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I will be teaching discrete mathematics. I’m wondering if anyone can tell me a couple topics that were classically in this class (in any undergraduate version) that were probably discarded over time, and a couple topics that either have been added to more modern forms of this class, or SHOULD be added.

Even better if there’s something more recent you can think of that was deleted in favor of something else.

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    $\begingroup$ Could you be a bit more specific about the contents of the course, or the country or even university where it takes place? I would not assume discrete math looks the same all of the world. $\endgroup$
    – Tommi
    Mar 20 at 12:10
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This is not a question that can be easily answered without careful historical research. Here are some guesses in the absence of such research.

What's been added?

  • Algorithm analysis: big-$O$ notation. Dijkstra's algorithm.
  • Aspects of complexity theory: polynomial-time vs. beyond polynomial.
  • Discussion of the TSP problem, Christofides' heuristic.
  • Cryptography, RSA encryption.
  • Graph Laplacian, possibly even touching eigenvalues.

What's been removed?

  • Some topics from discrete probability, e.g., Birthday paradox.
  • Some topics from linear algebra, e.g., Cramer's rule.
  • Some advanced material on solving recurrence relations, e.g., second-order recurrences, multiple roots.
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  • $\begingroup$ Wait, can I use Discrete Math as a vehicle to teach the graph Laplacian ? I just became interested in teaching this... $\endgroup$ Mar 20 at 16:40
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    $\begingroup$ @JamesS.Cook ... a particularly bad reason to teach the course $\endgroup$ Mar 20 at 20:25
  • $\begingroup$ @GeraldEdgar noted :) $\endgroup$ Mar 21 at 2:55
  • $\begingroup$ A few years ago I got a couple of books -- Introduction to Finite Mathematics by Kemeny/Snell/Thompson (1957) and Finite Mathematical Structures by Kemeny/Mirkil/Snell/Thompson (1959) -- at at used bookstore that, from their prefaces and from the book reviews I was able to locate, seem to be the most significant "first texts" in discrete math (then called finite math; FYI, I taught 2 sections of a course with the name "Finite Mathematics" in Spring 1986, much lower level than those 2 books), (continued) $\endgroup$ Apr 1 at 5:15
  • $\begingroup$ a course that seemed to gain a bit of traction beginning in the early 1960s and whose importance in adding to the mathematics curriculum was widely written about in various MAA and NCTM publications in the early 1960s. $\endgroup$ Apr 1 at 5:15
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If you are teaching to an audience that will largely be computer science majors (which is often the case), then you should look at the ACM guidelines for an undergraduate computer science curriculum, which includes guidelines for what should be in a discrete math course. Looking at older versions of these guidelines will also give you some sense of how this course has changed.

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You should look at the stated contents of the course you are being asked to teach. Then take a look at what they already have learned when taking this course (perhaps add a bit of refresher, or give them a summary text). Next look at the use they'll have of the material included in the course in later courses, or perhaps in their later life.

The above should give a decent skeleton, fill in gaps, check how deep to dig into e.g. proofs (generally useful for mathematics, required ---but not really stated like that--- for programming and other areas) or techniques in combinatorics, graph theory, ...

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