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The number of real roots of an algebraic equation with real coefficients whose real roots are simple over an interval, the endpoints of which are not roots, is equal to the ...

Let sigma_0(n) and sigma_1(n) denote the number and sum of the divisors of n, respectively (i.e., the zeroth- and first-order divisor functions). A number n is called sublime ...

There are two problems commonly known as the subset sum problem. The first ("given sum problem") is the problem of finding what subset of a list of integers has a given sum, ...

The sum rule for differentiation states d/(dx)[f(x)+g(x)]=f^'(x)+g^'(x), (1) where d/dx denotes a derivative and f^'(x) and g^'(x) are the derivatives of f(x) and g(x), ...

Let h>=2 and let A_1, A_2, ..., A_h be sets of integers. The sumset A_1+A_2+...+A_h is the set of all integers of the form a_1+a_2+...+a_h, where a_i is a member of A_i for ...

A number of attractive 26-compounds of the regular tetrahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...

In the notation of Watson (1966), theta=zd/(dz).

The space E of a fiber bundle given by the map f:E->B, where B is the base space of the fiber bundle.

The 3-node tournament (and directed graph) illustrated above (Harary 1994, p. 205).

A statement which is rigorously known to be correct. A statement which is not true is called false, although certain statements can be proved to be rigorously undecidable ...