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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 2.0-2.2; Slides: More on vectors |
3Blue1Brown videos:
1,
2,
3,
4;
More on vectors; Q&A |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| Wed, Oct 21 | Random variables | MML 6.0-6.2 | Videos from Ryan Adams:
1,
2;
Q&A |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| 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 | |||