Week 29 — Coding Projects

Core

Implement modular arithmetic utilities and explore group structure computationally.

• NumPy: Implement addition and multiplication mod n. Compute units mod n. Generate Cayley tables for small groups.
• Metal: Batched modular arithmetic on buffers as an integer compute exercise. · Reading: MBT — integer compute basics, generic compute buffer passes.
• Vulkan: Integer storage-buffer compute kernels. · Reading: Vulkan Book — integer storage-buffer compute.
• CUDA: Large-batch modular arithmetic kernels for integer ALU throughput. · Reading: CUDA Book — integer ALU kernels and throughput.
• Stretch: Visualize subgroup structure for small cyclic groups. Add permutation-group toy examples on CPU.
• Verify: Operations are closed mod n · Unit elements are correctly detected · Cayley tables match theory for small n.