Math-art gallery

A dedicated space for algebra-flavoured mathematics at UI: multiplication-table patterns, symmetry diagrams, Cayley graphs, subgroup lattices, and clean posters built from groups and rings.

Project ideas in algebra art

To make it easier to start, here are some project ideas that lecturers, tutors, or NAMSSN organisers can adapt. These are templates, not records of past submissions. They can be used as assignment prompts, competition themes, or voluntary projects.

Project idea
Times-table circle patterns

Place $n$ equally spaced points on a circle, label them $0,1,\dots,n-1$, and join point $i$ to $ki \bmod n$ for a fixed integer $k$. The picture shows orbits and cycles in the ring $\mathbb{Z}_n$ and its units.

Suitable for: Level 100–200 (introductory algebra).
Tools: any graphing or drawing software, or neat hand-drawn work.

Project idea
Symmetries of a regular polygon

Draw a regular polygon and illustrate its symmetries as elements of the dihedral group $D_n$. Rotations and reflections can be separated by colour or style to highlight the group structure.

Suitable for: Level 200 (first course in groups).
Tools: GeoGebra, TikZ, or precise hand-drawn diagrams.

Project idea
Cayley graph of a small group

Choose a small group such as $S_3$ or $D_8$, select generators, and draw its Cayley graph. The aim is to see how algebraic relations appear as loops and cycles in the diagram.

Suitable for: Level 300–400 (Abstract Algebra).
Tools: GAP or SageMath for data, then a plotting tool or TikZ for the picture.

Project idea
Subgroup lattice on one page

For a finite group with a manageable number of subgroups, build a subgroup lattice diagram. Use height to represent subgroup order and emphasise normal or maximal subgroups by colour.

Suitable for: Level 300–400 (group theory and related courses).
Tools: Hand-drawn work or TikZ; GAP can assist with listing subgroups.

Project idea
Poster: “One group or ring I understand”

Design an A4 or A3 poster that explains a single group or ring: its elements, operation table, simple examples, and one or two key theorems, supported by a clean diagram.

Suitable for: Any level where groups or rings are taught.
Tools: LaTeX–TikZ, Canva, PowerPoint, or neat hand lettering.

Project idea
Residue classes and units in $\mathbb{Z}_n$

Arrange the elements of $\mathbb{Z}_n$ on a circle, highlight the units in a different colour, and show visually how the units form a group under multiplication modulo n.

Suitable for: Level 200–300 (rings and modular arithmetic).
Tools: GeoGebra, Python plots, or careful hand-drawn work.

Lecturers and tutors can choose one or two of these ideas per semester, adapt the instructions, and invite students to submit their best attempt. The gallery then records the strongest examples from each run of the course.