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To anyone who has, or is earning, a degree in computer science:
What do you think is the bare minimum of topics that should be covered in a first course on discrete math or discrete mathematical structures?
Please list 3-10 topics, as specific or as as general as you like.

In other news: Today is the two-year anniversary of my GreatestJournal and the three-year anniversary of my LiveJournal.

Highlights, 27 Feb 2003 - 26 Feb 2004
(When I have more time, I will put 2004 and 2005 highlights here.)



Mar. 3rd, 2006 03:29 pm (UTC)
Proof techniques (to be used throughout)
Induction (in tandem with "proof by induction")
Recursive definition (in tandem with "induction")
Logic (in tandem with learning "proof by contradiction")
Basic Set Theory (following from logic and recursive definition)
Mathematical notiation (following from set notation; summation and the like work well with similar notation from sets; might also be taught as part of induction)
Functions, their notations, and their terminology (isomorphism, image, pre-image, etc.)
Combinitorics and counting arguments
Trees (in tandem with the tree definition in graphs)
Mar. 3rd, 2006 03:31 pm (UTC)
Oh, and of course asymptotic notations and definitions, including O,o,Omega,omega,Theta
Mar. 7th, 2006 12:22 pm (UTC)
Asymptotic analysis
Absolutely. I think in the first year or two, basic analysis of algorithms is many times more important for a CS major, or for a mathematical computing or statistical computing person, than covering fundamentals of real and complex analysis.

Being able to do fancy things with limits and abstract algebra, even number theory beyond modulo arithmetic, relative primaility, and concepts such as the Sieve of Eratosthenes for finding primes, can wait, IMO. A math major might learn it at the same time; but even she doesn't have to have it before understanding the most basic things about analyzing and dissecting algorithms to comprehend how to prove them correct and characterize their running time in a formal way.

Mar. 7th, 2006 12:05 pm (UTC)
Discrete math curricula: thanks for the list
Here is an explanation for my query. I'll follow up in a couple of days.

Thanks again,
Mar. 7th, 2006 02:31 pm (UTC)
Re: Discrete math curricula: thanks for the list
Glad to help.

My list is informed by two factors.

1 By my first discrete math class, which I loved (was taught by Jeff Erickson, who rocks the house down), and found excessively helpful.

2. There is something to be said for being exposed to notations and diagramatic techniques, that what you are trying to do in this class is give them the ability to read these kinds of materials. Just the notations of combinitorics, and then showing how the arguement "selecting a president, and then selecting 4 more for the executive committee can be done in the same number of ways as selecting 5 executives, and then a president from among them" is written, is something rather helpful. I know that likely the largest trouble I had in math classes (but not in CS, due to my introduction) was that I learned to think about the ideas, but in my own terminology, and then I had impedence mismatches later.

Mar. 7th, 2006 11:16 pm (UTC)
Re: Discrete math curricula: thanks for the list

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