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Questions tagged [discrete-mathematics]

The study of discrete mathematical structures. Consider using a more specific tag instead, such as: (combinatorics), (graph-theory), (computer-science), (probability), (elementary-set-theory), (induction), (recurrence-relations), etc.

Discrete mathematics is not the name of a branch of mathematics, like number theory, algebra, calculus, etc. Rather, it's a description of a set of branches of math that all have in common the feature that they are "discrete" rather than "continuous".

The term "discrete mathematics" is therefore used in contrast with "continuous mathematics," which is the branch of mathematics dealing with objects that can vary smoothly (and which includes, for example, calculus). Whereas discrete objects can often be characterized by integers, continuous objects require real numbers.

Though there cannot be a definite number of branches of Discrete Mathematics, the following topics are almost always covered in any study regarding this matter −

  • Sets, Relations and Functions
  • Mathematical Logic
  • Group theory
  • Counting Theory
  • Probability
  • Mathematical Induction and Recurrence Relations
  • Graph Theory
  • Trees
  • Boolean Algebra

For an overview, see the Wikipedia entry on Discrete mathematics.

and http://www.cs.yale.edu/homes/aspnes/classes/202/notes.pdf

Consider using a more specific tag instead, such as: , , , , , , , , etc.

32903 questions
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How many cheaters in a gaming community would be required to "ruin" the game?

Recently I was playing an online game. I was frequently beaten by someone who was performing suspiciously well. I told a friend why I didn't really like playing this game, and his response was "It happens, but I think that only 2% of these players…
DeepDeadpool
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How to solve $f(n) = 6f(n-1) - 9f(n-2)$ for $n \ge 2$ with $f(0) = 0$ and $f(1) = 1$?

The method I found for solving recursive equations starts like this: First, I express the equation with the help of polynomials $q$, so $$q^n = 6q^{n-1} - 9q^{n-2}.$$ This is equivalent to $$q^2 = 6q - 9,$$ which can be solved with the…
Julian
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How can I find a logically equivalent equation by only using negation and conjunction?

So I am trying to finish up my discrete math homework, but I am completely stumped as to how I am supposed to solve this problem. My teacher wants me to find a logically equivalent equation for p v q that does not include exclusive or, implication,…
SlackStack
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For what values of $a$, $b$ and $c$ is $f(x) = ax^2 + bx + c$ (i) one-to-one? (ii) onto?

Let $a$, $b$ and $c$ be real numbers and consider that $f$ maps $\mathbb{R}$ to $\mathbb{R}$. For what values of $a$, $b$ and $c$ is $f(x) = ax^2 + bx + c$ (i) one-to-one? (ii) onto?
UH1
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Discrete Math Course

I am in currently in college, wanting to study applied mathematics and physics. How many discrete math courses am I required to take; is it necessary that I take any at all?
Mack
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Prove that for all sets A,B,C if B $\subseteq$ C then A $\cup$ B $\subseteq$ A $\cup$ C

I don't really know what to do with unions, can someone help me? I assume $B\subseteq C$, (I want to show that $A\cup B \subseteq A\cup C$) suppose $A\cup B \subseteq A\cup C$ and let $x\in A\cup C$ so that $x\in A$ or $x\in C$... I don't really…
Ryan Pang
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Describing a sequence of terms

I'm currently in a Discrete Mathematics class in college, and my professor is giving a quiz soon and told us what will be on it. Problem is, I missed a day of class and I have no idea to figure out what he was saying when he gave us this…
Benjamin Kovach
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Tower of Hanoi confusion from Concrete Mathematics

so I just started reading Concrete Mathematics as a precursor to The Art of Computer Programming vol. 1. I'm on page 3 and I'm already struggling. Anyway, the recurrence is stated to be: $2T_{n-1} +1$ But I don't understand how this works. If $n$ is…
Cory Madden
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Principal disjunctive normal form conversion problem.

I am solving a question where I have to convert $(\neg P \ \lor Q)$ this equation into principal disjonction normal form. so far I know that to convert it I have to multiply 1 with it. ie; $(\neg P \ \lor Q) \land T$, where $T$ is true. now in the…
Atanu Mondal
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Hasse Digram Leveling

I have the following Hasse diagram for the divides relation on the set $\{1,2,3,4,5,6,7,8,9,10\}$. I felt that everything is in the right place, but my professor is saying that one of the elements is not on the correct level. I looked up some more…
russjohnson09
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Expected number of triangles with random lines

Take the square $[0,1]^2$ and divide it up with $n$ random lines. We can choose our random lines by choosing one point randomly on one of the four sides and then choosing another point randomly lines and also what is the probability that no region…
user402817
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Rates, Distance and Time Problem 45

2 vehicles left the town $A$ and $C$ at the same time to ride to the other town, crossing each other at town $B$ and both traveling at different steady speeds. The vehicle from town $A$ finished the trip from town $B$ to town $C$ in 45 minutes at a…
Valerie
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Probability that Area is Greater than 1/2

Take the area $[0,1]^2$ which is intersected by $n$ random lines. The way we can choose these $n$ random lines is by choosing two points on the border of the square and connecting them. If we do this, what is the probability that a region formed by…
user402817
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Why does this numerical overflow error result in vectors with smaller sums?

This is, I think, a math puzzle, but it will take a bit to explain. I wanted to create a subset of loosely defined "similar" digits from the MNIST dataset. MNIST is a dataset of grayscale, handwritten digits, 0-9. They are represented as ($32 \times…
jds
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Are there values $k$ and $\ell$ such that $n$ = $kd$ + $\ell$? Prove.

Suppose that n $\in$ $\mathbb Z$ and d is an odd natural number, where $0 \notin\mathbb N$. Prove that $\exists$ $\mathcal k$ and $\ell$ such that $n =\mathcal kd +\ell$ and $\frac {-d}2 < \ell$ < $\frac d2$. I know that this is related to…
Christina
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