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Serre's problem, also called Serre's conjecture, asserts that the implication "free module ==> projective module" can be reversed for every module over the polynomial ring ...

Set theory is the mathematical theory of sets. Set theory is closely associated with the branch of mathematics known as logic. There are a number of different versions of set ...

A problem also known as the points problem or unfinished game. Consider a tournament involving k players playing the same game repetitively. Each game has a single winner, ...

Order the natural numbers as follows: Now let F be a continuous function from the reals to the reals and suppose p≺q in the above ordering. Then if F has a point of least ...

A correction which must be applied to the measured moments m_k obtained from normally distributed data which have been binned in order to obtain correct estimators mu^^_i for ...

The randomization of a deck of cards by repeated interleaving. More generally, a shuffle is a rearrangement of the elements in an ordered list. Shuffling by exactly ...

The Siegel theta function is a Gamma_n-invariant meromorphic function on the space of all p×p symmetric complex matrices Z=X+iY with positive definite imaginary part. It is ...

The Sierpiński carpet is the fractal illustrated above which may be constructed analogously to the Sierpiński sieve, but using squares instead of triangles. It can be ...

There are several fractal curves associated with Sierpiński. The area for the first Sierpiński curve illustrated above (Sierpiński curve 1912) is A=1/3(7-4sqrt(2)). The curve ...

As proved by Sierpiński (1960), there exist infinitely many positive odd numbers k such that k·2^n+1 is composite for every n>=1. Numbers k with this property are called ...