Basic Concepts in Mathematical Biology
Build mathematical models for biological rhythms and dynamics
Basic Concepts in Mathematical Biology introduces mathematical modelling approaches for dynamic biological phenomena, focusing on differential equations and nonlinear dynamics to reveal patterns in systems ranging from neural firing to gene expression and circadian rhythms.
The course combines phase-space visualization, oscillatory-systems analysis, and synchronization theory with practical examples so learners with a calculus background can build transferable quantitative skills for neuroscience and physiological modelling.
At a Glance
Basic Concepts in Mathematical Biology is an online course taught by Professor Myung of Taipei Medical University that introduces how differential equations and nonlinear dynamics describe physiological and cellular processes.
It broadly covers mathematical modeling fundamentals, phase-space visualization, oscillatory systems and limit cycles, and synchronization as applied to rhythms like neural firing and circadian clocks.
| Level | Intermediate |
| Rating | 4.6 out of 5 |
| Duration | 4+ weeks |
| Languages | English |
| Certificate | Certificate of achievement available |
| Access | Free access during the course with option to upgrade for extended access and certificate; also available via FutureLearn subscription |
| Course includes |
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| Price | Free to access limited content; optional paid upgrade for certificate and extended access; also available with subscription |
What This Course Teaches
By course end, learners will gain measurable competencies for modeling and analysing dynamic biological systems, from constructing differential-equation models to evaluating rhythmic behaviour and synchronization. Competencies include applying mathematical models to biological and neural systems and analysing oscillatory stability and synchronization using nonlinear dynamics methods.
How the Course Is Structured
The course is organised as a short, focused programme spanning 9 modules delivered over 4 weeks, with each week grouping sessions on modelling, oscillations, nonlinear dynamics, and synchronization.
Course content is arranged sequentially as individual syllabus sessions so learners progress module-by-module toward a final review and feedback session.
Curriculum overview
01 Fundamentals of Mathematical Biology and Linear Kinetics ▾
Evaluates biological dynamism using differential equations and linear kinetics, using analogies such as a water-tank to contextualise equilibrium and rate processes.
02 Stability, Chaos, and Real-World Applications in Nonlinear Dynamics ▾
Introduces stability, equilibrium, and chaotic behaviour in nonlinear systems and demonstrates how small parameter changes can produce complex outcomes in biological contexts.
03 Understand Oscillations and Differential Equation Models ▾
Covers how oscillatory behaviour is modelled with differential equations and how dynamic variables describe rhythmic patterns in biological systems.
04 Visualize Biological Dynamics in Phase Space ▾
Explores phase space, vector fields, and trajectory visualisation as tools to understand how system states evolve over time.
05 Explore Nonlinear Dynamics in Biological Systems ▾
Examines nonlinear transformations and their role in producing complex, often counterintuitive behaviours observed in biological models.
06 Analyze Stability and Cycles in Nonlinear Systems ▾
Focuses on vector fields, nullclines, limit cycles and bifurcations to analyse stability, sustained oscillations, and transitions in system behaviour.
07 Basic Concepts of Synchronization ▾
Introduces mathematical concepts of synchronization, demonstrates different types of coupled oscillators, and explains structures such as the Arnold tongue.
08 Circadian Clocks and Cellular Models ▾
Applies synchronization models like the Kuramoto model to cellular circadian clocks and examines double-plot actograms to study population-level timing.
09 Course Feedback and Final Review ▾
Provides an opportunity to review key concepts from the course, reflect on learning progress, and submit feedback on the course experience.
Audience & Requirements
This course targets graduate students, researchers, and advanced undergraduates in biology, neuroscience, and related life sciences who need mathematical tools to model dynamic biological processes.
It is best suited to learners who are bridging quantitative methods and biology and already have a calculus background.
- Graduate students and researchers in biology or neuroscience seeking modelling skills.
- Early-career scientists who need to analyse rhythmic physiological or cellular data.
- Interdisciplinary researchers bridging mathematics and life sciences.
- Coursework or exam candidates needing focused training in dynamical systems for biology.
- Calculus and basic familiarity with differential equations.
- Undergraduate-level understanding of biology or neuroscience concepts.
- Comfort reading mathematical notation and following quantitative arguments.
Final Verdict
Given its strong user rating, broad uptake, and the availability of a verified certificate via an optional upgrade or subscription, this course is a cost-effective way to acquire practical mathematical modelling skills for biological systems.
It is particularly worthwhile for learners who already meet the calculus prerequisite and want a compact, application-focused introduction to differential equations, oscillations, and synchronization in biology; those without the necessary math background should prepare with a targeted calculus or differential-equations refresher first.
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