IDC6940/MAT6903/MAT6910/STA6950 - Capstone Projects

Project Instructions

Please read the following instructions:

You will need to select a specific study area to concentrate on, which may be a subject new to you. You will start the process by conducting an in-depth exploration of the chosen topic and then demonstrate the application of the new methodology using a real-world dataset that is both relevant and captivating. Completing the project requires submitting a comprehensive written paper alongside an engaging oral presentation supported by slides.

Important

GitHub Page Template Project: https://github.com/capstone4ds/capstone4ds_template

Topics to consider:

Applied Math:

• Computational algorithms for solving large linear systems, such as QR factorization, Gaussian Elimination (LU factorization), singular value decomposition (SVD), Iterative methods.
• Numerical solutions for PDE models, such as heat equations and Poisson equations.
• Numerical solutions for page ranking, such as power iteration, ect.
• Community detection for complex networks, or centrality for networks.
• Optimization problems
• Inverse problems and image processing

Data Science:

• Machine Learning and Predictive Analytics: Developing models to predict outcomes based on historical data.
• Natural Language Processing (NLP): Techniques for analyzing and understanding human language in text form.
• Big Data Analytics: Handling and analyzing extremely large datasets to uncover hidden patterns and insights.
• Data Visualization: Techniques for representing data graphically to aid understanding and decision-making.
• Deep Learning: Use of neural networks with multiple layers for complex pattern recognition tasks.
• Reinforcement Learning: Training models to make sequences of decisions by rewarding desired outcomes.

Statistics:

• Mathematical Statistics: distributions and their properties
• Bayesian Statistics: Use of Bayes’ theorem for updating probabilities as new data is acquired.
• Survival Analysis: Statistical methods for analyzing time-to-event data, common in medical research.
• Multivariate Analysis: Techniques for understanding patterns in data involving multiple variables.
• Non-parametric Methods: Statistical methods that do not assume a specific data distribution.
• Time Series Analysis: Techniques for analyzing data points collected or recorded at specific time intervals.
• Statistical Learning and Inference: Methods for making predictions and understanding data patterns through statistical models.

Interdisciplinary:

1. Computational Biology and Bioinformatics Mathematical Modeling of Gene Regulatory Networks: Using differential equations and network theory to model and understand complex biological systems. Statistical Methods for Genomic Data Analysis: Developing new statistical techniques to analyze high-throughput genomic data, such as RNA-Seq or genome-wide association studies (GWAS). Machine Learning for Protein Structure Prediction: Applying deep learning techniques to predict the three-dimensional structure of proteins from amino acid sequences.
2. Financial Mathematics and Econometrics Quantitative Risk Management: Using stochastic processes, Monte Carlo simulations, and optimization techniques to model and manage financial risks. Time Series Analysis in Financial Markets: Applying statistical methods to analyze and forecast financial time series data, such as stock prices or interest rates. Algorithmic Trading and Data Science: Developing machine learning algorithms for automated trading strategies based on historical and real-time market data.
3. Environmental Science and Climate Modeling Mathematical Modeling of Climate Change: Using differential equations and numerical methods to model and predict climate patterns and their impact on ecosystems. Statistical Analysis of Environmental Data: Developing statistical models to analyze and interpret large datasets related to air quality, water resources, or biodiversity. Big Data Analytics for Environmental Monitoring: Applying data science techniques to analyze satellite imagery and sensor data for tracking environmental changes.
4. Public Health and Epidemiology Epidemiological Modeling: Using mathematical models to simulate the spread of infectious diseases and evaluate the effectiveness of intervention strategies. Statistical Methods for Health Data: Developing new techniques for analyzing healthcare data, including survival analysis, causal inference, and longitudinal studies. Data Science for Precision Medicine: Applying machine learning to personalize treatment plans based on patient data, including genetics, lifestyle, and clinical history.
5. Urban Planning and Smart Cities Optimization in Transportation Networks: Using mathematical optimization to design efficient public transportation systems and reduce traffic congestion in urban areas. Data-Driven Urban Analytics: Applying data science methods to analyze urban data, such as traffic patterns, energy usage, and social dynamics, for smarter city planning. Statistical Modeling of Housing Markets: Using econometric and statistical models to study housing market trends, pricing dynamics, and the impact of policy interventions.
6. Robotics and Autonomous Systems Mathematical Control Theory: Developing control algorithms for autonomous robots using differential equations and optimization techniques. Reinforcement Learning for Autonomous Navigation: Applying reinforcement learning to teach robots or autonomous vehicles to navigate complex environments. Statistical Methods for Sensor Fusion: Developing techniques for combining data from multiple sensors to improve the accuracy and reliability of autonomous systems.
7. Social Sciences and Behavioral Economics Mathematical Models of Social Networks: Using graph theory and network analysis to study the structure and dynamics of social networks. Statistical Analysis of Behavioral Data: Applying statistical methods to analyze data on human behavior, preferences, and decision-making processes. Data Science for Political Forecasting: Using machine learning and data analytics to predict election outcomes, public opinion trends, and policy impacts.
8. Healthcare and Biomedical Engineering Medical Imaging Analysis: Applying machine learning and statistical methods to analyze medical images, such as MRI or CT scans, for disease diagnosis and treatment planning. Mathematical Modeling of Biological Systems: Using differential equations and computational models to study physiological processes, such as cardiovascular dynamics or neural activity. Data Science for Health Informatics: Developing data-driven approaches to improve healthcare delivery, including patient outcome prediction, hospital resource management, and electronic health record (EHR) analysis.

Note

You are free to propose a topic if there is something you are interested in but is missing from the list. The instructor must approve the methodology to ensure that it meets the expectations of a capstone project.

Useful links

• Data Sets: https://acohenstat.github.io/Datasets/
• GitHub Page for the project: https://github.com/acohenstat/STA6257_Project