Christopher FarahSpatial Information Science & Engineering
University of MaineOrono, ME
I am interested in point set and algebraic topology. At present, I am investigating the embedding of homology theory onto sensor nodes in a wireless sensor network as a means of identifying topological properties of the monitored region. This is one of many facets of work that has been initiated by Mike Worboys. In order to simulate the nework protocol, Opnet software is being used. The use of opnet was motivated by Ali Abedi, who created and maintains the WiSeNets lab.
Qualitative Analysis of a Scalar Field via a WSN pdf.
This abstract introduces the use of the Euler characteristic, which I am now generalizing with homology theory using Betti numbers.
This is an independent effort to generalize results regarding subsets of R^n after undergoing m mutually orthogonal projections, with m less than n. In particular, given a subset X of R^n, I investigate the least number of projections that will ensure convexity and the least number in which convexity can obtained.
Though this is a new interest, I find the initial work developed by Edelsbrunner, Chavelle, Guibas, etc., to be fascinating.
I regularly give talks on higher topics in mathematics to primary school students. Some of the topics are: What is the Shape of the Universe?, Paradox in Language, andBeyond the 3rd Dimension
Some courses/classes that I have taught:
Add Maths for university-bound students interested in math/science, Herzlia High School & Reddam House College, Cape Town, SA, 2001-2004.
College Algebra, St Louis University, St Louis, Missouri, 1999-2001.
Algebra and Geometry, Haimbili Haufiku, Eenhana, Namibia, 1996-1997.
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