This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)
Math & Counting Operations on Lists
Ordinary mathematical functions in Mathematica are always "listable", so that they are immediately applied in parallel across lists. Mathematica provides a wide variety of tightly integrated functions for analyzing elements in lists of any size and structure.
{..}+{..}, etc. — automatically operate in parallel on list elements
Listable attribute carried by math functions specifying automatic threading over lists
Length number of elements in a list
Total total from adding up elements in a list
Accumulate  ▪ Differences  ▪ Ratios  ▪ Fold
Count count how many elements match a pattern
Tally tally the number of copies of each distinct element
Max  ▪ Min  ▪ Commonest  ▪ Sort  ▪ SortBy  ▪ Ordering
BinCounts count the number of elements in a sequence of bins
Mean  ▪ Variance  ▪ Median  ▪ Interpolation  ▪ Nearest  ▪ ...
Dot  ▪ Norm  ▪ Normalize  ▪ Projection  ▪ ...
Set-Oriented Operations
Union  ▪ Intersection  ▪ Complement  ▪ Subsets