Julia: Solving Real-World Problems with Computation, Fall 2026
(course material work in progress)

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.
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.

Check out our interactive lecture material on computationalthinking.mit.edu!

Fall 2026 course page, under construction.

• Instructor: Alan Edelman
• Cross-listed as: 1.C25/6.C25/12.C25/16.C25/18.C25/22.C25
• Time: Mondays and Wednesdays, 2:30 PM to 4:00 PM
• Room: 45-102
• MIT listing: Department of Mathematics course list

Teaching Experiment

We are working with two core beliefs:

1. Humans like to learn, at least when it is not too stressful.
2. LLMs can help us leapfrog our learning.

We will use LLMs to learn something beyond our prerequisites. Perhaps some of you will learn general relativity, a sophisticated climate model, Lie algebra, or how a car does regenerative braking, but the key requirements are:

1. The material is something you conventionally would not have the background for, and you are on the honor system here.
2. You learn it, create a Julia notebook (LLMs allowed!), and teach it to all of us, seminar style.

For the rest of the class, we want you engaged and asking questions.

For a current example of this approach, see the Navier–Stokes in the news Pluto notebook.

Grading

Projects may be completed individually or in small groups, with each student responsible for understanding and presenting their part.

• Homework: 25%
• Two class presentations: 25%
• Class participation and questions: 15%
• Final Project Notebook: 35%

Homework 1

Homework 1: Getting Started and Multiple Dispatch was released Monday, September 14, 2026 and is due Monday, September 21, 2026 at 11:59pm Eastern time. A readable static HTML version will be generated automatically.

This assignment combines the setup and introductory Julia exercises from the former HW0 with the types and multiple-dispatch exercises from the former HW1.

Homework 2

Homework 2: Choose a reach project is the first step toward the final project. Choose an ambitious topic, explain why it is a reach for you, begin asking questions and learning, and create a first Julia notebook with an interactive element when appropriate. LLMs are allowed, but students may also work without them. This assignment will be refined as the projects develop. A readable static HTML version will be generated automatically.

The first homework gets everyone set up and introduces the Julia ideas needed for the projects later in the semester. The project proposal will follow separately.

Homework 3

Homework 3: Automatic Differentiation introduces dual numbers, forward- and reverse-mode differentiation, and Jacobians. It is due Monday, October 19, 2026 at 11:59 PM EDT. A readable static HTML version will be generated automatically.

Homework 4

Homework 4: How Are We Learning? asks you to reflect honestly on how the course is working, investigate one gap in your understanding, and propose concrete improvements to the course and your own learning. It is due Monday, November 2, 2026 at 11:59 PM EST.

Homework 5

Homework 5: Understanding Something Deeply builds on Homework 4: choose one part of your presentation to explain deeply and make a serious start. This prepares you for a 10–12 minute end-of-semester presentation, with additional time for questions. The homework is due Monday, November 23, 2026 at 11:59 PM EST.

Calendar

Dates follow the MIT Registrar calendar.

#	Day	Date	Lecturer	Note
1	W	Sep 9	Edelman
2	M	Sep 14	Edelman	Julia and Navier-Stokes
3	W	Sep 16	Edelman	Julia speed, random variables as types
4	M	Sep 21	Urschel	John Urschel on floating point formats
5	W	Sep 23	Edelman	Automatic differentiation
6	M	Sep 28	Edelman	Reverse mode automatic differentiation
7	W	Sep 30	John Urschel	Ranking teams with linear algebra
8	M	Oct 5	Edelman	Applied math in the age of AI and TOP500 supercomputers
9	W	Oct 7	Edelman
	M	Oct 12		Indigenous Peoples Day - holiday
10	T	Oct 13	Maxwell Zhou	The Hodgkin–Huxley model and Evans function; Monday schedule of classes
10	T	Oct 13	Laura Lerebours
11	W	Oct 14	Michelle Chen	Finding Invisbile Planets with Gravity
11	W	Oct 14	Logan Reich	General Circulation Models (static HTML)
12	M	Oct 19	Kathleen Zhang, Krishna Parvataneni	Stochastic Volatility: Black–Scholes, Heston, and Rough Bergomi (static HTML)
12	M	Oct 19	Favio Lesnjak	Kepler: Harmony to Chaos (static HTML)
13	W	Oct 21	Thomas Shoales	Burst Altitude Effect on Radioactive Deposition (static HTML)
14	M	Oct 26	Mary Feliz, Drew Hussar	The Phase Problem in Crystallography (static HTML)
14	M	Oct 26	Rochelle Griffith	How a balanced ocean makes eddies (static HTML)
15	W	Oct 28	Jhanny Jimenez	How many GPUs should I rent? — Queueing theory (static HTML)
15	W	Oct 28	Yusef Hosein, Lexcea King	Is That My Hand? — Bayesian Causal Inference in Human Body (static HTML)
16	M	Nov 2	An Dinh	TCP Congestion Control (static HTML)
16	M	Nov 2	Maximo Del Pino	Why Creditors Accept Less (static HTML)
17	W	Nov 4	Jon Ebataleye	Echo State Networks (static HTML)
17	W	Nov 4	Nathan Zhu	Ball Trajectories in Baseball (static HTML)
18	M	Nov 9	Angelina Ning
	W	Nov 11		Veterans Day - holiday
19	M	Nov 16	Raffaele Ferrari	Introduction to atmospheric radiation budget
20	W	Nov 18	Raffaele Ferrari	Introduction to atmospheric dynamics using Oceananigan
21	M	Nov 23	Michelle Chen	Student presentations
	W	Nov 25		Class canceled for Thanksgiving
22	M	Nov 30		Student presentations
23	W	Dec 2		Student presentations
24	M	Dec 7		Student presentations
25	W	Dec 9		Class party

