian Elimination, Groups, Vector Spaces, and Gaussian Elimination
Mon, Sep 14 Linear maps, change of basis MML 2.7-2.8; Slides: Linear Mappings Linear Mappings;
3Blue1Brown videos: 1, 2, 3;
Q&A
Assignment 1 due
Wed, Sep 16 Norms and inner products MML 3.1-3.3; Slides: Norms and inner products Dot products (3Blue1Brown);
Norms and inner products;
Q&A

Precept Orthogonality MML 3.4-3.8.1; Slides: Orthogonality Angles & Orthogonality, Orthogonal Bases, Orthogonal Complement
Orthogonal Projection onto 1D Subspaces

Mon, Sep 21 Projections and Overdetermined Systems MML 3.8.2-3.9; Slides: Orthogonal Projections and Overdetermined Linear Systems,
Gram-Schmidt Orthogonalization
Orthogonal Projections and Overdetermined Linear Systems,
Gram-Schmidt Orthogonalization;
Q&A
Assignment 2 due
Wed, Sep 23 Eigenvectors and eigenvalues; Determinant and Trace MML 4.1-4.2; Slides: Matrix Trace and Invariants 3Blue1Brown videos: 1, 2;
Matrix Trace and Invariants;
Q&A

Precept Eigendecomposition MML 4.4, Slides, Eigendecomposition colab, Ellipse colab, Eigendecomposition and Diagonalization colab walkthrough
Mon, Sep 28 Singular Value Decomposition MML 4.5-4.6; Slides: SVD SVD;
Q&A
Assignment 3 due
Wed, Sep 30 SVD for PCA and MDS MML 10.1-10.6; Slides: PCA and MDS PCA and MDS;
Q&A

Precept LU and Cholesky decompositions MML 4.3; Slides: LU and Cholesky LU & Cholesky Decomposition Part 1 LU & Cholesky Decomposition Part 2
Mon, Oct 5 Q&A for midterm Midterm information and sample questions Q&A Assignment 4 due
Wed, Oct 7 Exam 1:    90 minutes, available noon EDT Wed through noon EDT Thu
Mon, Oct 12 No class, no precept - fall break!
Wed, Oct 14 Differentiation and partial derivatives MML 5.1-5.2 Videos from Ryan Adams: 1, 2, 3, 4;
Q&A

Precept SVD review; answer questions about midterm
Mon, Oct 19 Differentiating vector- and matrix-valued functions MML 5.3-5.5; Slides: Differentiating vector- and matrix-valued functions; Optional: MML 5.6-5.8 Gradient and directional derivative;
Differentiating vector- and matrix-valued functions;
Q&A

Wed, Oct 21 Random variables MML 6.0-6.2 Videos from Ryan Adams: 1, 2;
Q&A

Precept Sampling from distributions Pseudorandom numbers and inverse transform sampling, colab Pseudorandom numbers and inverse transform sampling
Mon, Oct 26 More on random variables MML 6.3-6.4; Cheat sheet on probability distributions Videos from Ryan Adams: 1, 2;
Q&A
Assignment 5 due
Wed, Oct 28 Independent and dependent random variables   Video from Ryan Adams;
Q&A

Precept Transforming random variables MML 6.7; Transforming random variables Transforming random variables
Mon, Nov 2 Aggregating random variables Cheat sheet on probabilistic identities and inequalities Video from Ryan Adams;
Q&A
Assignment 6 due
Tue, Nov 3 Election day - please vote, if able!
Wed, Nov 4 Multivariate Gaussian distributions MML 6.5 Video from Ryan Adams;
Video on the Box-Muller transform

Precept Computing expectation Expectation exercises - Solutions
Mon, Nov 9 Monte Carlo integration Monte Carlo slides Monte Carlo integration;
Q&A
Assignment 7 due
Wed, Nov 11 Information theory   Video from Ryan Adams;
Q&A

Precept More on Monte Carlo More on Monte Carlo Video
Mon, Nov 16 Optimization basics MML 7.0-7.1 Video from Ryan Adams;
Q&A
Assignment 8 due
Wed, Nov 18 Convex optimization MML 7.3 Video from Ryan Adams
Q&A

Precept Constrained optimization MML 7.2; Slides on Constrained Optimization
Mon, Nov 23 Q&A for final Final exam information and sample questions Q&A Assignment 9 due
Sun, Dec 13 Exam 2:    180 minutes, will be available 1:30 EST Sunday through 1:30 EST Monday

Last update 23-Nov-2020 12:58:09
smr at princeton edu