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Connected Mathematics is a comprehensive mathematics program intended for U.S. students in grades 6–8.The curriculum design, text materials for students, and supporting resources for teachers were created and have been progressively refined by the Connected Mathematics Project (CMP) at Michigan State University with advice and contributions from many mathematics teachers, curriculum ...
A topological space is said to be connected if it is not the union of two disjoint nonempty open sets. [2] A set is open if it contains no point lying on its boundary; thus, in an informal, intuitive sense, the fact that a space can be partitioned into disjoint open sets suggests that the boundary between the two sets is not part of the space, and thus splits it into two separate pieces.
In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint non-empty ...
This graph becomes disconnected when the right-most node in the gray area on the left is removed This graph becomes disconnected when the dashed edge is removed.. In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more ...
In 1996 the Association for Women in Mathematics gave her their Louise Hay Award. [2] She was named a University Distinguished Professor at Michigan State in 1998. [1] In 2002, the Connected Mathematics project endowed the Lappan-Phillips-Fitzgerald Endowed Chair in Mathematics Education at Michigan State, named after Lappan and the other two founders of the project.
A topological space is called simply connected if it is path-connected and any loop in defined by : can be contracted to a point: there exists a continuous map : such that restricted to is . Here, S 1 {\displaystyle S^{1}} and D 2 {\displaystyle D^{2}} denotes the unit circle and closed unit disk in the Euclidean plane respectively.
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A strongly connected component C is called trivial when C consists of a single vertex which is not connected to itself with an edge, and non-trivial otherwise. [1] The yellow directed acyclic graph is the condensation of the blue directed graph. It is formed by contracting each strongly connected component of the blue graph into a single yellow ...