Basic Concepts in Mathematical Biology
Learn to model biological systems using differential equations, nonlinear dynamics, and mathematical approaches.
Duration
4 weeksWeekly study
2 hours100% online
How it works
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.
Syllabus
Week 1
Fundamentals of Mathematical Modeling and Differential Equations
Fundamentals of Mathematical Biology and Linear Kinetics
In this session, we evaluate biological dynamism using differential equations. By synthesizing fundamental change rates and analyzing linear kinetics via a water tank analogy , you will contextualize system equilibrium.
Stability, Chaos, and Real-World Applications in Nonlinear Dynamics
Explore how nonlinear systems behave through stability, equilibrium, and chaos. Learn how small changes lead to complex outcomes, and how these principles are applied to interpret and analyse real-world dynamic systems.
Week 2
Oscillatory Systems and Phase Space Representation
Understand Oscillations and Differential Equation Models
Learn how oscillations are modeled using differential equations and how dynamic variables describe behavior in biological systems.
Visualize Biological Dynamics in Phase Space
Explore phase space and vector fields to visualize oscillations and understand how system trajectories evolve over time.
Week 3
Nonlinear Dynamics and Limit Cycles
Explore Nonlinear Dynamics in Biological Systems
Explore how nonlinear systems shape biological dynamics. Learn nonlinear transformations, oscillatory behavior, and phase space visualization to understand complex system behavior.
Analyze Stability and Cycles in Nonlinear Systems
Explore vector fields, nullclines, and limit cycles to understand stability, sustained oscillations, and how bifurcation drives changes in system behavior.
Week 4
Synchronization and Physiological Rhythms
Basic Concepts of Synchronization
Professor Myung will introduce the basic mathematical concepts of synchronization, demonstrating different types of coupled oscillators and the Arnold tongue.
Circadian Clocks and Cellular Models
Professor Myung will explore cellular synchronization within the circadian clock, demonstrating the Kuramoto model and analyzing doubleplot actograms in real-time.
Course Feedback and Final Review
This session provides an opportunity to review the course as a whole and reflect on your learning experience. Please consider the key concepts you have encountered and share your overall feedback on the course.
When would you like to start?
Start straight away and join a global classroom of learners. If the course hasn’t started yet you’ll see the future date listed below.
Available now
Learning on this course
On every step of the course you can meet other learners, share your ideas and join in with active discussions in the comments.
What will you achieve?
By the end of the course, you‘ll be able to...
- 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
Who is the course for?
This course is ideal for graduate students and researchers in biology, neuroscience, or life sciences seeking mathematical tools for biological modelling.
Who will you learn with?
Professor
College of Humanities and Social Sciences
Taipei Medical University
Who developed the course?
Taipei Medical University
Taipei Medical University (TMU) has been a leader in Taiwan’s healthcare system for over half a century due to its research, teaching excellence, internationalization and outstanding medical service.
Ways to learn | Buy this course | Subscribe & save | Start learning today |
|---|---|---|---|
| Choose the best way to learn for you! | $154/one-off payment | $335.99 for a whole year Automatically renews | Free |
| Fulfill your current learning need | Develop skills to further your career | Try this course - with limits | |
| Access to this course | tick | tick | Limited to 4 weeks |
| Access to 1,000+ courses | cross | tick | cross |
| Learn at your own pace | tick | tick | cross |
| Discuss your learning in comments | tick | tick | tick |
| Certificate when you're eligible | Printed and digital | Digital only | cross |
Cancel for free anytime |
Ways to learn
Choose the best way to learn for you!
Subscribe & save
$335.99 for a whole year
Automatically renews
Develop skills to further your career
- Access to this course
- Access to 1,000+ courses
- Learn at your own pace
- Discuss your learning in comments
- Digital certificate when you're eligible
Cancel for free anytime
Buy this course
$154/one-off payment
Fulfill your current learning need
- Access to this course
- Learn at your own pace
- Discuss your learning in comments
- Printed and digital certificate when you’re eligible
Start learning today
Free
Try this course - with limits
- Limited to 4 weeks
Find out more about certificates, Unlimited or buying a course (Upgrades) Sale price available until 2 November 2026 at 23:59 (UTC). T&Cs apply. | |||
Find out more about certificates, Unlimited or buying a course (Upgrades)
Sale price available until 2 November 2026 at 23:59 (UTC). T&Cs apply.
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