What would I get in discrete math?

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yavinfour
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What would I get in discrete math?

Postby yavinfour » Fri Apr 03, 2009 11:12 pm UTC

i'll be taking that subject next semester and i'm just curious of what makes it fun to study?

Actually i've checked it on wikipedia and i think its kinda 50% interesting and 50% boring..
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jestingrabbit
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Re: What would I get in discrete math?

Postby jestingrabbit » Sat Apr 04, 2009 12:03 am UTC

Fun is way to objective a term to apply here, for me at least.

For me, the interesting things that I learnt in discrete mathematics were solving linear recurrence relations, graph theory and propositional logic. The class I took also had a strong focus on proof, which was useful for later years.
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Re: What would I get in discrete math?

Postby notallama » Sat Apr 04, 2009 2:46 am UTC

first half of it was a pretty good math class, but nothing really special.
lots of proofs, and a few cool theorems. a lot of it was stuff i already did in calc (because i took the advanced calc) or computer science classes, though.

the second half was completely awesome.

some stuff i learned in the second half (i just had my last class in it today):

counting and probability:
-binomial theorem/pascal's triangle (this thing shows up /everywhere/)
-polya's counting theorem

generating functions:
-they're fucking cool

graphs:
-planar graphs
-dijkstra's algorithm (i already knew it from wikipedia, though)

regular languages:
-regular expressions
-finite state automata (deterministic and non)
-converting between the two

tarski's fixed point theorem:
-induction
-coinduction

and it all ties together. we would go back and prove the old stuff with the new stuff to get shorter proofs and such.

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Re: What would I get in discrete math?

Postby t0rajir0u » Sat Apr 04, 2009 4:08 am UTC

I guess part of how excited you get about discrete math is how excited you get about computer science. It's fair to say that a lot of what has driven the recent interest in discrete math is the importance it plays in computer science. On the other hand, there's an awful lot of discrete math to enjoy for its own sake, and furthermore it's not usually something a high-school or even a non-CS or non-math undergraduate is usually exposed to, so I think it's worth learning.

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Re: What would I get in discrete math?

Postby GreedyAlgorithm » Sun Apr 05, 2009 2:11 am UTC

Counting and probability are phenomenal. The best evar.
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Re: What would I get in discrete math?

Postby the tree » Mon Apr 06, 2009 8:28 am UTC

I got an introduction to formal logic and set theory first, which is just generally useful for everything ever. Following was a bunch of different stuff as already mentioned - discrete maths is actually a fairly broad subject - there's all types of things that you may be focussing on.

Knowing some basic set theory is the first step towards sounding clever than everyone else* "omigod there's leik a little infinity and a less little infinity, wtf?"

*that's how I chose to phrase that sentance.

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Re: What would I get in discrete math?

Postby romulox » Mon Apr 06, 2009 7:16 pm UTC

You can also get neat stuff like: pigeonhole principle or ramsey theory (though probably not in lower level course), partial orders, inclusion-exclusion, combinatorial proof methods, recurrence relations, generating functions (these are bad to the bone), all sorts of nice things from Graph Theory, maybe an introduction to logic via boolean algebra, maybe some circuit design, lots of counting, breadth/depth first searching. Lots of other stuff listed in previous posts.

The subject is very rich, and portions of it are quite young. Even though it is often geared toward computer science majors, mathematics majors would be apt to take it, as there is much they can learn. Non-cs/math majors could also take it since the courses are usually self contained (calc, etc., are not prereqs).

Also depending on how the course is taught you may or may not have seen any of the material in other classes (I hadn't seen anything except for relations in previous classes, when I took my first discrete course).

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Re: What would I get in discrete math?

Postby yavinfour » Tue Apr 07, 2009 10:10 am UTC

now i think i'm gonna fuckn like it~!!

they said its important for programming...right? :?:
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Re: What would I get in discrete math?

Postby the tree » Tue Apr 07, 2009 8:34 pm UTC

You can't describe the efficiency of an algorithm without counting - so yes, yes it is.

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Re: What would I get in discrete math?

Postby Anubis » Thu Apr 09, 2009 4:59 am UTC

My discrete math class was mostly voting methods and fair division, with a little bit of graph theory. Is this a high school class?

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Re: What would I get in discrete math?

Postby negatron » Sat Apr 11, 2009 8:57 pm UTC

yavinfour wrote:they said its important for programming...right? :?:

This is what I've heard being mentioned when I got into it. Not so much it turns out.

A book such as "introduction to algorithms" and related curriculum is far more useful for advanced programming.

If you're rolling your own Integrators, for example, you should study discrete mathematics inside-out, however it is a rare event that you will use the majority of what you're going to learn, although I suspect it depends on the course. You might get something less theoretical than what I've seen. Discrete mathematics vaguely describes the plethora of content you could be exposed to.

Overall it is worthwhile and you should probably go for it, however if you have to choice to do so, you wouldn't be out of place skipping all the stuff about proofs and even sequences. The good stuff seems to come in at the later half, so be patient.
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Re: What would I get in discrete math?

Postby t0rajir0u » Sat Apr 11, 2009 10:37 pm UTC

negatron wrote:This is what I've heard being mentioned when I got into it. Not so much it turns out.

That depends on what you see as the difference between programming, computer science, and theoretical computer science. Discrete math is fundamental to computer science (one might argue that computer science is just a subfield of discrete math) and indispensable in TCS, but as far as actually writing code goes that depends a lot on what kind of code you're writing.

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Re: What would I get in discrete math?

Postby negatron » Sat Apr 11, 2009 10:51 pm UTC

t0rajir0u wrote:one might argue that computer science is just a subfield of discrete math

Hardware architecture is a subfield of computer science. Since hardware architecture is not a subfield of discrete mathematics this cannot possibly be true.

Discrete mathematics is mathematics closely applicable to computer science but it's really just mathematics in it's own right.
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Re: What would I get in discrete math?

Postby t0rajir0u » Sat Apr 11, 2009 11:22 pm UTC

negatron wrote:Hardware architecture is a subfield of computer science.

Hardware architecture is a subfield of electrical engineering :P This is semantics, but from the perspective of a theoretical computer scientist hardware architecture gets in the way of generality, which is the reason they ignore constant factors.

(That is to say: if you accept that Alan Turing is the founder of computer science, I am defining "computer science" to be the study of Turing machines, not the study of computers.)

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Re: What would I get in discrete math?

Postby negatron » Sat Apr 11, 2009 11:29 pm UTC

t0rajir0u wrote:Hardware architecture is a subfield of electrical engineering :P)

Clearly we need to move from a category tree to meta-tagging. :)
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Re: What would I get in discrete math?

Postby jestingrabbit » Sat Apr 11, 2009 11:40 pm UTC

negatron wrote:
t0rajir0u wrote:one might argue that computer science is just a subfield of discrete math

Hardware architecture is a subfield of computer science. Since hardware architecture is not a subfield of discrete mathematics this cannot possibly be true.


If you examine 9.3 and 9.4 here you might notice that there are those who would disagree with you.
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