Discrete Math Glossary

I’ve been getting bogged down in discrete lately, trying to keep up with all the concepts. The tricky thing is this: while most of the concepts are easy to understand, the nuances can trip you up when you’re dealing with a lot of ideas at once.

I was hanging out at a coffee shop downtown with Chason last week when I decided to start a glossary. I was having a hell of a time understanding what an “inverse image” was. The more I tried to get it, the more I realized I was having trouble because I didn’t understand a bunch of root concepts fully. So, I did something I’ve done in the past – I started a glossary.

This isn’t just a glossary of terms. It’s a particular phrasing of ideas designed to goose me into remembering something if I’ve forgotten it. In the spirit of Griffith’s physics books, I try to include a rigorous definition, and a friendly informal one. I wish all texts did this.

Check it out! I’ll be updating as I learn, and perhaps it’ll be useful to some of you struggling in this area.

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11 Responses to Discrete Math Glossary

  1. Westicle says:

    “Subset” could be another addition. In fact, a lot of my Calc II terms feel like they could fit into this, but I’m not sure exactly how many of those would apply to what you’re using this for.

  2. ryan says:

    So far it looks like you have some discrete specific words and some more general terms. Maybe break it down into more catagories?

  3. Nick says:

    Reminds me of when I took Discrete Math several years ago. I still recognise a lot of the terminology from your Glossary.

    I remember enjoying Logic, Graph Theory and Proofs from when I did it.

    (There’s nothing more badass than being able to tell someone their argument is logically invalid)

    Flipping through my old text I see a section on Recursion and Recurrence Relations, but I only recall covering this in my Advanced Algorithms course.

    Memories. :-)

  4. battharqa says:

    Glad to see a new post, and a useful one at that

    • MD says:

      Ditto. Would love to see Chapter 7 of the ‘Wanna to be a Webcartoonist’ series – makes for some great reading that.

  5. anatman says:

    you might want to get a copy of combinatorics by béla bollobás. it is a quite readable text about some fairly advanced topics. it has a very useful notation summary/glossary at the beginning that helped me, as a self taught math aficionado, work through it without too much trouble. the isbn is 0-523-33703-4. cambridge university press.

  6. scutterman says:

    Firebug killed that page, does that often happen with google docs?

  7. kitukwfyer says:

    I make glossaries for a lot of my classes, most painfully for astrophysics, but I admit I’m hardly so thorough. I will gladly take advantage of your work. *Bookmarked* :)

  8. William Furr says:

    I failed discrete the first time I took it in college. Embarrassing for an honors CS student. I didn’t take it very seriously or see much use for it, and didn’t show up for some of the tests (since there was no schedule, I hate that).

    Anyway, the summer after I read Cryptonomicon by Neal Stephenson, still one of my favorite novels of all time, and chock full of computer science theory and discrete mathematics, integral to the plot. After reading it, I realize that discrete mathematics is the foundational mathematics for CS and really should be taught at the high school level, if not in middle school.

    So I got an A when I retook the class.

    Since then, I’ve become convinced that following arithmetic, before algebra even, should be number theory and logic.

  9. MG says:

    Hmm, not a bad idea. I think I’ll do this for Statistics (I have a test coming up soon!)

  10. Altik_0 says:

    This is actually quite brilliant. I think I’ll sit down and churn through some Linear Algebra terms tomorrow night!

    btw: few helpful hints which may or may not be helpful:
    -One-to-one is also known as injective (thus the ‘bi’ in bijective)
    -A countable set will always make a bijection with Z+, but it can also be shown to be countable if it makes an injection, because any subset of a countable set is countable as well. (Simplifies some of the proofs you have to do with countability of sets)

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