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If f:M->N, then the tangent map Tf associated to f is a vector bundle homeomorphism Tf:TM->TN (i.e., a map between the tangent bundles of M and N respectively). The tangent ...

A Pythagorean triple is a triple of positive integers a, b, and c such that a right triangle exists with legs a,b and hypotenuse c. By the Pythagorean theorem, this is ...

The Higman-Sims graph is the unique strongly regular graph on 100 nodes (Higman and Sims 1968, Brouwer 1983, Brouwer and Haemers 1993). It was also constructed independently ...

Unlike quadratic, cubic, and quartic polynomials, the general quintic cannot be solved algebraically in terms of a finite number of additions, subtractions, multiplications, ...

The Riemann zeta function is an extremely important special function of mathematics and physics that arises in definite integration and is intimately related with very deep ...

A Banach space is a complete vector space B with a norm ||·||. Two norms ||·||_((1)) and ||·||_((2)) are called equivalent if they give the same topology, which is equivalent ...

An almost integer is a number that is very close to an integer. Near-solutions to Fermat's last theorem provide a number of high-profile almost integers. In the season 7, ...

The 2-1 equation A^n+B^n=C^n (1) is a special case of Fermat's last theorem and so has no solutions for n>=3. Lander et al. (1967) give a table showing the smallest n for ...

Given a complex Hilbert space H with associated space L(H) of continuous linear operators from H to itself, the bicommutant M^('') of an arbitrary subset M subset= L(H) is ...

Given a complex Hilbert space H with associated space L(H) of continuous linear operators from H to itself, the commutant M^' of an arbitrary subset M subset= L(H) is the ...