Independent Study
A curated collection of original papers authored through personal exploration, curiosity-driven inquiry, and independent research across mathematics and related fields. Each paper reflects a deep engagement with the subject, beyond formal coursework or institutional mandates.
Papers
You can download a PDF version of the paper by clicking the title of the paper.
This paper explores the Rubik’s Cube through the lens of group theory, treating the cube not just as a puzzle but as a rich algebraic structure. It introduces the concept of the Rubik’s Cube group, examines the underlying permutation group acting on the cube’s stickers, and investigates properties like commutativity, subgroup structures, and move generators. Through a series of carefully chosen problems, the paper builds intuition for abstract algebraic ideas such as order of elements, cycles, conjugation, and group actions — using the cube as both model and metaphor. Designed as an entry point for students into the world of algebraic thinking, the paper balances rigor with accessibility, inviting readers to experience pure mathematics in a tangible and playful form.