Matroid theory concerns a combinatorial abstraction of linear dependence, which, in turn, can be viewed as an abstraction of the cyclic structure of graphs. Matroids are fundamental objects in combinatorial optimization. The course includes: Basic definitions and examples, duality, minors and unions, connectivity, submodularity, graphic matroids, representable matroids (those that come from vector spaces), binary matroids (representable over GF(2)), regular matroids (representable over all fields).
Text: Matroid Theory, James G. Oxley, Oxford University Press, 1992. ISBN: 0-19-853563-5.
Prerequisites: Some exposure to Linear Algebra, Abstract Algebra, and Graph Theory, or permission of the instructor.