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The statement that this is the only quadratic pairing function is known as the Fueter–Pólya theorem. [9] Whether this is the only polynomial pairing function is still an open question. When we apply the pairing function to k 1 and k 2 we often denote the resulting number as k 1, k 2 . [citation needed]
Logo of the International Mathematical Olympiad. The first of the International Mathematical Olympiads (IMOs) was held in Romania in 1959. The oldest of the International Science Olympiads, the IMO has since been held annually, except in 1980.
Society of Applied Mathematics and Mechanics, Germany; Slovak Mathematical Society; Society of Mathematicians, Physicists and Astronomers of Slovenia; Spanish Society of Statistics and Operations Research [8] St. Petersburg Mathematical Society, Russia; Swedish Mathematical Society; Swiss Mathematical Society; Trinity Mathematical Society ...
In arithmetic geometry, the Tate–Shafarevich group Ш(A/K) of an abelian variety A (or more generally a group scheme) defined over a number field K consists of the elements of the Weil–Châtelet group (/) = (,), where = (/) is the absolute Galois group of K, that become trivial in all of the completions of K (i.e., the real and complex completions as well as the p-adic fields obtained from ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Among other statements, Poitou–Tate duality establishes a perfect pairing between certain Shafarevich groups.Given a global field , a set S of primes, and the maximal extension which is unramified outside S, the Shafarevich groups capture, broadly speaking, those elements in the cohomology of (/) which vanish in the Galois cohomology of the local fields pertaining to the primes in S.
The Geometry of Schemes. Graduate Texts in Mathematics. Vol. 197. Springer-Verlag. ISBN 0-387-98637-5. Zbl 0960.14002. Lang, Serge (1988). Introduction to Arakelov theory. New York: Springer-Verlag. ISBN 0-387-96793-1. MR 0969124. Zbl 0667.14001. Silverman, Joseph H. (1994). Advanced Topics in the Arithmetic of Elliptic Curves. Graduate Texts ...
Additional Mathematics in Malaysia—also commonly known as Add Maths—can be organized into two learning packages: the Core Package, which includes geometry, algebra, calculus, trigonometry and statistics, and the Elective Package, which includes science and technology application and social science application. [7]