Open course · Universities of Verona and Trento
Technology and Innovation in Sport
A hands-on introduction to mathematical modeling in sport science: how models are built and calibrated, where they fail, and how to use them in research and practice.
- modules
- 6
- modules
- extra models
- 6
- extra models
- of study
- ~5 h
- of study
- and open
- Free
- and open
The course
Six modules, one idea at a time
Each module builds on the previous one, with interactive charts you can change and checkpoint questions at the end.
- 1 35–45 min
Mathematical models
What a model is, its parts, and the steps from observation to a model you can use.
- Variables and parameters
- HRmax = 220 − age
- Force-length
- Hill equation
- VO₂max from climbs
- 2 45–60 min
Model calibration
Fitting parameters to data, the limits of a famous formula, and why extrapolation and overfitting mislead.
- RMSE
- Excel Solver
- Interpolation vs extrapolation
- Overfitting
- 3 40–50 min
Static models
The power-duration curve, VO₂ and lactate kinetics, and the Banister model of supercompensation.
- Critical power and W′
- 3-min all-out test
- VO₂ kinetics
- Banister model
- 4 50–65 min
Dynamic systems
Differential equations solved step by step: VO₂ dynamics, a bike suspension, and the motion of a cyclist.
- First-order systems
- Mass-spring-damper
- Equation of motion
- Finite differences
- 5 40–50 min
AI models
Neural networks from a single neuron, the curse of dimensionality, and how a language model predicts text.
- Perceptron
- ReLU
- Training vs validation
- LLMs
- 6 40–50 min
The power of models
Models behind real decisions, association vs causation, and one equation that appears everywhere.
- Insurance and crash data
- Spurious correlations
- One equation, many fields
Go further
Extra models
Each page works through one model from research in more depth, with its own interactive chart.
W′ balance
How W′ is used up above critical power and recovered below it, interval by interval.
- Critical power
- HIIT
- Excel
Glycemic response
A machine-learning model that predicts the shape of the glucose response to a meal.
- CGM
- Machine learning
- Nutrition
Reactive hypoglycemia
How the timing of a pre-exercise meal changes the risk of a glucose drop, from 6,761 athletes.
- CGM
- Meal timing
- Probability
Static vs dynamic VO₂
The same incremental test read with a static and with a dynamic model, side by side.
- VO₂
- Steady state
- Time constant
Loop gain and oscillatory breathing
Why a feedback loop with a delay oscillates, from a shower with a long pipe to a real exercise test.
- Feedback
- Delay
- CPET
Workout Reserve
Ten exponentially weighted means of power that track the margin to your best, in real time.
- EWM
- Fatigue
- Pacing
Talks
Presentations
Slides from lectures and conferences, some with live models and charts.
About the course
Where the course comes from, what it covers, exam preparation for in-person students, and the terms for reusing the material.
Study with NotebookLM
A free Google NotebookLM notebook built on the course, as an extra study aid. I cannot guarantee the accuracy of what Gemini generates.
Support this project
If my work has helped you, you can support it by buying me a coffee. It helps me maintain and improve the course.