In computing, a Monte Carlo algorithm is a randomized algorithm whose running time is deterministic, but whose output may be incorrect with a certain (typically small) probability. The related class of Las Vegas algorithms is also randomized, but in a different way: they take an amount of time that varies randomly, but always produce the correct answer.
more from Wikipedia
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: 1000 = 10 = 10 × 10 × 10. More generally, if x = b, then y is the logarithm of x to base b, and is written logb(x), so log10(1000) = 3. Logarithms were introduced by John Napier in the early 17th century as a means to simplify calculations.
more from Wikipedia
Analysis of algorithms
In computer science, the analysis of algorithms is the determination of the amount of resources (such as time and storage) necessary to execute them. Most algorithms are designed to work with inputs of arbitrary length. Usually the efficiency or running time of an algorithm is stated as a function relating the input length to the number of steps or storage locations (space complexity).
more from Wikipedia
Big O notation
In mathematics, big O notation is used to describe the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions. It is a member of a larger family of notations that is called Landau notation, Bachmann–Landau notation, or asymptotic notation. In computer science, big O notation is used to classify algorithms by how they respond (e.g. , in their processing time or working space requirements) to changes in input size.
more from Wikipedia
Upper and lower bounds
In mathematics, especially in order theory, an upper bound of a subset S of some partially ordered set (P, ≤) is an element of P which is greater than or equal to every element of S. The term lower bound is defined dually as an element of P which is less than or equal to every element of S. A set with an upper bound is said to be bounded from above by that bound, a set with a lower bound is said to be bounded from below by that bound.
more from Wikipedia
Domain of a function
In mathematics, the domain of definition or simply the domain of a function is the set of "input" or argument values for which the function is defined. That is, the function provides an "output" or value for each member of the domain. For instance, the domain of cosine is the set of all real numbers, while the domain of the square root consists only of numbers greater than or equal to 0 (ignoring complex numbers in both cases).
more from Wikipedia
Asymptotically optimal algorithm
In computer science, an algorithm is said to be asymptotically optimal if, roughly speaking, for large inputs it performs at worst a constant factor (independent of the input size) worse than the best possible algorithm. It is a term commonly encountered in computer science research as a result of widespread use of big-O notation.
more from Wikipedia
Function (mathematics)
In mathematics, a function is a relation between a set of inputs and a set of potential outputs with the property that each input is related to exactly one output. An example of such a relation is defined by the rule f(x) = x, which relates an input x to its square, which are both real numbers. The output of the function f corresponding to an input x is denoted by f(x) (read "f of x"). If the input is –3, then the output is 9, and we may write f(–3) = 9.
more from Wikipedia