A four-week mathematics research program for A-level students (ages 16–18), exploring graph theory, network controllability, combinatorics, and discrete geometry through hands-on exploration, open problems, and interactive tools.
🌐 Live site: amessbee.github.io/rise
RISE introduces students with no university mathematics background to active research problems — questions that professional mathematicians are still working on. By the end of the program, every student can explain an open problem, state a theorem they have proved themselves, and deliver a polished 12–15 minute research presentation.
Core mathematical content:
| Track | Topics |
|---|---|
| Graphs & Networks | Graph theory, Euler's theorem, planarity, coloring |
| Network Controllability | Zero forcing sets, the forcing game, propagation sequences |
| Combinatorics | Sequences, Erdős–Szekeres theorem, PMI sequences |
| Discrete Geometry | Centerpoint theorem, Helly's theorem, Tukey depth |
| Communication | Scientific storytelling, slides/posters, Q&A skills |
4 weeks × 4 days × 4 hours = 64 hours of contact time.
| Week | Theme | Days |
|---|---|---|
| 1 | Graphs and Networks | Days 1–4 |
| 2 | Controlling Networks: Zero Forcing | Days 5–8 |
| 3 | Sequences and Geometry | Days 9–12 |
| 4 | Research Communication | Days 13–16 |
→ See plan.md for the full day-by-day coordinator guide with timing, facilitator notes, problem sets, and student host assignments.
Printable A4 handouts, one per topic. Each contains definitions, worked examples, puzzles, homework problems, and at least one genuinely open problem.
| Handout | Topic | Key Result |
|---|---|---|
| Survey | Background assessment | — |
| Networks Intro | Graphs, trees, planarity | Euler's theorem, V−E+F=2 |
| Zero Forcing | Zero forcing sets and game | Z(G) characterizes controllability |
| Sequences & PMI | Subsequences, Erdős–Szekeres | Any mn+1 elements → long monotone run |
| Centerpoint | Centerpoint theorem | Every point cloud has a "robust centre" |
| Presentation Guide | Research communication | Four-act structure, slide design, Q&A |
Run directly in your browser — no installation required.
| Demo | What it does |
|---|---|
| 🎮 Zero Forcing Game | Color vertices blue and simulate the forcing propagation on paths, cycles, grids, stars, and the Petersen graph |
| 📊 PMI Grid Explorer | Explore zero forcing propagation sequences on grid graphs and see their 2D monotone structure |
| 📍 Centerpoint Visualizer | Add points by clicking, then see the coordinatewise median, true centerpoint, and Tukey depth heatmap |
| 🔢 Sequences & Patience Sort | Enter a sequence and watch patience sorting animate the LIS discovery step by step |
Open any notebook in Google Colab (no installation needed) or run locally with Jupyter.
| Notebook | Topics | Open in Colab |
|---|---|---|
| Zero Forcing | NetworkX graphs, Z(G) computation, propagation visualisation |  |
| Centerpoint & Tukey Depth | 2D point clouds, Tukey depth, approximate centerpoint finder | |
| Sequences & Erdős–Szekeres | Patience sorting, LIS, tight examples, 2D increasing subsequences | |
The six student coordinators are: Danish, Uzayr, Nimra, Ahsan, Maaz, Basit.
Each of the 16 program days has a host slot in plan.md. To claim a day:
- Open
plan.md - Find the day you want to host
- Replace
—in the> **Host:** —line with your name - Commit and push (or ask the lab coordinator to record it)
The host assignment table near the top of plan.md gives an overview of all 16 days.
rise/
├── README.md ← you are here
├── plan.md ← full coordinator guide
├── handouts/
│ ├── survey.md
│ ├── networks_intro.md
│ ├── zero_forcing.md
│ ├── sequences_pmi.md
│ ├── centerpoint.md
│ └── presentation_guide.md
├── interactive/
│ ├── zero_forcing_game.html ← browser-based zero forcing game
│ ├── pmi_grid.html ← PMI propagation sequence explorer
│ ├── centerpoint.html ← centerpoint & Tukey depth visualizer
│ └── sequences.html ← patience sorting & LIS animator
└── notebooks/
├── zero_forcing.ipynb
├── centerpoint.ipynb
└── sequences_erdos.ipynb
Program designed by Dr. Mudassir Shabbir, Theory Group, Department of Computer Science, LUMS.
Student coordinators: Danish, Uzayr, Nimra, Ahsan, Maaz, Basit.
Mathematical content covers active research in graph controllability, zero forcing sets, and discrete geometry conducted at the Theory Group, LUMS. Interactive tools and notebooks were developed as part of the RISE program.