Ardila’s matroid course, rewritten by topic: independence, duality, flats, minors, and representability.
Vectors, graphs, and matchings as three pictures of independence.
The independent-set axioms, and linear, graphic, and transversal matroids.
Basis axioms and the basis-exchange property.
The greedy algorithm characterises matroids.
Circuit axioms and elimination.
Dual matroids, and duality for linear, graphic, and transversal matroids.
Rank functions and closure operators.
Flats, geometric lattices, and simple matroids.
Deletion, contraction, and minors in the three models.
Forbidden minors, the Fano matroid, and representability.
Algebraic dependence and algebraic matroids.
Degree sequences and paths.