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2. Transcendental number theory - Wikipedia

   en.wikipedia.org/wiki/Transcendental_number_theory

   Noncommutative algebra. v. t. e. Transcendental number theory is a branch of number theory that investigates transcendental numbers (numbers that are not solutions of any polynomial equation with rational coefficients), in both qualitative and quantitative ways.

3. Transcendental number - Wikipedia

   en.wikipedia.org/wiki/Transcendental_number

   In mathematics, a transcendental number is a real or complex number that is not algebraic: that is, not the root of a non-zero polynomial with integer (or, equivalently, rational) coefficients. The best-known transcendental numbers are π and e. [1][2] The quality of a number being transcendental is called transcendence.

4. Möbius function - Wikipedia

   en.wikipedia.org/wiki/Möbius_function

   The Möbius function is a multiplicative function in number theory introduced by the German mathematician August Ferdinand Möbius (also transliterated Moebius) in 1832. [i][ii][2] It is ubiquitous in elementary and analytic number theory and most often appears as part of its namesake the Möbius inversion formula.

5. Diophantine approximation - Wikipedia

   en.wikipedia.org/wiki/Diophantine_approximation

   Diophantine approximation. In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria. The first problem was to know how well a real number can be approximated by rational numbers. For this problem, a rational number p / q is a "good ...

6. Number theory - Wikipedia

   en.wikipedia.org/wiki/Number_theory

   Mathematics. 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]

7. Algebraic number theory - Wikipedia

   en.wikipedia.org/wiki/Algebraic_number_theory

   Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers , finite fields , and function fields .

8. Dirichlet's approximation theorem - Wikipedia

   en.wikipedia.org/wiki/Dirichlet's_approximation...

   In his Essai sur la théorie des nombres (1798), Adrien-Marie Legendre derives a necessary and sufficient condition for a rational number to be a convergent of the simple continued fraction of a given real number. [4] A consequence of this criterion, often called Legendre's theorem within the study of continued fractions, is as follows: [5 ...

9. Glossary of mathematical symbols - Wikipedia

   en.wikipedia.org/wiki/Glossary_of_mathematical...

   Glossary of mathematical symbols. A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various ...