The student demonstrates consistent and correct use of mathematical notation, symbols, and terminology. However, key terms/variables are not clearly defined, leading to potential confusion. The introduction lacks a description of the main concepts, specifically Markov chains and probability vectors, which is essential for clarity. Furthermore, the placement and explanation of mathematical calculations and data presentation need improvement. Although the student uses multiple forms of mathematical representation appropriately, there are issues with stating the degree of accuracy for rounded values and labeling graphs, tables, and diagrams. Overall, the student effectively applies deductive methods and logical proofs in their work.