Mathematical Biology
Overview
Designed for graduate students in the MSc program in Biomedical Engineering and Physics at Cinvestav Monterrey, this course serves as a comprehensive introduction to the intersection of mathematics and life sciences. The curriculum bridges the gap between abstract mathematical theory and biological reality, focusing on Nonlinear Dynamics, Bifurcation Theory, and the art of Mathematical Modeling.
What You Will Learn
Students will explore biological phenomena across a vast spectrum—from the molecular mechanisms of a single cell to the complex interactions within entire ecosystems. By investigating classic models, you will master advanced mathematical and numerical-analysis techniques essential for modern research.
Key Topics in the Curriculum
- Fundamental Dynamics: Explore ordinary differential equations through intriguing questions like “Why don’t clouds fall?” and the mechanics of microbial swimming.
- Growth & Decay Models: Understand the stochastic processes behind exponential growth, radiocarbon dating, and the theoretical limits of bacterial populations.
- Population & Evolutionary Dynamics: Analyze logistic growth, inter-species competition, and how mathematical steady states explain Darwinian evolution and population extinction.
- Epidemiology & Ecology: Study the SIR model to understand disease transmission, the impact of vaccination, and predator-prey relationships through Competitive Lotka-Volterra equations.
- Biological Oscillators: Master the dynamics of biological rhythms, ranging from the Van der Pol oscillator to the foundational Hodgkin-Huxley and Fitzhugh-Nagumo models of neural activity.
Learning Outcome
By the conclusion of the term, students will possess a robust, working knowledge of Mathematical Biology, equipped with the tools to simulate, analyze, and predict the behavior of complex biological systems.
Support Material
Numerical Excercises
To assist with your studies, some numerical excercises are available in this GitHub Repository
Additional References
- Mathematics as a Laboratory Tool by J. Milton and T. Ohira.
- Nonlinear Dynamics and Chaos by S. H. Strogatz.