This is a new course offered by the Applied Math department, which I will teach starting from Fall 2025.
The course is intended to provide an introduction to data-driven mathematical methods for modelling and prediction of complex systems in science, medicine, and technology. Topics include singular value decomposition, sparsity and compressed sensing, calibration and parameter inference for differential equation models, as well as neural networks and data-driven methods for dynamical systems. Throughout the course, students will learn to use modern data science methods and apply recent advances in data-driven methods to a wide range of applications.
Outline: A tentative list of topics covered in the course:
- Review on ODE models and dynamical systems
- Review on numerical methods for ODEs
- Intro to optimization in vector spaces
- SVD decomposition
- QR decomposition
- Notion of pseudo-inverse
- Least-squares method
- Sparsity and compression
- Compressed sensing
- Sparse Optimization Methods, Sparse Recovery, and Sparse Models Examples
- Regression and model selection
- Curve fitting, nonlinear regression, gradient descent
- Model selection
- Uncertainty analysis
- Model calibration and parameter inference
- Applications in biology, medicine
- Multi-layer neural networks and activation functions
- Backpropagation algorithm
- Stochastic gradient descent
- Convolutional neural networks
- Neural networks for dynamical systems
- Dynamic mode decomposition
- Sparse identification of nonlinear systems
- Koopman operator theory and data-driven Koopman analysis
Evaluation: The assessment scheme is split into 4 biweekly assignments, a midterm, a group project and a final exam.
Why take this course: Data-driven mathematical models are at the heart of innovation across science, medicine, and technology—shaping the way we understand and solve real-world problems. Whether you're aiming for a career in research or industry, this course will give you a strong foundation in the mathematics of data science. In this interdisciplinary course, you'll learn powerful mathematical and computational techniques to extract insights from data and develop models that matter. You'll put your calculus, linear algebra, and programming skills into action through hands-on projects and exciting applications. Hope to see you at the first offering of this class in the Fall 2025 semester!
Feel free to reach out to me at roberto.guglielmi@uwaterloo.ca if you have any questions regarding the course.
