MATH 496 — Independent Study (UIC Math)

Independent Study with Prof. Laura P. Schaposnik (2–3 credits)

Instructor: Prof. Laura P. Schaposnik (Mathematics, UIC)
Contact: schapos@uic.edu
Meeting cadence: Weekly or bi‑weekly (to be agreed individually), in person or on zoom
Credits: 2 or 3 (see workload & deliverables below)

What is MATH 496?

MATH 496 (Independent Study) is a for‑credit, student‑driven research or reading project. You will choose a focused topic, meet regularly to set milestones, and produce a substantial final output. Projects can be theoretical, computational, expository, or applied, and may range from a research‑style mini‑paper to a polished expository article, a reproducible code notebook, or a small public‑facing resource.

Typical areas include (but are not limited to): geometry & topology, Higgs bundles and moduli spaces, integrable systems & quantization, networks and contagion models, reaction-diffusion and pattern formation, data visualization for mathematical communication, and bilingual STEM outreach grounded in rigorous mathematics.

Who can enroll?

  • Motivated undergraduates or graduate students with sufficient background for the chosen topic.
  • You should be comfortable with independent reading and writing in LaTeX. Prior coursework will vary by project; we will agree on an appropriate scope at the outset.
  • Enrollment requires permission of the instructor and a short one‑page proposal (template below).

Credits, Workload & Deliverables

Choose 2 or 3 credits based on your goals and bandwidth. We will right‑size the topic accordingly.

2 credits (reading/expository or scoped computational project)

  • Time expectation: consistent weekly effort across the term.
  • Deliverables:
    1. 1‑page proposal (Week 1).
    2. Short milestone plan (Week 2).
    3. Progress memo mid‑term (≈2 pages).
    4. Final expository note (≈6–10 pages) or a reproducible code notebook with a clear README.
    5. Lightning talk (5–8 minutes).

3 credits (deeper research/exposition or extended computational study)

  • Time expectation: larger weekly commitment across the term.
  • Deliverables:
    1. 1‑page proposal (Week 1).
    2. Detailed milestone plan (Week 2).
    3. Mid‑term report (≈4–6 pages) with preliminary results.
    4. Final paper‑style write‑up (≈10–15 pages) or a code + data + analysis package with documentation and figures.
    5. Short talk (10–12 minutes) and optional poster.

✱ Page counts are guidelines; quality, rigor, and clarity matter more than length. We will tailor expectations to your topic.

Timeline (suggested)

  • Week 0–1: Topic discussion; submit proposal; enroll.
  • Week 2: Agree on milestones and reading list; set meeting rhythm.
  • Weeks 3–6: Execute plan; regular check‑ins (notes/logs).
  • Mid‑term: Progress memo/report.
  • Weeks 7–12: Deepen results; draft figures/examples; iterate.
  • Final weeks: Deliver final write‑up & talk; archive materials (PDF + code).

How to propose a 496

Email schapos@uic.edu with subject “MATH 496 — [Your Name] — Proposal” and include:

  1. Your name, program, year (and relevant courses).
  2. Credit choice (2 or 3).
  3. A 1‑page proposal summarizing:
    • Topic & motivation (what/why)
    • Initial questions or goals (how you’ll make progress)
    • Expected outputs (paper, code, visuals, talk)
    • Initial references (2–5 items)
  4. A short availability note for weekly meetings.

I will reply with feedback and, if approved, permission to register and a shared checklist for the term.

Sample project ideas

  • Geometry & Physics: Spectral data for rank‑2 Higgs bundles; toy models of exact WKB; monodromy and character varieties (expository or computational).
  • Networks & Dynamics: SIR/Voter models on graphs; influence maximization heuristics; reaction–diffusion pattern formation in 2D domains.
  • Computational & Visualization: Reproducible notebooks for a classical theorem; interactive visualizations of graph algorithms; curated figure sets for teaching.
  • Outreach (rigorous & bilingual): Short, math‑faithful modules for K‑12 on symmetry, tilings, or networks; data‑driven infographics with clear pedagogy.

If you bring your own idea, great : let’s scope it together.

Expectations & policies (high level)

  • Meetings: Please keep appointments or reschedule ahead of time. Send a brief agenda or log in advance of each meeting.
  • Academic integrity: Cite all sources; if you adapt code or figures, credit clearly.
  • Accessibility: If you need accommodations, contact the UIC Disability Resource Center and let me know so we can plan accordingly.
  • Archiving: Final materials (PDF, slides, and if applicable, code/data) should be submitted in an organized folder.

Last updated: November 04, 2025