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The theorem involves sets of strings, all having the same length , over a finite alphabet, together with a group acting on the alphabet. A combinatorial cube is a subset of strings determined by constraining some positions of the string to contain a fixed letter of the alphabet, and by constraining other pairs of positions to be equal to each other or to be related to each other by the group ...
Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and ...
Hasse–Arf theorem (local class field theory) Hasse–Minkowski theorem (number theory) Heckscher–Ohlin theorem ; Heine–Borel theorem (real analysis) Heine–Cantor theorem (metric geometry) Hellinger–Toeplitz theorem (functional analysis) Hellmann–Feynman theorem ; Helly–Bray theorem (probability theory)
Chapter 1. On the divisibility of numbers Chapter 2. On the congruence of numbers Chapter 3. On quadratic residues Chapter 4. On quadratic forms Chapter 5. Determination of the class number of binary quadratic forms Supplement I. Some theorems from Gauss's theory of circle division Supplement II. On the limiting value of an infinite series ...
A typical sequence of secondary-school (grades 6 to 12) courses in mathematics reads: Pre-Algebra (7th or 8th grade), Algebra I, Geometry, Algebra II, Pre-calculus, and Calculus or Statistics. However, some students enroll in integrated programs [3] while many complete high school without passing Calculus or Statistics.
German mathematician Carl Friedrich Gauss said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theory also studies the natural, or whole, numbers. One of the central concepts in number theory is that of the prime number , and there are many questions about primes that appear simple but whose ...
In mathematics, the curve complex is a simplicial complex C(S) associated to a finite-type surface S, which encodes the combinatorics of simple closed curves on S.The curve complex turned out to be a fundamental tool in the study of the geometry of the Teichmüller space, of mapping class groups and of Kleinian groups.
In mathematics, the local Langlands conjectures, introduced by Robert Langlands (1967, 1970), are part of the Langlands program.They describe a correspondence between the complex representations of a reductive algebraic group G over a local field F, and representations of the Langlands group of F into the L-group of G.