Real-world problems
We will take applications such as climate change and show how you can participate in the big open source community looking to find solutions to challenging problems with exposure to github and parallel computing.
Highlights
Corgi in the washing machine
You will learn mathematical ideas by immersion into the mathematical process, performing experiments, seeing the connections, and seeing just how much fun math can be.
Revolutionary interactivity
Our course material is built using real code, and instead of a book, we have a series of interactive notebooks. On our website, you can play with sliders, buttons and images to interact with our simulations. You can even go further, and modify and run any code on our website!
Learning Julia
In literature it’s not enough to just know the technicalities of grammar. In music it’s not enough to learn the scales. The goal is to communicate experiences and emotions. For a computer scientist, it’s not enough to write a working program, the program should be written with beautiful high level abstractions that speak to your audience. This class will show you how.
Why is this course different?
We believe many classes cover what we call the vertices — specific topics in computer science, math, or an application.
A student is left to figure out the edges, meaning the intellectual connections between the topics on their own as they mature.
Some classes have you learn a math topic and you can then for homework implement an algorithm or application. The goal
for this class, is to accelerate the process by which a student can participate in the exciting world of software development
be it the big open source universe or privately, by seeing how math with CS abstractions can allow for applications that can
be part of a big huge ecosystem rather than a one-off homework.
… and have more fun in the process!
Subjects
Tribute to Nick Higham (1961-2024)
Images as Data and Arrays
Automatic Differentiation
Transformations with Images
Transformations II: Composability, Linearity and Nonlinearity
The Newton Method
Dynamic Programming
Seam Carving
Taking Advantage of Structure
Principal Component Analysis
Sampling and Random Variables
Modeling with Stochastic Simulation
Random Variables as Types
Random Walks
Random Walks II
Discrete and Continuous
Linear Model, Data Science, & Simulations
Optimization
Time stepping
ODEs and parameterized types
Why we can't predict the weather
Our first climate model
GitHub & Open Source Software
Snowball Earth and hysteresis
Advection and diffusion in 1D
Resistors, stencils and climate models
Advection and diffusion in 2D
Climate Economics
Solving inverse problems
Three fields, one course
Computer Science
- visualization
- structure, abstraction
- type systems
- multiple dispatch
- dynamic dispatch
- two-language problem
- expression problem
- functional programming
- arrays
- matrices
- dataframes
- git, github
- version control
- collaboration
- devops
- language design
- constraint solvers
- mathematical programming solvers
- heuristics
- DSLs
Mathematics
- matrices
- stencils
- univariate/multivariate functions
- vector calculus
- matrix calculus
- sequence convergence
- principal component analysis
- dimensionality reduction
- matrix rank
- projections, rotations
- eigenvalues
- singular value decomposition
- outliers, noise
- data bulk, data center
- statistics
- correlation
- random sampling
- probability density function
- monte carlo methods
- random walks
- continuous limit
- ordinary differential equations
- curve fitting
- partial differential equations
- finite differences
- discretization
- bifurcations
- hysteresis
- optimization
- gradient descent
- global optimization
- constrained optimization
- nonlinear optimization
- inverse modeling
Applications
- social science
- epidemic modelling
- agent based modelling
- climate economics
- climate science
- weather forecasting
- ocean/atmosphere models
- optimisation
- path finding
- image data
- image filtering
- seam carving
- data analysis
- model fitting
- random data
Details
See also the course repository github.com/mitmath/computational-thinking.
Meet our staff
Lecturers: Alan Edelman, David P. Sanders, Charles E. Leiserson
Technical lead: Fons van der Plas
Assistants: Bola Malek, Logan Kilpatrick
Guest lecturers: Henri F. Drake, Fons van der Plas, more to be announced
Get the T-shirt
There is a MIT Computational Thinking t-shirt available for those who really enjoyed the course, you can find it on the Julia Language's Bonfire Shop.
Introduction video from Fall 2020
How to cite
If you use or are inspired by any material, would you be so kind to prominently display
Some material on this website is based on:
Computational Thinking, a live online Julia/Pluto textbook. (computationalthinking.mit.edu)
