Differences between Array and Algorithm

Differences between Array and Algorithm

·         ALGORITHM

 In mathematics and computer science, an algorithm is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, and automated reasoning.

 

An algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing "output" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.

 

Though al-Kārizmī's algorism referred to the rules of performing arithmetic using Hindu–Arabic numerals and the systematic solution of linear and quadratic equations, a partial formalization of what would become the modern algorithm began with attempts to solve the Entscheidungs problem (the "decision problem") posed by David Hilbert in 1928. Subsequent formalizations were framed as attempts to define "effective calculability" or "effective method"; those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, Emil Post's "Formulation 1" of 1936, and Alan Turing's Turing machines of 1936–7 and 1939. Giving a formal definition of algorithms, corresponding to the intuitive notion, remains a challenging problem.

·        ARRAY

In math, an array refers to a set of numbers or objects that will follow a specific pattern. An array is an orderly arrangement, often in rows, columns or a matrix. Arrays are used in multiplication and division as it shows a great visual to show how multiplication can be shown as repeated addition and division can be shown as fair shares.

 

There are many authentic examples of arrays that help with the understanding of how using arrays can help students to see efficient strategies. Consider a box of chocolates or a crate of oranges that have an arrangement of 12 across and 8 down (8 across, 5 down, 12 across 12 down etc.). Rather than count each one, they multiply 12 x 8 which aids understanding about why it's an efficient strategy to use multiplication and see why multiplication works.

 

Pronunciation: A Ray

 

Arrays are most helpful when teaching young learners to multiply. We often refer to multiplication as fast adding. When a child sees arrays of chocolates, eggs, fruit etc. it provides an authentic experience for making the link to multiplication.