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In mathematics, an embedding (or imbedding [1]) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup. When some object X {\displaystyle X} is said to be embedded in another object Y {\displaystyle Y} , the embedding is given by some injective and structure-preserving map f : X → ...
To embed data analysis by students into classroom practices, it requires time, training, and action. [17] The strategies that students use to evaluate their own learning vary in effectiveness. In a meta-analysis, Dunlosky, Rawson, Marsh, Nathan & Willingham ranked ten learning strategies based on the projected impact each would have on achievement:
Wolfram contends that this approach is fundamentally different from most of the use of Computers in the classroom (or Computer-based mathematics education), [8] whose role is to help to teach students to perform hand calculations, rather than to perform those computations and is also distinct from delivery tools such as E-learning systems.
There were opportunities for peer observation and reflective practice. The research element recorded classroom practice and assessed participants' reactions and learning, eliciting messages for embedding basic ICT and OER use in teacher education. Findings were presented at the eLearning Africa Conference in Lusaka in May 2010.
The embedding of X into Y is a compact operator: any bounded set in X is totally bounded in Y, i.e. every sequence in such a bounded set has a subsequence that is Cauchy in the norm ||•|| Y. If Y is a Banach space, an equivalent definition is that the embedding operator (the identity) i : X → Y is a compact operator.
A smooth embedding is an injective immersion f : M → N that is also a topological embedding, so that M is diffeomorphic to its image in N. An immersion is precisely a local embedding – that is, for any point x ∈ M there is a neighbourhood, U ⊆ M, of x such that f : U → N is an embedding, and conversely a local embedding is an ...
In mathematics, one normed vector space is said to be continuously embedded in another normed vector space if the inclusion function between them is continuous. In some sense, the two norms are "almost equivalent", even though they are not both defined on the same space. Several of the Sobolev embedding theorems are continuous embedding theorems.
For example, if X and Y are smooth over a scheme S and if i is an S-morphism, then i is a regular embedding. In particular, every section of a smooth morphism is a regular embedding. [1] If is regularly embedded into a regular scheme, then B is a complete intersection ring. [2]
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