Basic Concepts in Mathematical Biology

Apply differential equations and nonlinear dynamics to biological systems

Explore biological systems from heartbeats to neural firing to gene expression follow patterns that mathematics can reveal. This course builds your mathematical literacy for life sciences through conceptual models and practical applications.

You’ll need a calculus background, making this ideal if you’re bridging quantitative methods with biological sciences and want to understand the maths behind living systems.

Understanding mathematical modelling fundamentals

Master how differential equations describe biological change over time. You’ll explore phase space as a way to visualise how systems behave and evolve.

Through intuitive models, you’ll learn to represent growth patterns, interactions between species or molecules, and the dynamics of biological processes. These foundational tools help you think quantitatively about life sciences.

Analysing oscillatory systems and their representation

Understand the mathematics behind biological rhythms, like neural firing patterns and circadian cycles. You’ll study phase portraits and limit cycles that help visualise these repeating patterns, and learn to analyse stability in oscillating systems. These concepts reveal why biological systems naturally settle into rhythmic behaviours and how to predict them mathematically.

Exploring nonlinear dynamics and synchronisation

Investigate how simple mathematical rules can generate complex, chaotic behaviour in biological systems. You’ll explore limit cycles in detail and study how different oscillating systems can synchronise with each other.

By connecting simple mathematical models to real biological phenomena you’ll build quantitative skills that bridge theory and biology.

You’ll walk away with the mathematical tools to model and understand the dynamic patterns underlying biological processes.

This course is ideal for graduate students and researchers in biology, neuroscience, or life sciences seeking mathematical tools for biological modelling.

This course is ideal for graduate students and researchers in biology, neuroscience, or life sciences seeking mathematical tools for biological modelling.

• Explore the basic principles of mathematical modeling in biological and neural systems
• Explain the concepts of differential equations as applied to biological oscillations
• Investigate the synchronization and stability of oscillations using tools from nonlinear dynamics
• Describe how simple toy models can represent gene expression oscillations and action potential generation
• Develop foundational skills in mathematical thinking and the quantitative integration of biological data