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A frequently studied problem in finite geometry is to identify ways in which an object can be covered by other simpler objects such as points, lines, and planes. In projective geometry, a specific instance of this problem that has numerous applications is determining whether, and how, a projective space can be covered by pairwise disjoint subspaces which have the same dimension; such a ...
Laws of Form (hereinafter LoF) is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy. LoF describes three distinct logical systems : The primary arithmetic (described in Chapter 4 of LoF ), whose models include Boolean arithmetic ;
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.
9 : PG(2, 9), and three more different (non-isomorphic) non-Desarguesian planes: a Hughes plane, a Hall plane, and the dual of this Hall plane. All are described in (Room & Kirkpatrick 1971). 10 : impossible as an order of a projective plane, proved by heavy computer calculation. [13] 11 : at least PG(2, 11), others are not known but possible.
Nevertheless, his views—however informal—are a valuable contribution to the philosophy and anthropology of mathematics. [2] His views anticipate, in some respects, the more detailed account of the cognitive basis of mathematics given by George Lakoff and Rafael E. Núñez in their Where Mathematics Comes From.
If n is a positive integer of the form 4k + 1 or 4k + 2 and n is not equal to the sum of two integer squares, then n does not occur as the order of a finite plane. The smallest integer that is not a prime power and not covered by the Bruck–Ryser theorem is 10; 10 is of the form 4k + 2, but it is equal to the sum of squares 1 2 + 3 2.
Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag.The books in this series, like the other Springer-Verlag mathematics series, are yellow books of a standard size (with variable numbers of pages).
The apparent plural form in English goes back to the Latin neuter plural mathematica , based on the Greek plural ta mathēmatiká (τὰ μαθηματικά) and means roughly "all things mathematical", although it is plausible that English borrowed only the adjective mathematic(al) and formed the noun mathematics anew, after the pattern of ...