Search for "Number theory" in article titles:

1. Number theory: The science of integers (cf. also Integer). (Mathematics) [100%] 2023-10-17
2. Number theory: Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Any attempt to conduct such a study naturally leads to an examination of the properties of prime numbers (the building blocks of integers) as ... [100%] 2023-06-11 [Number theory]
3. Number theory: Number theory is a branch of mathematics involving the study of the properties and relationships of numbers. Number theory typically deals only with integers (as opposed to all real numbers). [100%] 2023-06-30 [Number Theory]
4. Number theory: 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 ... (Mathematics of integer properties) [100%] 2024-08-30 [Number theory]
5. Number Theory: "Mathematics is the queen of the sciences and number theory is the queen of mathematics." —Gauss This topic is about Number Theory, or in simple language study of properties of integers. Number theory is the branch of pure mathematics concerned ... [100%] 2023-12-13 [Secondary Math Courses]
6. Number Theory Foundation: The Number Theory Foundation (NTF) is a non-profit organization based in the United States which supports research and conferences in the field of number theory, with a particular focus on computational aspects and explicit methods. The NTF funds the ... (Organization) [81%] 2023-12-14 [Number theory]
7. Probabilistic number theory: In mathematics, Probabilistic number theory is a subfield of number theory, which explicitly uses probability to answer questions about the integers and integer-valued functions. One basic idea underlying it is that different prime numbers are, in some serious sense ... [81%] 2023-11-06 [Number theory]
8. Infrastructure (number theory): In mathematics, an infrastructure is a group-like structure appearing in global fields. In 1972, D. (Number theory) [81%] 2023-10-28 [Algebra] [Algebraic structures]...
9. Number Theory Library: NTL is a C++ library for doing number theory. NTL supports arbitrary length integer and arbitrary precision floating point arithmetic, finite fields, vectors, matrices, polynomials, lattice basis reduction and basic linear algebra. [81%] 2023-12-13 [C++ libraries] [Free mathematics software]...
10. Analytic number theory: In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dirichlet ... (Exploring properties of the integers with complex analysis) [81%] 2023-10-01 [Analytic number theory]
11. Number Theory Foundation: The Number Theory Foundation (NTF) is a non-profit organisation based in the United States of America which supports research and conferences in the field of number theory. The NTF funds the Selfridge prize which is awarded at the ANTS ... [81%] 2023-09-30
12. Number Theory Library: NTL is a C++ library for doing number theory. NTL supports arbitrary length integer and arbitrary precision floating point arithmetic, finite fields, vectors, matrices, polynomials, lattice basis reduction and basic linear algebra. (Software) [81%] 2023-12-01 [C++ libraries] [Free mathematics software]...
13. Analytic number theory: A branch of number theory. Analytic number theory deals with the problems of distribution of primes, studies the behaviour of number-theoretic functions, and the theory of algebraic and transcendental numbers. (Mathematics) [81%] 2023-10-18 [Number theory]
14. Additive number theory: Additive number theory is the subfield of number theory concerning the study of subsets of integers and their behavior under addition. More abstractly, the field of additive number theory includes the study of abelian groups and commutative semigroups with an ... (Study of subsets of integers and behavior under addition) [81%] 2023-12-13 [Additive number theory]
15. Multiplicative number theory: Multiplicative number theory is a subfield of analytic number theory that deals with prime numbers and with factorization and divisors. The focus is usually on developing approximate formulas for counting these objects in various contexts. [81%] 2023-10-02 [Analytic number theory]
16. 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 ... (Study of algorithms for performing number theoretic computations) [81%] 2023-10-03 [Computational number theory] [Number theory]...
17. Basic Number Theory: Basic Number Theory is an influential book by André Weil, an exposition of algebraic number theory and class field theory with particular emphasis on valuation-theoretic methods. Based in part on a course taught at Princeton University in 1961-2, it ... (Book about number theory) [81%] 2023-12-18 [Mathematics books] [Algebraic number theory]...
18. Typographical Number Theory: Typographical Number Theory (TNT) is a formal axiomatic system describing the natural numbers that appears in Douglas Hofstadter's book Gödel, Escher, Bach. It is an implementation of Peano arithmetic that Hofstadter uses to help explain Gödel's incompleteness theorems. (Axiomatic system) [81%] 2023-09-30 [Formal theories of arithmetic]
19. Basic Number Theory: Basic Number Theory is an influential book by André Weil, an exposition of algebraic number theory and class field theory with particular emphasis on valuation-theoretic methods. Based in part on a course taught at Princeton University in 1961-2, it ... (Book about number theory) [81%] 2023-12-13 [Mathematics books] [Algebraic number theory]...
20. Elementary number theory: The branch of number theory that investigates properties of the integers by elementary methods. These methods include the use of divisibility properties, various forms of the axiom of induction and combinatorial arguments. (Mathematics) [81%] 2023-10-17 [Number theory]
21. Partition (number theory): In number theory and combinatorics, a partition of a positive integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands ... (Number theory) [81%] 2023-12-26 [Number theory] [Combinatorics]...
22. Algebraic number theory: The branch of number theory with the basic aim of studying properties of algebraic integers in algebraic number fields $ K $ of finite degree over the field $ \mathbf Q $ of rational numbers (cf. Algebraic number). (Mathematics) [81%] 2023-12-13
23. Additive number theory: The branch of number theory dealing with problems involving the partitioning (or decomposition) of integers into summands of a given type, and also with the algebraic and geometric analogues of such problems concerning algebraic number fields and sets of lattice ... (Mathematics) [81%] 2023-12-13
24. Transcendental number theory: 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. The fundamental theorem of algebra tells us that if ... (Study of numbers that are not solutions of polynomials with rational coefficients) [81%] 2023-10-29 [Analytic number theory]
25. Transcendental number theory: 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. The fundamental theorem of algebra tells us that if ... (Study of numbers that are not solutions of polynomials with rational coefficients) [81%] 2024-04-10 [Analytic number theory]
26. 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 ... (Branch of number theory) [81%] 2024-07-18 [Algebraic number theory] [Number theory]...
27. Abstract prime number theory: In various branches of number theory, abstract algebra, combinatorics, and elsewhere in mathematics, it is sometimes possible and convenient to formulate a variety of enumeration or counting questions in a unified way in terms of the concept of an arithmetical ... (Mathematics) [70%] 2023-11-14
28. Crossing number (knot theory): In the mathematical area of knot theory, the crossing number of a knot is the smallest number of crossings of any diagram of the knot. It is a knot invariant. (Knot theory) [70%] 2024-01-09 [Knot invariants]
29. Abstract analytic number theory: The central concept in abstract analytic number theory is that of an arithmetical semi-group $G$ (defined below). It turns out that the study of such semi-groups and of (real- or complex-valued) functions on them makes it possible ... (Mathematics) [70%] 2023-08-18
30. Algorithmic Number Theory Symposium: Algorithmic Number Theory Symposium (ANTS) is a biennial academic conference, first held in Cornell in 1994, constituting an international forum for the presentation of new research in computational number theory. They are devoted to algorithmic aspects of number theory, including ... (Biennial conference series on computational number theory) [70%] 2024-01-10 [Computational number theory]