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  2. Embedding - Wikipedia

    en.wikipedia.org/wiki/Embedding

    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 → ...

  3. Nash embedding theorems - Wikipedia

    en.wikipedia.org/wiki/Nash_embedding_theorems

    The technical statement appearing in Nash's original paper is as follows: if M is a given m-dimensional Riemannian manifold (analytic or of class C k, 3 ≤ k ≤ ∞), then there exists a number n (with n ≤ m(3m+11)/2 if M is a compact manifold, and with n ≤ m(m+1)(3m+11)/2 if M is a non-compact manifold) and an isometric embedding ƒ: M → R n (also analytic or of class C k). [15]

  4. Immersion (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Immersion_(mathematics)

    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 ...

  5. Data-driven instruction - Wikipedia

    en.wikipedia.org/wiki/Data-driven_instruction

    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:

  6. Graph embedding - Wikipedia

    en.wikipedia.org/wiki/Graph_embedding

    An embedded graph uniquely defines cyclic orders of edges incident to the same vertex. The set of all these cyclic orders is called a rotation system.Embeddings with the same rotation system are considered to be equivalent and the corresponding equivalence class of embeddings is called combinatorial embedding (as opposed to the term topological embedding, which refers to the previous ...

  7. Principles and Standards for School Mathematics - Wikipedia

    en.wikipedia.org/wiki/Principles_and_Standards...

    The Principles and Standards for School Mathematics was developed by the NCTM. The NCTM's stated intent was to improve mathematics education. The contents were based on surveys of existing curriculum materials, curricula and policies from many countries, educational research publications, and government agencies such as the U.S. National Science Foundation. [3]

  8. Closed-subgroup theorem - Wikipedia

    en.wikipedia.org/wiki/Closed-subgroup_theorem

    In mathematics, the closed-subgroup theorem (sometimes referred to as Cartan's theorem) is a theorem in the theory of Lie groups.It states that if H is a closed subgroup of a Lie group G, then H is an embedded Lie group with the smooth structure (and hence the group topology) agreeing with the embedding.

  9. Elementary equivalence - Wikipedia

    en.wikipedia.org/wiki/Elementary_equivalence

    An embedding h: N → M is called an elementary embedding of N into M if h(N) is an elementary substructure of M. A substructure N of M is elementary if and only if it passes the Tarski–Vaught test: every first-order formula φ(x, b 1, …, b n) with parameters in N that has a solution in M also has a solution in N when evaluated in M.

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