Mathematics Stack Exchange
Mathematics Stack Exchange

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.

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How many numbers in the range from $0$ to $10^9 − 1$ contain the digit $3$?

How many numbers in the range from $0$ to $10^9 − 1$ contain the digit $3$? So pretty much how many numbers from the between $0$ and $999,999,999$ contain the digit "$3$" ? Please give an arithmetic expression if possible. Help would be much…
kiasy
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How many solutions are there?

The problem from some math competition (multiple-choice test): Consider an equation $\lfloor\sqrt{12}x\rfloor=\lfloor\frac{7}{2}x\rfloor$, where $\lfloor x\rfloor$ denotes integer part of $x$ (entier). This equation: A. has exactly 1 real…
Paweł Orliński
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Decimal representation of the binary number $10001011$

So $10001011$ is an 8-bit two’s complement. Now what is the Decimal representation of the number $x$ represented by $10001011$? My steps: $10001011 -1$ and I get $01110110$ Flip the digits and you get $10001001$ Now I'm supposed to convert $1000$…
kiasy
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Eight-bit two’s complement question

Consider an 8-bit two’s complement register R. What are the least and greatest decimal integers that can be stored in R? Help would be much appreciated.
kiasy
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coin toss probabilities

Flip 100 coins define a random variable that counts the number of heads probability of getting exactly 5 heads probability of getting at least 1 head find the expected number of heads using the random variable defined above So far I know there…
SSS
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How many ways are there to choose a unordered box of 12 balls from 21 different balls?

How many ways are there to choose a unordered box of 12 balls from 21 different balls? I can only think 21 choose 12, but I don't think its right though.
SSS
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Counting problem about housing

suppose there are 3 rooms in a dormitory: one single, one double, and one for four students. How many ways are there to house 7 students in these rooms? The answer is 7$\times$(5+4+3+2+1), but I don't understand why, can anyone explain this to me?
SSS
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Find m and n in the given equation:

Sorry new to this forum and don't know how to format: If $m,n\in\Bbb N$ satisfy $6^{2m+2}\cdot 3^n=4^n\cdot 9^{m+3}$, then $n$ and $m$ must be ... what? This is for my discrete mathematics class. I tried taking ln/log of both sides but got…
user1010282
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finding function such that $f(2x) = f(x) + 1$

Q1. How to find a function $f(x)$ satisfying the recurrence relation $$f(2x) = f(x) + 1$$ Q2. Also how to prove that the closed form for the recurrence relation $$f(n) = f \left( \left \lfloor \frac n 2 \right \rfloor \right ) + 1$$ with…
Mula Ko Saag
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Big theta notation question

can someone please explain to me the big theta notation and big omega and also How i can show that $$ 3x+7\quad \text{is}\quad \Theta (x); $$ I don't really get how growth of functions works.
Out Of Bounds
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In the following list of equivalence classes, find two classes which are equal

Consider the equivalence relation n $\Bbb R$ - {$0$}: $a$~$b$ if and only if $\dfrac {a}{b} \in \Bbb Q $ In the following list of equivalence classes, find two classes which are equal: [$\sqrt 3$] , [$1$], [$\sqrt {12}$], [$\sqrt 6$] I have no idea…
user109886
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binary trees and rules for their creation

I am learning about binary trees. I was given following rules for their creation: A single leaf node is a binary tree. If t1 and t2 are binary trees, then the result of joining them under a single node is a binary tree. I suspect that the tree in…
Adam
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Prove that if $7$ divides $6^n + 1$ then $n$ is odd

Prove that if $7$ divides $6^n + 1$ then $n$ is odd Attempt: We'll prove the contrapositive: $n$ is not odd if $7$ does not divide $6^n + 1$
user114795
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If $n$ is a natural number, then what are the possible values(s) of gcd $(n+1, 2-n)$?

If $n$ is a natural number, then what are the possible values(s) of gcd $(n+1, 2-n)$? There are six options: $1,2,3,4,5,6$ I think the answer is $1$
user114795
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Stars and Bars - Marbles

Suppose you have 4 different types of marbles to choose from. How man unique bags can you create with 10 marbles per bag such that each bag has at least one of each type of marbles. My approach: 'Stars and Bars' method: **********||| Therefore,…
Sc4r
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