The student has demonstrated a consistent and correct use of mathematical notation, symbols, and terminology throughout the exploration. They have appropriately utilized computer notation only when it was software-generated, with clear indication. The introduction effectively described the main concepts, such as Markov chains, and key terms were appropriately defined and explained when first introduced. Multiple forms of mathematical representation were used judiciously, and all mathematical calculations were explained, including the description of data presentation. Additionally, the student utilized a deductive method and provided logical proofs where appropriate. The graphs, tables, and diagrams were appropriately labeled at the bottom, enhancing the clarity of the presentation.