Lecture 1: Communicate with Computation

• Slides: Introduction to class
• Notebooks: Intro to Julia, Julia tutorial, Hyperbolic Corgi, Images, and Abstraction

Lecture 2: Julia and Navier-Stokes

• Claude session: Navier–Stokes discussion
• Julia tutorial: Jeremiah's Nice C25 Tutorial
• Notebook: Navier–Stokes in the news (static HTML)

Lecture 3: Julia speed, random variables as types

• Notes: Random Variables as Types (static HTML), Julia Is Fast

Lecture 4: John Urschel on floating point formats

Lecture 5: Automatic differentiation

• Notebooks: Julia Is Fast, Automatic Differentiation

Lecture 6: Reverse mode automatic differentiation

• Notebook: Reverse Mode AutoDiff

Lecture 7: Ranking teams with linear algebra

• Notebook: Ranking College Football Teams

This notebook expects accompanying team_data.csv and game_data.csv files.

Lecture 8: Applied math in the age of AI and TOP500 supercomputers

• TOP500 supercomputer rankings

October 14: General Circulation Models — Logan Reich

• Pluto notebook: General Circulation Models — from radiative balance to a coupled Earth system
• Static HTML: Read the notebook with rendered results. This snapshot uses the default parameter values; open the Pluto notebook in Julia to change sliders and rerun the models.

October 19: Option pricing — Kathleen Zhang and Krishna Parvataneni

• Pluto notebook: Option pricing: from Black–Scholes to rough volatility
• Static HTML: Read the notebook with rendered results. This snapshot uses the default parameter values; open the Pluto notebook in Julia to change sliders and rerun the models.

October 19: Kepler: Harmony to Chaos — Favio Lesnjak

• Pluto notebook: Kepler: Harmony to Chaos
• Static HTML: Read the notebook with rendered results. This snapshot uses the default parameter values; open the Pluto notebook in Julia to change sliders and rerun the models.

October 21: Fallout by Height — Thomas Shoales

• Pluto notebook: Fallout by Height: How burst altitude controls radioactive deposition
• Static HTML: Read the notebook with rendered results. This snapshot uses the default parameter values; open the Pluto notebook in Julia to change sliders and rerun the models.
• Images: Keep hiroshima.jpg and bravo_map.jpg in the same folder as the notebook when running it locally.

October 26: The Phase Problem in Crystallography — Mary Feliz and Drew Hussar

• Pluto notebook: The Phase Problem in Crystallography
• Static HTML: Read the notebook with rendered results. This snapshot uses the default parameter values; open the Pluto notebook in Julia to change sliders and rerun the models.
• Illustration: Keep phase_problem_crystallography.png in the same folder as the notebook when running it locally. Illustration by explorebiology / XBio, CC BY 4.0, unchanged.

October 26: How a balanced ocean makes eddies — Rochelle Griffith

• Pluto notebook: How a balanced ocean makes eddies
• Static HTML: Read the notebook with rendered results. This snapshot uses the default parameter values; open the Pluto notebook in Julia to change sliders and rerun the models.

October 28: How many GPUs should I rent? — Jhanny Jimenez

• Pluto notebook: How many GPUs should I rent? — A crash course in queueing theory
• Static HTML: Read the notebook with rendered results. This snapshot includes the checkpoint answers and model comparison curves; open the Pluto notebook in Julia to change controls and rerun the simulations.

October 28: Is That My Hand? — Yusef Hosein and Lexcea King

• Pluto notebook: Is That My Hand? — Bayesian Causal Inference in Human Body
• Static HTML: Read the notebook with rendered results. This snapshot uses the default parameter values; open the Pluto notebook in Julia to change sliders and rerun the models.

November 2: TCP Congestion Control — An Dinh

• Pluto notebook: TCP Congestion Control
• Static HTML: Read the notebook with rendered results. This snapshot uses the default parameter values; open the Pluto notebook in Julia to change sliders and rerun the models.

November 2: Why Creditors Accept Less — Maximo Del Pino

• Pluto notebook: Why Creditors Accept Less — A stochastic model of corporate debt restructuring
• Static HTML: Read the notebook with rendered results. This is Maximo’s saved snapshot; open the Pluto notebook in Julia to change controls and rerun the simulations.

November 4: Ball Trajectories in Baseball — Nathan Zhu

• Pluto notebook: Ball Trajectories in Baseball
• Static HTML: Read the notebook with rendered results. Open the Pluto notebook in Julia to rerun the calculations.
• Demo video: The introductory video was not supplied. If available, place baseball_demo.mp4 beside the notebook to include it.

Previous Offering

• Fall 2024