A report onMathematics and Computer science

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

- Mathematics

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

- Computer science

Logic

Study 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.

Algorithm

In mathematics and computer science, an algorithm is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation.

Computability theory

Computability 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.

Mathematical logic

Mathematical logic is the study of formal logic within mathematics.

Computer 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.

Cryptography

Practice and study of techniques for secure communication in the presence of adversarial behavior.

Practice and study of techniques for secure communication in the presence of adversarial behavior.

Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, electrical engineering, communication science, and physics.

Deductive reasoning

Mental process of drawing deductive inferences.

Mental process of drawing deductive inferences.

The semantic approach is also referred to as the model-theoretic approach since the branch of mathematics known as model theory is often used to interpret these sentences.

But the subject of deductive reasoning is also pertinent to the computer sciences, for example, in the creation of artificial intelligence.

Epistemology

Branch of philosophy concerned with knowledge.

Branch of philosophy concerned with knowledge.

Certain forms exempt disciplines such as mathematics and logic from these requirements.

Work in this area spans several academic fields, including philosophy, computer science, economics, and statistics.