matroids.pdf
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What is a Matroid? Matroids have become ubiquitous in modern mathematics, and a common selling point for matroids revolves around the many different ways to define them. Miraculously, these ’cryptomorphic axiomatizations’ all turn out to give the same object. Matroids are meant to generalize various mathematical objects. I’ll give one definition, and then I’ll discuss two such objects: graphs and vector spaces. Some Set Terminology The set {1, 2, 3} is a subset of the set {1, 2, 3, 4}, and we write this using the notation {1, 2, 3} ⊂ {1, 2, 3, 4}. Further examples area {1, 4} ⊂ {1,…
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