Course Textbook: Mathematical Statistics and Data Analysis by John A. Rice

Course Syllabus

Midterm Exam 1

Midterm Exam 2

Final

There are 38 lecture notes, but the final only covers 1 through 19. There are some practice problems after lecture 19.

Course Textbook: A First Course in Probability (9th edition)

All Lecture Notes

Quiz 1

Quiz 2

Midterm Exam

Final Exam with Solution

Professor Paul Tokorcheck taught this class in a very good fashion. Although “Number Theory” sounds intimidating, it is not. The course content, though abstract, was greatly demonstrated and proved by the instructor. He was also kind enough to write a recommendation letter for the Continuing Students Scholarship.

Course Textbook: Elementary Number Theory by David M. Burton

Additional Useful Reference: Book of Proof

Note: This class has no official lecture notes, but one good way to refer to the content is through the textbook.

Course Syllabus

Exercise List

Midterm Exam 1

Midterm Exam 2

Final Exam

Course Textbook: Differential Equations and Linear Algebra by Stephen W. Goode

All Lecture Notes

Weekly Quizzes

Practice Midterm

Practice Final

Midterm Exam

Final Exam

Course Textbook: Essential Calculus by James Stewart

Lecture Notes

Exercise List

Midterm Exam 1

Midterm Exam 2

Final Review

Final Review Solutions

Final Exam

Course Textbook: Artificial Intelligence: A Modern Approach by Stuart Russell and Peter Norvig (4th edition)

Course Syllabus

Projects

Homework

Course Textbook: Introduction to Java Programming and Data Structures by Y. Daniel Liang (12th edition)

Course Syllabus

Programming Assignments

My solution to the first two programming assignments can be found here.

Please refer to the course website for more information including course syllabus and assignments!

Course Textbook: Algorithm Design by Jon Kleinberg and Eva Tardos

A Useful Course on Coursera: Data Structures and Algorithms Specialization

Please refer to the course website for more information!

My solution to the six programming assignments can be found at this GitHub repository.

Course Textbook: Essential Discrete Mathematics for Computer Science, by Harry Lewis and Rachel Zax

Course Syllabus

Midterm

Final Exam

Course Textbook: Not Available

Midterm

Final

Final Project: Golden Cross & Death Cross EMA Trading Strategy

A group project implementing a momentum-based trading strategy using 8-period and 25-period Exponential Moving Averages (EMAs) on the S&P 500 Energy Sector. The strategy uses Golden Cross signals (8EMA crossing above 25EMA) to trigger buys and Death Cross signals to trigger sells, achieving a 17% annual return vs. 10% buy-and-hold, with a Sharpe Ratio of 0.68 vs. 0.37 for the benchmark.

Final Project: Stock Return Predictability with XGBoost and Random Forest

A group project examining whether combining momentum and fundamental factors can produce a strategy that captures momentum gains while remaining effective long-term. Using CRSP/Compustat data (2012–2024), the study trains XGBoost and Random Forest models to forecast next-month stock returns, evaluated against a Fama-French 3-Factor benchmark via decile portfolios and a Winner-Minus-Loser (WML) long-short portfolio. XGBoost achieved a 26.11% WML return and Sharpe of 0.96 in the test period (2022–2024).

Final Project: Adaptive Q&A Assistant Using LLM and Neural SSM

A group project (with Taosheng Yin, Shiwen Zou, and Yechao Chen) building a context-aware chatbot that dynamically switches between Explainer, Tutor, and Concise response modes. Traditional stateless chatbots fail when user intent is implicit or evolves across turns — the system addresses this by coupling a Neural State-Space Model (SSM) that maintains a latent conversation state hₜ with a DistilBERT-based regime classifier and explicit intent overrides. The SSM update rule hₜ = fθ(hₜ₋₁, xₜ, zₜ) enables the controller to learn smooth dialog phase transitions. Evaluated on a synthetic multi-turn dataset, the SSM regime model achieved 96.50% test accuracy versus 56.37% for the text-only baseline, with markedly improved stability across conversation turns.

Final Project: Statistical Arbitrage Pair Trading Using Cointegration, Mean Reversion, and Bayesian Optimization

A group project (with Hiu Chun Chan, Saurabh Kulkarni, and Weiyi Wang) implementing a complete end-to-end stat-arb pipeline on S&P 500 equities. The universe is constructed from constituents that remain in the index continuously over 2016–2020, narrowed to the top 50 by market cap, generating 1,225 candidate pairs. Each pair is screened via Engle-Granger cointegration test, ADF stationarity test, and correlation filter. Spread dynamics are modeled using an Ornstein-Uhlenbeck process (dXₜ = κ(μ − Xₜ)dt + σdWₜ), with the half-life t½ = ln2/κ used to discipline maximum holding periods. The Backtrader-based engine trades on z-score entry/exit signals with dollar-neutral sizing and stop-losses, while Bayesian optimization (via skopt) tunes lookback window, entry threshold, stop-loss factor, and holding-time factor to maximize the Sharpe ratio in-sample (2016–2020). Out-of-sample evaluation (2021–2025) on the primary COST–NEE pair yields a Sharpe of 1.69, 6.28% total return, and 64.9% win rate; the best alternative pair ACN–TXN achieves a 16.5% return, Sharpe of 1.66, 90% win rate, and only 8% max drawdown.

Final Project: Regime-Based Factor Investing Strategy

A group project developing a novel regime-aware long-short factor investing strategy using CRSP data (1990–2023). Market regimes are identified along two dimensions — macroeconomic regime (Bull/Bear/Sideways via term spread between the 10-year Treasury and 3-month T-Bill) and market concentration regime (Narrow/Normal/Broad via Gini coefficient and HHI) — forming a 3×3 matrix of nine distinct regimes. For each regime, an optimal combination of six factor signals (momentum, growth, quality, volatility, value, profitability) is selected, and stocks are ranked by composite Z-score into top/bottom quintile long-short portfolios rebalanced monthly. The strategy generates statistically significant CAPM and FF3 alpha, outperforms the market across all major bear market episodes (151.51% during the GFC), and achieves a maximum drawdown of −45.32% vs. the market’s −50.31%.