Examples for

Discrete Mathematics

Discrete mathematics deals with areas of mathematics that are discrete, as opposed to continuous, in nature. Sequences and series, counting problems, graph theory and set theory are some of the many branches of mathematics in this category. Use Wolfram|Alpha to apply and understand these and related concepts.

Combinatorics

Use the ideas of permutation and combination to find binomial coefficients or integer partitions or to do other forms of counting.

Compute binomial coefficients (combinations):

30 choose 18

Compute a Frobenius number:

Frobenius number {4, 7, 12}

Find the partitions of an integer:

integer partitions of 10
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Point Lattices

Compute the properties of these discrete subsets of Euclidean space. Deal with regular or rooted lattices. Compare them.

Compute the properties of a lattice:

face-centered cubic

Compute the properties of a root lattice:

A4 root lattice

Compare several lattices:

simple cubic, simple hexagonal
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Ackermann Function

Work with the famous function known for being a total computable function that is not primitive recursive.

Evaluate the Ackermann function:

ackermann[2,3]
what is ackermann 4,1?
ack(2,ack(2,1))
Graph Theory

Work with known graphs or specify your own via adjacency lists. Check for isomorphism, compute the shortest path and more.

Compute the properties of a named graph:

Pappus graph

Compare several graphs:

Petersen graph, icosahedral graph

Analyze a graph specified by adjacency rules:

1->2, 2->3, 3->1, 3->4, 4->1
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Sequences

Deduce patterns in incompletely specified sequences or series. Sum infinite series or perform other operations on them.

Compute a possible formula and continuation for a sequence:

1, 4, 9, 16, 25, ...

Sum an incompletely specified infinite series:

1/2 + 1/4 + 1/8 + 1/16 + ...
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Step-by-Step Solutions for Discrete Mathematics

RELATED EXAMPLES

  • Applied Mathematics
  • Logic & Set Theory
  • Number Theory
    • Recurrences

    Solve recurrences, specify initial values or attempt to model sequences with recurrences.

    Solve a recurrence:

    g(n+1)=n^2+g(n)

    Specify initial values:

    f(n)=f(n-1)+f(n-2), f(1)=1, f(2)=2

    Find a recurrence satisfied by a given sequence:

    fibonacci(n) recurrence
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