COS 302  Mathematics for Numerical Computing and Machine Learning 
Fall 2020 

Course home  Outline and Lectures  Assignments 
Date  Topic  Readings  Videos  Assignments 

Mon, Aug 31  Course introduction  Slides  Class recording  Questionnaire 
Wed, Sep 2  Vectors, matrices, linear systems  MML 2.02.2; 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. 15,
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 2.42.6; 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 2.72.8; Slides: Linear Mappings 
Linear Mappings;
3Blue1Brown videos: 1, 2, 3; Q&A 
Assignment 1 due 
Wed, Sep 16  Norms and inner products  MML 3.13.3; Slides: Norms and inner products 
Dot products (3Blue1Brown);
Norms and inner products; Q&A 

Precept  Orthogonality  MML 3.43.8.1; Slides: Orthogonality  Angles & Orthogonality, Orthogonal Bases, Orthogonal Complement
Orthogonal Projection onto 1D Subspaces 

Mon, Sep 21  Projections and Overdetermined Systems 
MML 3.8.23.9;
Slides:
Orthogonal Projections and
Overdetermined Linear Systems,
GramSchmidt Orthogonalization 
Orthogonal Projections and
Overdetermined Linear Systems,
GramSchmidt Orthogonalization; Q&A 
Assignment 2 due 
Wed, Sep 23  Eigenvectors and eigenvalues; Determinant and Trace  MML 4.14.2; 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 4.54.6; Slides: SVD 
SVD;
Q&A 
Assignment 3 due 
Wed, Sep 30  SVD for PCA and MDS  MML 10.110.6; 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 5.15.2  Videos from Ryan Adams:
1,
2,
3,
4;
Q&A 

Precept  SVD review; answer questions about midterm  
Mon, Oct 19  Differentiating vector and matrixvalued functions  MML 5.35.5; Slides: Differentiating vector and matrixvalued functions; Optional: MML 5.65.8 
Gradient and directional derivative;
Differentiating vector and matrixvalued functions; Q&A 

Wed, Oct 21  Random variables  MML 6.06.2  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 6.36.4; 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 BoxMuller 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 7.07.1 
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 