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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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Inequality involving sum of binomials

Given $x \in \left[0\,;\,1\right]$, is there a closed form solution (or a very good approximation?) for the tightest (i.e. minimal) offset $l$ such that : $$ \sum_{k\in\left[m - l\,;\,m+l\right]} {n \choose k}\,p^k\,(1-p)^{n-k} > x $$ where $$m =…
Julien__
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6-digit passcode that contain exactly one multiple of 3 if digits can be repeated.

Each element being any digits from 0 to 9. How many possible passcodes are there? Tried doing $3 * 6 * 9 * 3 * 6 * 9$ but that's not exactly ONE multiple of 3.
James Madison
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An interesting maths trick with maths background.

Here is a maths trick: Bob, a magician ask his partner, Peter to leave the room. Then the audience tells Bob two numbers: $n$, which indicates a sign (and let’s consider that the possible signs are the positive integers from 1 to $k$), and $x$, a…
Pet123
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For the set X = { 2,3,6,12,24,36}, a relation ≤ is defined as x ≤ y if x divides y. Draw the Hasse diagram for (X,≤)

For the set X = { 2,3,6,12,24,36}, a relation ≤ is defined as x ≤ y if x divides y. Draw the Hasse diagram for (X,≤) . Answer the following: (i) What are the maximal and minimal elements? (ii) Give one example of chain & antichain. (iii) Is the…
Bhakti
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Math not based on the 1 value

Hello is there any kind of math that is not based on the concept of 1 but only on continuous expressions? Maybe is this what vector are? If this question is stupid, answer me and I'll erase it. Thanks!
Nicolas Manzini
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how many positive dividers that aren't multiple of 2 are there in the number 52920?

i need to know how many positive dividers that aren't multiple of 2 are there in the number 52920. How do i eliminate multiples of 2?
Pedro Quintans
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reversible integer transform

Let be x, y two natural integers. Define the following transform: X=x+(x-y). Y=y-(x-y). If the difference d=x-y tends to 0, we have X=x and Y=y. The above transform has the property that is reversible in integer domain. I have $ (x,y) \in…
Ion Caciula
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Drawing Hasse Diagrams and determining whether or not they are total order relations

• T is defined on the set {a, b, c, d, e}, • aTc, bTc, cTd, eTb and e not T a, • T is a partial order relation. Draw a Hasse diagram for every possible relation that T could be and, for each, write down whether it is a total order relation. The…
Handsome Woman
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what is the general formula to convert a base 10 number to a base 2 number?

I have this question where I need to convert to base 2. what is the general formula that takes a natural number and converts it into its base 2 number?
mikio
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Problem Involving Operations

There are 2 operations: Z and Y. If Z is included as an operation, it adds one. This means 7+Z+Z+Z would essentially, be 7+1+1+1 and would, therefore, equal 10. If Y is included as an operation, it would turn a number into its negative reciprocal.…
Brooklyn
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Please explain: For any integer $n \ge 4$, let $B_n$ be the number of ccc-free bitstrings of length $n$. Which of the following is true?

Consider strings of characters, where each character is an element of the set $\{a, b, c\}$. Such a string is called ccc-free, if it does not contain ccc. For any integer $n \ge 4$, let $B_n$ be the number of ccc-free bitstrings of length $n$. Which…
JVAN
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Symmetrical, Transitional and Antisymmetrical question!

If $R \subseteq A \times A$ is it true that $R$ is symmetrical since $xRy$ then $yRx$ ? I have written that this is also antisymmetrical if both $x\leq y$ and $y\leq x$ if $x =y$ How does I then make $R \subseteq A \times A$ transitive?
user8322
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Please explain: How many such strings have the following properties

We consider strings consisting of 12 characters, where each character is an element of the set {a, b, c, d, e}. The positions in such strings are numbered as 1,2,3,...,12. How many such strings have the property that each even position contains an…
JVAN
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How would I find the asymptotic value for this function in big theta notation?

$ \frac{5}{n} + log_3 n + 11√n $ Can someone please explain to me what steps I would do for this? I really don't understand what I should do to find the asymptotic value.
aqw143
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Some Discrete Mathematics questions

I have 4 questions, 3 of which I typed up my proposed solutions for. I need help with the 4th problem still. $1.)$ A sequence is defind by letting $b_0=5$ and $b_k=4+b_{k-1}$ for all integers $k \geq 1$. Show that $b_n \gt 4n$ for all integers $n…
Math is hard
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