KL7015 - Complex and Random Systems

You will learn through a series of lectures, seminars and problem-solving/computer-based workshops which include classroom discussions and presentations. Lectures allow you to witness the development of the theory of random matrices to provide with predictions of certain observables in complex systems, and understand how to apply the required techniques coming from several areas in mathematics.
Seminar classes and problem-solving/computer-based workshops will be scheduled weekly to allow exploration of the theoretical background to the techniques covered in the lectures.

Formative feedback is available weekly in the classes as you get to grips with new techniques and solve problems. In addition, we operate an open door policy where you can meet with your module tutor to seek further advice or help if required.

Direct contact with the teaching team during the lectures and seminars will involve participation in both general class discussions as well as one to one discussions during the seminars. This gives you a chance to get immediate feedback pertinent to your particular needs in this session. Further feedback and discussion with the teaching team are also available at any time through our open door policy. In addition, all teaching materials, selected computer programmes and supplementary material (such as interesting articles) are available through the e-learning portal.

All modules at Northumbria include a range of reading materials that students are expected to engage with. Online reading lists (provided after enrolment) give you access to your reading material for your modules. The Library works in partnership with your module tutors to ensure you have access to the material that you need.

Knowledge & Understanding:
1. Use specific random matrix ensembles to represent a large systems with complex interaction between their components
2. Evaluate observables and analyse statistical distributions

Intellectual / Professional skills & abilities:
3. Construct suitable models based on qualitative properties of systems and data sets.
4. Classify and assess occurrence of possible scenarios.

Personal Values Attributes (Global / Cultural awareness, Ethics, Curiosity) (PVA):
5. Critically appraise suitability of models and validation of assumptions.

SUMMATIVE
1. Coursework: 50% - 1,3
(Assignment with set questions and problems - wordcount: max 1000 words + derivations + codes + graphs and plots)


2. Group project: 50% - 1,2,4,5
(Group work: 20min presentation with electronic slides + 10min questions/answers and discussion)
FORMATIVE
Formative assessment will be available on a weekly basis in the seminars through normal lecturer-student interactions and discussions around the seminar questions, allowing them to extend, consolidate and evaluate their knowledge.

Formative feedback will be provided on student work and errors in understanding will be addressed reactively using individual discussion. Solutions for seminar tasks will be provided after the students have attempted the questions, allowing students to receive feedback on the correctness of their solutions and to seek help if matters are still not clear.

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In “Random and complex systems” you will learn techniques to model statistical properties of systems with a large number of components using random matrix ensembles. Random matrices, originally introduced in high energy physics to describe properties of heavy atoms, have become a powerful tool for modelling a variety of systems with random and complex features. Applications range from physics (e.g. condensed matter to quantum gravity), mathematics (number theory, combinatorics), complexity science (traffic, communication, biological networks) and economics (stock and option pricing in financial markets).

You will learn through a combination of lectures andseminars. The lectures give a formal introduction to the theoretical aspects while the workshops enables one to deepen the knowledge by applying the theory to problems to more practical questions arising from physics, and complexity science. The workshops will be an opportunity to span the wide range of applications of random matrices, thus also strengthening your transferable skills and employability.

You will be assessed through a coursework and a group project presentation