Mathematic Computer Science

Computer science is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. Computer science encompasses many branches; some emphasize the computation of specific results (such as computer graphics), while others (such as computational complexity theory) relate to properties of computational problems. Still others focus on the challenges in implementing computations. For example, programming language theory studies approaches to describing a computation, while computer programming applies specific programming languages to craft a solution to some concrete computational problems.


In mathematics and computing, an algorithm is a procedure (a finite set of well-defined instructions) for accomplishing some task which, given an initial state, will terminate in a defined end-state. The computational complexity and efficient implementation of the algorithm are important in computing, and this depends on suitable data structures.
Informally, the concept of an algorithm is often illustrated by the example of a recipe, although many algorithms are much more complex; algorithms often have steps that repeat (iterate) or require decisions (such as logic or comparison). In most higher level programs, algorithms act in complex patterns, each using smaller and smaller sub-methods which are built up to the program as a whole. In many programming languages, algorithms are implemented as functions or procedures.
The concept of an algorithm originated as a means of recording procedures for solving mathematical problems such as finding the common divisor of two numbers. The concept was formalized in 1936 through Alan Turing's Turing machines and Alonzo Church's lambda calculus, which in turn formed the foundation of computer science.
Most algorithms can be directly implemented by computer programs; any other algorithms can at least in theory be simulated by computer programs.

Alan Mathison Turing (June 23, 1912 – June 7, 1954) was a British mathematician, logician, and cryptographer. Turing is often considered to be the father of modern computer science.
With the Turing test, Turing made a significant and characteristically provocative contribution to debates regarding artificial intelligence: whether it will ever be possible to say that a machine is conscious and can think. He provided an influential formalisation of concepts of algorithm and computation with the Turing machine, formulating the now widely accepted "Turing" version of the Church–Turing thesis: that any practical computing model has either the equivalent or a subset of capabilities of a Turing machine. During World War II, Turing worked at Bletchley Park, Britain's codebreaking centre and was for a time head of Hut 8, the section responsible for German Naval cryptanalysis. He devised techniques for breaking German ciphers, including the method of the bombe, an electromechanical machine which found settings for the Enigma machine.
After the war, he worked at the National Physical Laboratory, creating an early design for a stored-program computer, but never actually built. In 1947 he moved to the University of Manchester, to work mainly on software for the Manchester Mark I, one of the earliest true computers.
In 1952, Turing was convicted of acts of gross indecency after he admitted a relationship with a man in Manchester. He was placed on probation and required to undergo hormone therapy. When Turing died in 1954, an inquest found that he had committed suicide by eating an apple laced with cyanide.