Suggested Project Topics

The singular value decomposition (SVD) is an important factorization of a matrix with interesting applications to a wide variety of areas such as image and signal processing, data compression, computational tomography, etc.. For one example of the the SVD can be applied to problems involving in face recognition, see Singular Value Decomposition, Eigenfaces, and 3D Reconstructions by Neil Muller, Lourenco Magaia, B.M. Herbst

See also, Professor SVD, by Cleve Moler.

You should consider this project if you like Linear Algebra. Some computing will be essential, but not necessarily anything too difficult.

A different example is Schwarz Methods for linear boundary value problems. These have existed for over 100 years, but are being ``rediscovered'' because they are so suitable for parallel computers

A project on this topic would mainly involve programming and algorithm design. Code could be tested on some Linux computers running software to emulate parallel and distributed systems.

The student who does this project should like programming. It would be useful to have studied numerical analysis.

Many networks that occur naturally have two properties: clustering and short average path-lengths. This is called the small world phenomenon and is related to research activities in very diverse areas. To verify this, check a web search engine for such topics as Six Degrees of Separation and The Kevin Bacon Game

A student working on this project will, at the very least, read a number of articles on the topic, learn enough mathematics to understand some of the theorems and conjectures in the area, and write some computer programs to simulate these networks.

The project would suit a student with interests in programming and graph theory. Some knowledge is stochastic processes and Markov chains would be useful.

Numerical Analysis is the area of mathematics that is concerned with the design and analysis of methods and algorithms for obtaining useful solutions to mathematical problems. Two of the main sources of problems are differential equations and linear algebra. The applications are far too numerous to mention.

The interested student should browse a few books in the library. For example Afternotes on Numerical Analysis and Afternotes goes to Graduate School (G.W. Stewart), Introduction of Numerical Analysis (Stoer and Bulirish),

Depending on the students' interests, projects may have little or no computing aspects, or may be strongly focused on computational problems, or something in between.

Why not come up with your own idea? A good place to start would be the Education articles in SIAM Review. Or you could go to the library and have a look at such titles as

• Amy Langville, Google's PageRank and beyond : the science of search engine rankings
• Michael Berry, Understanding search engines : mathematical modeling and text retrieval
• John Fauvel, Music and mathematics: from Pythagoras to fractals
• Gardner, Martin, The night is large : collected essays, 1938-1995