Homework 4: How Are We Learning?

Due Monday, November 2, 2026 at 11:59 PM EST.

We are experimenting with Julia and LLMs to learn beyond our usual prerequisites and teach one another.

I’m concerned that impressive notebooks and presentations can hide gaps in understanding. Examine how this experiment is working, then deepen your understanding of one small part of it.

Plan to spend about two hours. Submit a short write-up with supporting calculations, sketches, or notebook cells.

The guidelines below are suggestions, not a rigid template. Your response does not have to follow them exactly: you may organize it differently, focus on the questions most relevant to your experience, and use a different length or format. You do not need to answer every question. What matters is honest reflection, a serious effort to deepen your understanding, and specific ideas for improving your learning and the course.

1. Take stock honestly

Write approximately 250–400 words addressing:

• Describe a moment when something became clearer. What helped?

• Describe a moment when you could follow an explanation, code, or AI response but could not explain it yourself.

• Give specific examples of how LLMs helped you learn—and may have let you move ahead without understanding.

• What about our class makes deep learning easier or harder? Consider preparation, presentation pace, background knowledge, participation, and feedback.

Honest criticism is welcome. Admitting confusion will not lower your grade.

2. Find the edge of your understanding

Choose one narrowly defined idea from your presentation or a classmate’s that you do not yet understand well.

Examples include why an equation has its form, what a parameter does, why an algorithm works, or how a simulation represents a physical process.

Without consulting resources or another person, spend ten minutes answering:

1. What problem does this idea help solve?

2. How does it work? Use a small example, sketch, or calculation.

3. What can you explain confidently, and where does your explanation break down?

Keep this first attempt, including mistakes and blanks. Do not polish it afterward.

3. Spend an hour going deeper

Work on the gap you identified. You may use any resources, including an LLM, classmates, and course staff.

Include:

• A small example you can work through yourself. Trace the reasoning or computation.

• A prediction before running code. Change one input or assumption, predict the result and explain why, then investigate.

• One assumption or limitation. When might the idea or model stop being useful?

• One point where you were stuck. Show what you tried and what helped—or what remains unresolved.

Suggestion: ask an LLM to quiz you on the depth of your understanding. You might use this prompt:

Quiz me on my understanding of [specific idea]. Ask one question at a time and wait for my answer before giving hints or explanations. Probe my reasoning with “why?” and “what if?” questions. Ask me to explain an equation in words, work through a small example, predict what changes when an assumption or parameter changes, and identify a limitation. Adapt your follow-up questions to expose gaps in my understanding rather than accepting a fluent answer.

Try answering each question yourself before asking for help. Check the LLM’s feedback against a reliable source, calculation, or experiment; it can make mistakes too. A classmate or course staff member can also quiz you.

If you use an LLM, include one short exchange that affected your understanding and explain how you checked its answer. No full conversation is needed.

4. Check what changed—and help improve the course

Close your resources. Explain the idea in your own words using a different small example.

Compare this with your first attempt:

• What can you now explain that you could not before?

• What remains unclear?

• What question could someone ask to check your understanding?

• What one concrete change should we make to the course, and what one change will you make to your learning process? How would each help?

Be specific: “Before each presentation, give us one prerequisite idea to study and one prediction to make” is more actionable than “We need more background.”

Assessment: specificity and honesty of reflection, sustained effort, and the quality of your reasoning and checks. You need not master an advanced topic in an hour. A carefully investigated gap is a successful outcome.