AI Use Cases for Mathematics at HWS

I'm a Mathematics student at HWS. My task: Explain a proof technique — Clarify how induction works with a simple example.

Start with a one-sentence definition, then explain it as if I'm 10, then give a real-world analogy. Finish by flagging anything scholars genuinely disagree about — and tell me what you're unsure of.

I'm a Mathematics student at HWS. My task: Define a group homomorphism intuitively — Build intuition first, then connect it back to the formal definition.

Define each term in one clear sentence, then give a concrete example of each in context. Once I've read them, quiz me on them one at a time and tell me what I got wrong and why.

I'm a Mathematics student at HWS. My task: Check a derivative or integral — Verify your computation of a tricky integral.

Walk me through how to do this step by step. Ask me any clarifying questions first, and show your reasoning so I can check it.

I'm a Mathematics student at HWS. My task: Summarize a textbook section — Condense a chapter on metric spaces into key ideas.

Give me (1) a three-sentence summary, (2) five bullet-point key claims, and (3) anything the author asserts without supporting evidence. Text below:

[PASTE THE TEXT HERE]

I'm a Mathematics student at HWS. My task: Brainstorm proof strategies — Suggest approaches to prove an inequality.

Give me 10 options grouped into 3 themes, then mark the 3 most original and explain what makes them stronger.

I'm a Mathematics student at HWS. My task: Generate practice problems — Produce extra exercises on eigenvalues to drill.

Generate 15 practice questions — a mix of multiple choice and short answer, aimed at the 'apply' and 'analyse' levels. Include an answer key with the reasoning for each.

I'm a Mathematics student at HWS. My task: Explain a counterexample — Show why a false conjecture fails with a concrete case.

Start with a one-sentence definition, then explain it as if I'm 10, then give a real-world analogy. Finish by flagging anything scholars genuinely disagree about — and tell me what you're unsure of.

I'm a Mathematics student at HWS. My task: Draft an email to a professor — Ask about office hours for a real analysis question.

Keep it under 150 words: polite, specific, with one clear ask. Give me two versions — one formal, one warmer. Don't include real names, ID numbers, or anything private.

I'm a Mathematics student at HWS. My task: Clarify notation — Explain what unfamiliar symbols in a paper mean.

Start with a one-sentence definition, then explain it as if I'm 10, then give a real-world analogy. Finish by flagging anything scholars genuinely disagree about — and tell me what you're unsure of.

I'm a Mathematics student at HWS. My task: Outline lecture concepts — List key theorems from a topology unit for review.

Give a topic-sentence outline only — not full prose. For each section, state the argument it makes and the evidence it would need.

I'm a Mathematics student at HWS. My task: Build a study guide of definitions, theorems, and proof sketches — Organize definitions, theorems, and proof sketches for an exam.

I have [X hours per week] and my exam is on [DATE]. Build a week-by-week plan with specific deliverables, and for each week give me a way to check I've actually learned it.

I'm a Mathematics student at HWS. My task: Debug a proof draft — Find the logical gap in your argument and suggest fixes.

Tell me what's wrong, explain why it happens, then give the corrected version. Walk through the fixed code line by line with a concrete input.

[PASTE YOUR CODE AND THE ERROR HERE]

I'm a Mathematics student at HWS. My task: Compare solution methods — Weigh substitution versus contour integration for a problem.

Give me a table of the key similarities and differences, then one short paragraph on which difference matters most and why.

I'm a Mathematics student at HWS. My task: Analyze a dataset statistically — Compute and interpret regression results on sample data.

I'm uploading my dataset. First describe what's in it and flag any data-quality problems, then answer my question, and show the code you ran so I can check it myself.

I'm a Mathematics student at HWS. My task: Plan a research reading sequence — Sequence papers building toward a senior thesis topic.

I have [X hours per week] and my exam is on [DATE]. Build a week-by-week plan with specific deliverables, and for each week give me a way to check I've actually learned it.

I'm a Mathematics student at HWS. My task: Explain a paper's main argument — Synthesize a research article's method and significance.

Start with a one-sentence definition, then explain it as if I'm 10, then give a real-world analogy. Finish by flagging anything scholars genuinely disagree about — and tell me what you're unsure of.

I'm a Mathematics student at HWS. My task: Write and debug simulation code — Build a Monte Carlo simulation and verify convergence numerically.

Tell me what's wrong, explain why it happens, then give the corrected version. Walk through the fixed code line by line with a concrete input.

[PASTE YOUR CODE AND THE ERROR HERE]

I'm a Mathematics student at HWS. My task: Model a dynamical system — Code and analyze a system of differential equations with checks.

Tell me what's wrong, explain why it happens, then give the corrected version. Walk through the fixed code line by line with a concrete input.

[PASTE YOUR CODE AND THE ERROR HERE]

I'm a Mathematics student at HWS. My task: Verify a computational proof — Use a proof assistant to formalize and check a theorem.

Tell me what's wrong, explain why it happens, then give the corrected version. Walk through the fixed code line by line with a concrete input.

[PASTE YOUR CODE AND THE ERROR HERE]

I'm a Mathematics student at HWS. My task: Design a numerical experiment — Structure and debug code testing a conjecture across cases.

Propose a research question, hypotheses, method, sample and sampling strategy, and the analysis plan. Then critique the weaknesses of your own design.