Course materials on github

All of the course materials from Fall 2017 were posted on Github, along with brief lecture summaries. You can view these materials and summaries directly on github.

(Teachers are welcome to re-use these github materials for other courses or semesters.)

Exams

• Exam 1 and solutions
• Exam 2 and solutions
• Exam 3 and solutions
• Final exam and solutions

Problem Sets

1. Problem set 1 and solutions
2. Problem set 2 and solutions
3. Problem set 3 and solutions
4. Problem set 4 and solutions
5. Problem set 5 and solutions
6. Problem set 6 and solutions
7. Problem set 7 and solutions
8. Problem set 8 and solutions
9. Problem set 9 and solutions
10. Problem set 10 and solutions
11. Problem set 11 and solutions
12. Problem set 12 and solutions

Lecture notes

• Overview
• Gaussian elimination
• Matrix-multiplication and LU notebook
• Matrix inverse and LU notebook
• Matrix inverses and complexity
• LU factorization notebook
• Graphs and networks notebook
• Multidimensional Newton’s method notebook
• Least-square fitting notebook
• Orthogonal polynomials
• Fourier sine series
• Determinants notebook
• Eigenvalues and polynomials
• Diagonalization
• Diagonalization
• Fibonacci numbers
• Markov matrices
• Markov matrices
• Analyzing Chutes & Ladders
• Ordinary differential equations (ODEs).
• Matrix exponentials eᴬ.
• SVD
• Statistics and PCA
• Notes on Jordan vectors
• Circulant matrices
• Errors and condition numbers
• Dense and sparse linear algebra
• Power method for eigenproblems

Using the Julia software

This semester, we used the Julia software for homework and lecture demonstrations. Julia is a programming language, but no "real" programming will be required in 18.06: we just used it as a "fancy calculator" that happens to have lots of linear algebra and other capabilities. You can run Julia online, without installing it, by logging into juliabox.com More information:

• Instructions/links for using Julia
• Overview slides
• Julia cheatsheet
• Tutorial notebook

Many of the lecture notes and problem sets above are in the form of Jupyter/IJulia notebooks. You can view these simply by following the links above, but you can also download them and run or modify them yourselves:

1. Click on one of the notebook or pset link above and then click on the download icon in the upper-right hand corner to download the file onto your computer
2. Log into juliabox (if you haven't installed Julia locally on your computer) and you will see a "dashboard" listing of notebooks. Drag the .ipynb (notebook) file from your computer onto this dashboard to upload it.
3. Click the notebook in the dashboard to run it.
4. You can run individual cells by typing "shift-enter". You can also run all of the cells at once (e.g. to create all of the interactive widgets) by choosing Run All from the Cell menu at the top. (Note: if you have installed Julia on your own computer, you will need to run Pkg.add("PyPlot") and Pkg.add("Interact") first, if you have not done so already, in order to install the packages needed for this notebook.)