What can I do with category theory?
The main benefit to using category theory is as a way to organize and synthesize information. This is particularly true of the concept of a universal property. We will hear more about this in due time, but as it turns out most important mathematical structures can be phrased in terms of universal properties.
Who created category theory?
Samuel Eilenberg
The classic is Categories for the Working Mathematician by Saunders Mac Lane who, along with Samuel Eilenberg, developed category theory in the 1940s.
What is the history of algorithms in mathematics?
Arithmetic algorithms, such as a division algorithm, was used by ancient Babylonian mathematicians c. 2500 BC and Egyptian mathematicians c. 1550 BC. Greek mathematicians later used algorithms in the sieve of Eratosthenes for finding prime numbers, and the Euclidean algorithm for finding the greatest common divisor of two numbers.
What is a prototypical example of an algorithm?
A prototypical example of an algorithm is the Euclidean algorithm to determine the maximum common divisor of two integers; an example (there are others) is described by the flowchart above and as an example in a later section.
What is the informal definition of an algorithm?
Informal definition. An informal definition could be “a set of rules that precisely defines a sequence of operations.” which would include all computer programs, including programs that do not perform numeric calculations. Generally, a program is only an algorithm if it stops eventually.
What are the steps involved in the development of algorithms?
Typical steps in the development of algorithms: 1 Problem definition 2 Development of a model 3 Specification of the algorithm 4 Designing an algorithm 5 Checking the correctness of the algorithm 6 Analysis of algorithm 7 Implementation of algorithm 8 Program testing 9 Documentation preparation