# A report on Mathematics, Mathematical logic and Computer science

Mathematical logic is the study of formal logic within mathematics.

- Mathematical logicMathematics is essential in many fields, including natural sciences, engineering, medicine, finance, computer science and social sciences.

- MathematicsOther first-level areas emerged during the 20th century (for example category theory; homological algebra, and computer science) or had not previously been considered as mathematics, such as Mathematical logic and foundations (including model theory, computability theory, set theory, proof theory, and algebraic logic).

- MathematicsComputer science research also often intersects other disciplines, such as cognitive science, linguistics, mathematics, physics, biology, Earth science, statistics, philosophy, and logic.

- Computer scienceEarly computer science was strongly influenced by the work of mathematicians such as Kurt Gödel, Alan Turing, John von Neumann, Rózsa Péter and Alonzo Church and there continues to be a useful interchange of ideas between the two fields in areas such as mathematical logic, category theory, domain theory, and algebra.

- Computer scienceComputer scientists often focus on concrete programming languages and feasible computability, while researchers in mathematical logic often focus on computability as a theoretical concept and on noncomputability.

- Mathematical logic2 related topics with Alpha

## Computability theory

0 linksComputability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees.

Many problems in mathematics have been shown to be undecidable after these initial examples were established.

## Logic

0 linksStudy of correct reasoning or good arguments.

Study of correct reasoning or good arguments.

Logic is studied in and applied to various fields, such as philosophy, mathematics, computer science, and linguistics.

It provides the foundation of modern mathematical logic.