- Explain the added value of computational modelling to science.
- Formulate suitable models for a range of realistic phenomena and justify modelling choices.
- Analyse and solve simple models analytically.
- Implement simple mathematical models in code and verify their correctness.
- Solve ordinary differential equations (ODEs) analytically (integration method) and numerically (Euler algorithm).
- Analyse the effects of discretisation and numerical approximations on simulation outcomes.
- Explain both the power and limitations of models.
- Understand the role of real data in modelling (excluding model fitting or selection techniques).
- Describe and interpret properties of various classes of models.
- Understand and implement network models and their role in modelling.
- Derive mathematical properties of networks, such as diameter and giant component size.
Computational modelling plays a critical role in evaluating complex systems, from weather forecasting to financial systems design. This course explores the possibilities and limitations of computational models, emphasizing the process of model construction, validation, and simulation.
Topics include:
- Introduction to modelling and simulation as the third paradigm of science.
- Methods for modelling real-world systems:
- Cellular automata
- Ordinary differential equations (ODEs)
- Complex networks
- Deriving mathematical results, e.g., integrating ODEs and network metrics.
- Practical experience through coding assignments (Python preferred).
- Example applications:
- Traffic congestion
- Gas molecule flow
- Disease spreading in connected networks
- Programming Skills: Python (preferred), or C/Java.
- Mathematics:
- Basic calculus
- Basic statistics (binomial distribution)
- Exponential and logarithmic functions
For more details on registration procedures and timelines, visit:
UvA Course Registration
- Lectures (Hoorcollege)
- Practical Coding Sessions (Laptopcollege)
- Self-study
- Independent Work (e.g., project/scriptie)
- Optional:
- A.B. Shiflet and G.W. Shiflet - Introduction to Computational Science, Princeton University Press (1st or 2nd edition).
- Laszlo Barabasi - Networks: Network Science:
- Optional:
- Maarten van Steen - Graph Theory and Complex Networks:
- Modelling and Simulation - A.G. Hoekstra and P.M.A. Sloot
- Slides and required reading material will be provided via Canvas.
- Graded based on submitted code and answer sheets for lab assignments.
- Final written exam covering all course materials.
- This course is part of the minor Computational Science and runs alongside Scientific Data Analysis.
- Mandatory Attendance: Lectures and practical sessions.
- The course is intensive and requires self-study.
Lab Assignments:
- All assignments are individual.
Final Exam:
- Written test at the end of the course.
Happy Learning! 🚀