Niall Madden

Teaching Archive

This is a list of all courses that I have taught since September 2000. There are links to some online content for the most recent instance of the course. Some links might be broken -- please let me know.
Important: These notes may not be relevant for courses that are now taught by someone else. Lecturers tend to redevelop courses; topics are continually updated.

2011/2012

Final Year Project (11/12)

• Brian Burns (Financial Mathematics and Economics) "Random Graphs". Brian studied links between linear algebra and graph theory, with an emphasis on the mathematics that can be used to study properties of very large graphs -- such as how the average path length of the graph depends on the number of vertices and edges. He also wrote some Octave/Matlab programmes the simulate and visualise large graphs.

2010/2011

Sabbatical!!

2009/2010

Final Year Projects (09/10)

• Jason Orr (Computer Science) "Crawling Through College". Jason designed and implemented an impressive web crawler in C, learning a lot about sockets and network programming in the process. He tested it on the NUI Galway site.
• Philip Mulryan (Computer Science) "Signal processing and Robotics Programming". The main output from Phil's project was a Lego NXT-based robot that could play tic-tac-toe. The language used was the C-lick NXC. The main challenges included mastering real-time programming, processing input from the robot's sensors, and designing an algorithm for the game.
• Jason Gill (Financial Mathematics) "Image compression and the Singular Value Decomposition". Jason studied the computation of the SVD, primarily using Householder reflectors, and the Golub-Kahan algorithm. He then used the SDV to implement some image processing algorithms, and analyse them in various norms.

2008/2009

Final Year Project (08/09)

• Daniel Finn (Financial Mathematics) "Numerical Solutions to Stochastic Differential Equations". Through careful study of Ito calculus, and stochastic Taylor series, Danny was able to analyse the popular Euler-Maruyama and Milstein methods, and apply them to some interesting SDEs.

2007/2008

Final Year Project (07/08)

• Sean Corcoran (Computer Science) "Webcrawling and Pagerank". A careful study of the fundamentals underpinning the famous Google PageRank Algorithm. Using data generated by a web-crawler that we wrote himself, Sean was able to "rank" pages on local server.
• Grainne Kenny (Financial Mathematics) "Ranking sports teams". In what was (as far as we knew at the time) a novel application of a PageRank algorithm, Grainne devise a variant to rank sports teams in knock-out competitions. The two main data sets were the results of the 2007 Rugby World Cup, and the 2007 National Hurling League (in spite of the name, the finals are played as a knock-out). During the project we found similar work by Langville and Meyer. Still, we had a lot of fun. We concluded that Ireland were ranked 12th of the 20 years in the 2007 RWC, and that Clare were ranked 2nd in the Hurling league.

2006/2007

Project (06/07)

• Aoife Hennessy (MSc in Communications and Information Systems) "A study of large scale eigenvalue problems in information search and retrieval". Aoife studied the analysis and application of Krylov subspace methods eigenvalue problems.

2005/2006

Project (05/06)

• Michael Meehan (BSc in Financial Mathematics and Economics) "Digital Image Processing and the mathematics involved".
• Oisin Kelly (BSc in Financial Mathematics and Economics) "Financial Option Valuation".

2004/2005

Projects (04/05)

• Aaron Hurley (MSc in Communications and Information Systems) "Audio Filtering with respect to Spectral Analysis, Synthetic Methods and Well Known Functions"
• Bebhinn O'Brien (BSc Computer Science) "The Numerical Simulation of Stochastic Differential Equations".
• Thomas O'Flaherty (BSc Computer Science) "Numerical Methods in Distributed Environments".

2003/2004

Projects (04/05)

• Anthony Coyne (BSc in Financial Mathematics and Economics) "Numerical option pricing and the Black-Scholes model using Matlab"
• Joseph Garvin (Higher Diploma in Mathematics) "Simulating Small World Networks".
• Lisa McGarrigle (BSc in Financial Mathematics and Economics). "Metrics for Matrices".

2002/2003

Projects (02/03)

• Marcella Doherty (Higher Diploma in Mathematics) "Numerical methods for stochastic differential equations".
• Brian Caffrey (BSc in Computing Studies and Mathematical Science). "Distributed Systems".

2001/2002

Projects (01/02)

• Karen Durkin (BSc in Financial Mathematics and Economics) "Numerical Analysis of the Black-Scholes Model".
• Neil Burke (BSc in Computer Studies and Mathematical Science) "Cubic Spline Interpolation: rational splines and convexity".
• Lorcan Connaughton (BSc in Financial Mathematics and Economics) "The Black-Scholes Model: a numerical approach".

2000/2001