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There's a recent book by Nicholas A. Scoville: Discrete Morse Theory, AMS Student Mathematical Library, 2019. Publisher's page: https://bookstore.ams.org/stml-90 MAA review: https://www.maa.org/press/maa-reviews/discrete-morse-theory It looks very accessible to the undergraduate - some background in proof writing is recommended as is some linear algebra, but ...


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