Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2025/26
This module is not approved as a discovery module
This module introduces technical real-world considerations such as the analysis of networks and complex systems. It builds on the mathematical foundations of algebra and graph theory and applies these to the analysis of networks. It compares and contrasts reductionism & superposition with non-linearity & complexity such as the messiness of the real world. The module combines ideas of networks with non-linear activation functions in order to model the dynamics of basic neural networks and uses libraries to perform standard neural network tasks such as predictive modelling and classification.
This module develops an appreciation of the tension between simple & exact mathematical models and the complexity of real-world situations with strongly coupled entities that exhibit non-linearities, feedback loops and evolution.
- learn to appreciate why this is particularly important in the context of data science and sustainability
- apply algebraic methods to the analysis of large networks and systems.
- be introduced to paradigms of complex physical systems, complex adaptive systems and agent-based modelling.
to appreciate how non-linearities and difficulties in defining the boundaries of the system make real-life systems more difficult to tackle, with emergent behaviour and evolution.
- apply such ideas to the design and analysis of basic artificial neural networks.
- use larger neural networks via libraries for basic machine learning tasks around supervised learning and classification.
On successful completion of the module students will have demonstrated the following learning outcomes relevant to the subject:
1. Explain and apply algebraic tools, techniques and theorems from graph theory to the analysis of community structures of large networks such as centrality, cliques and connectedness.
2. Communicate how interconnectedness in the real world can lead to complexity, such as in organisations, data science and sustainability, clearly identifying and explaining key features of complex dynamics.
3. Computationally model basic complex systems such as a simple neural network with non-linear activation.
4. Use appropriate programming libraries, training and validation to perform neural network tasks such as prediction and classification in supervised learning.
5. Communicate the ability of complex adaptive systems to evolve, and apply appropriate optimisation paradigms in data science such as gradient descent, evolutionary optimisation, Adam or binary cross entropy.
Skills Learning Outcomes
On successful completion of the module students will have demonstrated the following skills learning outcomes:
a. Use mathematical and computational models to represent real-world scenarios and evaluate the validity of conclusions.
b. Collaboratively investigate a scientific topic and communicate findings.
c. Articulate ethical questions around data science, complexity and sustainability.
d. Communicate the tensions between simple mathematical modelling and the complexities of the real world.
1. Graphs and Networks, adjacency, diameter, search etc; network analysis: connectedness, neighbourhoods, spectrum, centrality etc
2. Libraries such as networkx and big data applications to large networks; random networks, preferential attachment model (e.g. the world wide web)
3. Complex systems: Non-linearity, stability and chaos; emergence, boundary, tipping points, wicked problems etc; complexity in the real world and systems thinking; reductionism vs complexity, superposition vs non-linearity; computational and software implementations e.g. NetLogo, Schelling model, complex physical systems, complex adaptive systems and agent-based modelling
4. Artificial Neural networks: non-linear activation functions, universal approximation theorems; from implementation of a small graph-based model to use in supervised machine learning; linear and non-linear differential equations and numerical implementation in python
5. Neural Network libraries for predictive modelling and classification tasks; Training/test split, loss function, cross-validation, overfitting; optimisation
6. Complex systems, sustainability and ethics; common patterns in real-world data
Methods of assessment
The assessment details for this module will be provided at the start of the academic year
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Practical | 11 | 2 | 22 |
| Practical | 11 | 3 | 33 |
| Independent online learning hours | 60 | ||
| Private study hours | 85 | ||
| Total Contact hours | 55 | ||
| Total hours (100hr per 10 credits) | 200 | ||
Learners will regularly produce work in the hands-on teaching sessions, and get peer and formative feedback, including for preparation for the group/individual projects and the portfolio. Some information searching, written work and presentation tasks will be set with feedback opportunities. The students can then act on this feedback for their projects or reflective portfolio.
Check the module area in Minerva for your reading list
Last updated: 30/04/2025
Errors, omissions, failed links etc should be notified to the Catalogue Team