Linbo Gong

Stochastic Optimization of the Cookie Clicker “Stock Market”

• Modeled the game’s price process with geometric Brownian motion and Monte Carlo simulations, then translated results into evidence-based buy/sell thresholds under uncertainty.
• Framed decision rules via first-passage / hitting-time logic and risk-reward tradeoffs, clarifying when to enter/exit and why.
• Performed sensitivity analysis on drift/volatility assumptions to test robustness; documented assumptions, edge cases, and limitations clearly.
• Bridged theory to practice: compared mean-reversion vs. momentum interpretations and discussed implications for position sizing and risk management.
• Produced a reproducible, well-structured write-up that communicates methods, intuition, and results to both technical and non-technical readers.

Generating Functions in Partition Theory (Number Theory)

• Built the generating-function framework for integer partitions and used it to obtain recurrence relations for p(n) with clear proofs and worked examples.
• Explained classic identities (e.g., Euler’s pentagonal-number theorem) and their computational consequences for efficiently evaluating partition counts.
• Connected partition theory to algorithmic thinking (recurrences, dynamic programming) and to combinatorial optimization analogies (e.g., knapsack-style counting).
• Emphasized rigorous exposition: precise definitions, lemma-proof structure, and careful handling of edge cases and asymptotic growth.
• Wrote a self-contained mini-primer that blends theory, computation, and exposition—useful for peer teaching and extension to related counting problems.