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Group theory has three main historical sources: number theory, the theory of algebraic equations, and geometry. The number-theoretic strand was begun by Leonhard Euler, and developed by Gauss's work on modular arithmetic and additive and multiplicative groups related to quadratic fields.
Transcendence theory is concerned with the converse question: given a complex number , is there a polynomial with rational coefficients such that If no such polynomial exists then the number is called transcendental. More generally the theory deals with algebraic independence of numbers. A set of numbers is called algebraically independent over ...
The Cole Prize in algebra was funded by Cole himself, from funds given to him as a retirement gift; the prize fund was later augmented by his son, leading to the double award. [1] [2] The prizes recognize a notable research work in algebra (given every three years) or number theory (given every three years) that has appeared in the last six years.
Computational number theory. In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithms for primality testing and integer factorization, finding solutions to ...
Classical Greek and Indian mathematicians made studies of the theory of rational numbers, as part of the general study of number theory. The best known of these is Euclid's Elements, dating to roughly 300 BC. Of the Indian texts, the most relevant is the Sthananga Sutra, which also covers number theory as part of a general study of mathematics.
v. t. e. Game theory is the study of mathematical models of strategic interactions among rational agents. [1] It has applications in many fields of social science, used extensively in economics as well as in logic, systems science and computer science. [2] Initially game theory addressed two-person zero-sum games, in which a participant's gains ...
In number theory, Lagrange's theorem is a statement named after Joseph-Louis Lagrange about how frequently a polynomial over the integers may evaluate to a multiple of a fixed prime. More precisely, it states that if p is a prime number, , and is a polynomial with integer coefficients, then either: where deg f(x) is the degree of f(x).
