The goal is to create a concept demo that has a useful interaction, connects it to the mathematics of the corresponding lecture, test the code, and explain what a learner should notice.

Team work and AI use

The concept demo is team work. Each team has two or three students. The team makes the final decisions about the mathematics, controls, code, tests, and explanation. Every member must understand the whole demo well enough to explain it.

You may use generative AI tools, but AI use is not required. You may use AI to discuss ideas, suggest code, find possible boundary cases, or review an explanation. You may not submit work from outside your team, copy an existing public demo, or treat an AI answer as proof that your demo is correct.

Every submission must include one concise AI use and verification record for the team. If the team did not use AI, write “No AI tool used.” If the team used AI, include the following information:

• Name each tool that you used.
• Summarize what you asked each tool to do. Do not paste a full transcript.
• State which suggestions or code you used and which important suggestions you rejected.
• Explain how you checked the mathematics and code. An AI response cannot serve as the check.

What to build

Choose one concept from a lecture, not an entire lecture. Examples include orthogonal projection onto a subspace, the union bound, Taylor series approximation, and the difference between convergence in probability and almost sure convergence.

Build one self contained static HTML page with HTML, CSS, and JavaScript. You may use a browser library such as D3, Three.js, or Plotly. Plain Canvas or SVG is also fine. The page must meet all of the following requirements:

• State the concept and its main definition, formula, or theorem in your own words.
• Ask the learner to make a specific prediction before using the controls.
• Include at least one meaningful control, such as a slider, draggable point, or toggle. The control must change a mathematical quantity or relationship that helps teach the concept.
• Show how the interaction connects to the mathematics. Display the relevant formula, values, graph, or geometric relationship as it changes.
• Include at least one boundary case, failure case, or common misconception. Explain what happens and why.
• Connect the concept to one consequence elsewhere in the course or in machine learning. State the connection in one or two sentences, and show it in the demo where you can.
• Use deterministic randomness when the demo uses random values. Provide a fixed seed, a visible seed control, or a fixed data set so another person can reproduce the same result.
• Include a team explanation of about 250 to 400 words. Explain what the controls show, how the demo connects to the mathematics, what the boundary case teaches, and why the connection you identified matters.
• Include the concise AI use and verification record described above.
• Include a short contribution statement naming each team member and what they did.
• Work when opened in a browser. The page must not require a build step or server, and it must not contain broken links or local file dependencies.

Design quality counts. Accepted demos are published on the course website under your team’s names, so aim for something you would be glad to see there. A correct but visually careless demo will lose points. See the grading rubric.

See the worked example on eigenvectors and eigenvalues for one possible structure. Your demo does not need to use the same visual design.

Submission

• Form a team of two or three students, then reserve one concept on the 2026 sign up sheet listed on the policy page by the end of the second week of the semester, Friday, September 11, 2026. Sign ups close on that date, so choose your concept from anywhere in the course, including lectures that have not been taught yet.
• Submit one .html file. Put your CSS and JavaScript in the file, or link to a library through a content delivery network. Do not submit local dependency folders.
• The demo is due one week after the lecture. A late demo loses 10 percent of the demo grade, 2 of 20 points, for each day it is late. Any part of a day counts as a full day. A demo more than ten days late receives no credit.
• Accepted demos are published on the course website with every team member credited.

Grading rubric (20 points)

The concept demo is worth 20 percent of the course grade, so one rubric point is one percent of your final grade.

Criterion	Points	What we’re looking for
Mathematical correctness	6	The definitions, formulas, displayed values, boundary case, and stated connection to other material are correct.
Interactivity that teaches	5	The learner makes a prediction, and each control changes a mathematical quantity or relationship. The page shows how the change connects to the mathematics. Random results can be reproduced when randomness is used.
Visual design and craft	4	The demo is well made, not merely unbroken. Clear visual hierarchy, readable typography, deliberate use of color and space, labelled axes and quantities, and interaction that feels responsive. Color, motion, and layout carry mathematical meaning rather than decoration. It reads well at common screen sizes and loads without console errors, broken links, or unnecessary large dependencies.
Clarity of explanation	3	A student who has not taken this course can understand the main idea. The team explanation is concise and uses clear labels and defined terms.
AI use and verification record	2	The record is complete and specific. Tools are named, requests are summarized, suggestions used and rejected are stated, and the mathematics and code are checked independently. An AI response cannot serve as the check. The contribution statement names each member and what they did.

A demo that is mathematically correct but static (a picture with no interaction) caps at 10/20. A demo that is interactive but wrong caps at 8/20.

What to avoid

• Recreating a textbook figure with no interactivity.
• Adding a control that does not teach the mathematics. For example, a color picker is not useful unless color represents a mathematical quantity.
• Copying an existing public demo or another team’s work.
• Choosing a broad scope. For example, “all of linear algebra” is not one concept.
• Using changing random samples without a way to reproduce them.
• Asking AI to check AI generated mathematics or code without an independent check.