This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)
Discrete Mathematics
Mathematica has been used to make many important discoveries in discrete mathematics over the past two decades. Its integration of highly efficient and often original algorithms together with its high-level symbolic language has made it a unique environment for the exploration, development, and application of discrete mathematics.
List and Set Operations
Tuples  ▪ Subsets  ▪ Union  ▪ Intersection  ▪ Complement
Permutations  ▪ Sort  ▪ Ordering  ▪ Signature  ▪ RandomSample  ▪ ...
Factorial  ▪ Binomial  ▪ Fibonacci  ▪ StirlingS1  ▪ PartitionsP  ▪ IntegerPartitions  ▪ FiniteGroupCount  ▪ ...
RSolve solve recurrence equations
FindSequenceFunction find functions for integer sequences
Strings and Digits
ReplaceList generate a list of forms matching a pattern
Graphs and Trees
GraphPlot, GraphPlot3D, LayeredGraphPlot lay out and draw graphs
TreePlot display trees
GraphData database of named and enumerated graphs and their properties
Combinatorial Optimization
FindMinimum, Minimize solve integer programming problems
FindShortestTour solve traveling salesman problems
And  ▪ Or  ▪ SatisfiableQ  ▪ BooleanFunction  ▪ BooleanMinimize  ▪ ...