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Questions tagged [discrete-mathematics]

Questions about discrete mathematics, the study of mathematical structures that are fundamentally discrete rather than continuous.

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values.

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How much math does one need to know to understand discrete math/structures for computer science?

Normally universities teach discrete math / discrete structure. My question is, how much math does one need to know to understand this area? Is calculus required or will precalculus do just fine? Does one need to have done proofs before to be able…
user2387
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Finite representations and programming languages Countably inifite

I'm going over some of the pre-requisite math regarding Automata theory, and finite representations. I read the following: If ∑ is a finite alphabet the set of all strings over the alphabet (∑*) is countably infinite. The set of all possible…
Andrew S
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A road-map for mathematics needed in CS?

Before asking my question, I have to give some background about myself. I live in Iraq and this made my education a total disaster. My middle/high school math skills are not that great and I never realized that until I got into college. I found out…
pisceswolf96
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Why are inversions useful in computer science?

In the second chapter of Cormen's textbook on Algorithms, he lists a discrete mathematics exercise on so-called "inversions", defined as follows: Let $A[1 \ldots n]$ be an array of $n$ distinct numbers. If $i < j$ and $A[i] > A[j]$, then the pair…
PP121
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Can maximal number in poset be more than one?

In poset maximal number is defined as: An element 'a' belongs to 'A 'is called a maximal number if there is no element 'c' in 'A' such that a is less than c. but it again says that there can be more than one maximal number. How can it be possible?
Binod Kafle
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An efficient way of calculating ((p*q)) where p and q are prime

Let $p$ and $q$ be prime numbers and $\phi$ Euler's totient function. Is there an efficient way of computing $\phi(\phi(p\cdot q)) = \phi((p-1)(q-1))$, that is not simply based on factoring $p-1$ and $q-1$? Obviously, if $p$ and $q$ do not equal…
Philipp
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DPLL algorithm: OLR vs. PLR

Can someone please show me examples of what is the difference between OLR (one literal rule) and PLR (pure literal rule) using the DPLL algorithm?
Sasha
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How to find the number of discrete states possible by current computers?

In his famous article, "Computing Machinery and Intelligence", Allan Turing talks about discrete-state machines and the largeness of the number of states provided by that time "state-of-the-art" machine, "Manchester Machine", which he states is…
Tiago Duque
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Prove that the union of multisets is idempotent

I am struggling with a proof from my discrete mathematics class. We have to prove that multiset union is idempotent, i.e. $M \sqcup M = M$, where $\sqcup $ denotes the union of multisets. We have defined multiset union (using lambda notation) as…
sigma
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Prove that two different concatenations of relations are equivalent

I've had this question on my exam today and I couldn't figure it out, I would like to know the answer. The question: Given relations $R$, $S$ on a set $U$. $R$ is transitive, $S$ is reflexive. Prove that $(R;S;R)^2$ is a subset of…
skiwi
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Computing with the Monster

The Monster M is the largest of the finite sporadic groups that arises in the classification of finite, simple groups in mathematics. M can be realized as a (very large!) set of 196882 X 196882 matrices with nothing more than entries of 1's and…
user11020
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How do you go from $\log P = \log N$ to the next step?

Let \begin{align*} &P=2^{\log_2 N}\\ &\Rightarrow \log_2 P = \log_2 N\\ &\Rightarrow P=N\\ &\Rightarrow 2^{\log_2 N}=N\,. \end{align*} I don't understand how can you just drop the logs and go straight to $P = N$. Can someone…
Strawberry
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Divide sequence of numbers from 1 to n into 2 groups with minimum difference

Let's say for some $n$ we have the sequence $1, 2, 3, \dots , n$, what we want with this sequence is to divide it in two sets such that each element of the sequence will be in only one set, and the difference in sums of the two sets will be minimum…
someone12321
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Big O help Discrete Math

Is 17x+11 a function of O(x^2)? My steps so far: 17x+11 < c.x^2 where x>k 17x+11/x^2 < C Im not too sure what to do next so I'd really appreciate if it someone could guide me. This question was not answered. The link that was provided exceeds what…
user40318
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Converting Base 16 to Base 8?

I understand the basic but what I dont understand is this: so base 16 to base 10 357/16 = 22.3125 but on this example im looking at says remainder 5?
Ceri Westcott
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