Number theory | Definition, Topics, & History | Britannica
6 天之前 · Number theory, branch of mathematics concerned with properties of the positive integers (1, 2, 3, …). Modern number theory is a broad subject that is classified into subheadings such as elementary number theory, algebraic number theory, analytic number theory, and geometric number theory.
Metaphysics and number theory - Encyclopedia Britannica
Pythagoreanism - Metaphysics, Number Theory, Philosophy: According to Aristotle, number speculation is the most characteristic feature of Pythagoreanism. Things “are” number, or “resemble” number.
Riemann hypothesis | Prime Numbers, Zeta Function & Complex …
2024年12月5日 · Riemann hypothesis, in number theory, hypothesis by German mathematician Bernhard Riemann concerning the location of solutions to the Riemann zeta function, which is connected to the prime number theorem and has important implications for the distribution of prime numbers.
Modular arithmetic | Number Theory, Congruence & Algorithms
2024年11月22日 · Modular arithmetic, in its most elementary form, arithmetic done with a count that resets itself to zero every time a certain whole number N greater than one, known as the modulus (mod), has been reached.
Modern algebra | Algebraic Structures, Rings & Group Theory
The basic rules, or axioms, for addition and multiplication are shown in the table, and a set that satisfies all 10 of these rules is called a field. A set satisfying only axioms 1–7 is called a ring , and if it also satisfies axiom 9 it is called a ring with unity.
Game theory | Definition, Facts, & Examples | Britannica
2024年10月24日 · A number of theories have been proposed, each applicable to different situations and each with its own concepts of what constitutes a solution. This article describes some simple games, discusses different theories, and outlines principles underlying game theory.
Number theory - Prime, Distribution, Theorem | Britannica
6 天之前 · Along with classical and analytic number theory, scholars now explored specialized subfields such as algebraic number theory, geometric number theory, and combinatorial number theory. The concepts became more abstract and the techniques more sophisticated.
Thermodynamics | Laws, Definition, & Equations | Britannica
2024年10月21日 · Thermodynamics, science of the relationship between heat, work, temperature, and energy. Thermodynamics deals with the transfer of energy from one place to another and from one form to another. The key concept is that heat is a form of energy corresponding to a definite amount of mechanical work.
Binomial theorem | Formula & Definition | Britannica
2024年11月23日 · Isaac Newton discovered about 1665 and later stated, in 1676, without proof, the general form of the theorem (for any real number n), and a proof by John Colson was published in 1736.
Addition, Subtraction, Multiplication & Division - Britannica
If a number system is restricted to the natural numbers, differences need not always exist, but, if they do, the five basic laws of arithmetic, as already discussed, can be used to prove that they are unique.