Could you recommend any approachable books/papers/texts about matroids (maybe a chapter from somewhere)? The ideal reference would contain multiple examples, present some intuitions and keep formalism to a necessary minimum.
I would appreciate any hints or appropriate sources.
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You could have a look at the relatively new book
Gary Gordon, Jennifer McNulty: Matroids. A Geometric Introduction, Cambridge University Press 2012.
From the description: "This book provides the first comprehensive introduction to the field which will appeal to undergraduate students and to any mathematician interested in the geometric approach to matroids. Written in a friendly, fun-to-read style and developed from the authors' own undergraduate courses, the book is ideal for students."
Dover has released a cheap version of Welsh's Matroid Theory - can't argue with the price. On the other hand, I've heard better things about Oxley's Matroid Theory.
(Apparently there is absolutely no creativity in naming books on Matroid Theory)