Unit name | Complex Networks 4 |
---|---|
Unit code | MATHM6201 |
Credit points | 20 |
Level of study | M/7 |
Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
Unit director | Dr. Ayalvadi Ganesh |
Open unit status | Not open |
Pre-requisites |
MATH11300 Probability 1 (or equivalent) and MATH 11005 Linear Algebra & Geometry (or equivalent). |
Co-requisites |
none |
School/department | School of Mathematics |
Faculty | Faculty of Science |
Complex networks is an area of intense current research with prevalent applications in a number of domains including communication, transport and power networks, biological regulatory networks and social networks. The last two decades have seen a great deal of progress in research on the structure and properties of such networks, and on algorithms operating over networks. With the recent appointment of staff in the area of complexity, with increasing student interest in modelling and analysing these areas of application, and with the current state of the subject, now is an opportune time to offer new units in this exciting area.
The lectures for this unit will be delivered in common with those for the proposed Level 6 unit Complex Networks 3 (MATH 36201), but successful completion of this unit will require greater depth of understanding and independent learning than that required for the Level 6 unit.
Aims
Understand how to mathematically model complex networks. Learn to analyse stochastic processes on networks.
Syllabus
Relation to Other Units
The unit introduces Markov chain models, seen in Applied Probability 2 (which is not a pre-requisite but is recommended) and applies them to the study of random processes on networks. Information Theory, Complex Networks, Financial Mathematics, and Queueing Networks, all involve the application of probability theory to problems arising in various fields.
Transferable Skills:
The ability to develop and analyse probabilistic models for a variety of algorithms and processes on complex networks.
Lectures and problem sheets, from which work will be set and marked, with outline solutions handed out a fortnight later. The student will read a research article and present a summary of it.
Readings will primarily be from journal articles and lecture notes. However, some books that contain relevant material are: