Search results
Results from the WOW.Com Content Network
Using K-theory, they constructed an example of a torsion cohomology class—that is, a cohomology class α such that nα = 0 for some positive integer n —which is not the class of an algebraic cycle. Such a class is necessarily a Hodge class.
Systems of linear equations form a fundamental part of linear algebra. Historically, linear algebra and matrix theory have been developed for solving such systems. In the modern presentation of linear algebra through vector spaces and matrices, many problems may be interpreted in terms of linear systems. For example, let
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.
One of the widely used types of impossibility proof is proof by contradiction.In this type of proof, it is shown that if a proposition, such as a solution to a particular class of equations, is assumed to hold, then via deduction two mutually contradictory things can be shown to hold, such as a number being both even and odd or both negative and positive.
Cantor–Bernstein–Schröder theorem (set theory, cardinal numbers) Cantor's theorem (set theory, Cantor's diagonal argument) Church–Rosser theorem (lambda calculus) Compactness theorem (mathematical logic) Conservativity theorem (mathematical logic) Craig's theorem (mathematical logic) Craig's interpolation theorem (mathematical logic)
A solution to this problem is an example of a Kirkman triple system, [3] which is a Steiner triple system having a parallelism, that is, a partition of the blocks of the triple system into parallel classes which are themselves partitions of the points into disjoint blocks.
The problem was first posed by Henry Dudeney in 1900, as a puzzle in recreational mathematics, phrased in terms of placing the 16 pawns of a chessboard onto the board so that no three are in a line. [2] This is exactly the no-three-in-line problem, for the case =. [3]
Zeros. Polynomials. Determinants. Number Theory. Geometry. The volumes are highly regarded for the quality of their problems and their method of organisation, not by topic but by method of solution, with a focus on cultivating the student's problem-solving skills. Each volume the contains problems at the beginning and (brief) solutions at the end.