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4 de abr. de 2024 · number theory, branch of mathematics concerned with properties of the positive integers (1, 2, 3, …). Sometimes called “higher arithmetic,” it is among the oldest and most natural of mathematical pursuits. Number theory has always fascinated amateurs as well as professional mathematicians.
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." [1]
Number theory is the study of properties of the integers. Because of the fundamental nature of the integers in mathematics, and the fundamental nature of mathematics in science, the famous mathematician and physicist Gauss wrote:
So what is "arithmetic," or number theory? Simply stated, number theory is concerned with questions about and properties of the integers \[\dots, -4, -3, -2, -1, 0, 1, 2, 3, 4, \dots\nonumber \] and closely-related numbers.
Number theory, also known as 'higher arithmetic', is one of the oldest branches of mathematics and is used to study the properties of positive integers. It helps to study the relationship between different types of numbers such as prime numbers, rational numbers, and algebraic integers.
Hace 5 días · Number theory is a vast and fascinating field of mathematics, sometimes called "higher arithmetic," consisting of the study of the properties of whole numbers. Primes and prime factorization are especially important in number theory, as are a number of functions such as the divisor function, Riemann zeta function, and totient function.
Course Description. This is the first semester of a one-year graduate course in number theory covering standard topics in algebraic and analytic number theory. At various points in the course, we will make reference to material from other branches of mathematics, including topology, complex analysis, representation theory, and algebraic … Show more
