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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]
A number that is not part of any friendly pair is called solitary. The abundancy index of n is the rational number σ(n) / n, in which σ denotes the sum of divisors function. A number n is a friendly number if there exists m ≠ n such that σ(m) / m = σ(n) / n. Abundancy is not the same as abundance, which is defined as σ(n) − 2n.
The lattice Con(A) of all congruence relations on an algebra A is algebraic. John M. Howie described how semigroup theory illustrates congruence relations in universal algebra: In a group a congruence is determined if we know a single congruence class, in particular if we know the normal subgroup which is the class containing the identity.
Modules of this type are called free and if R has invariant basis number (e.g. any commutative ring or field) the number n is then the rank of the free module. If M n ( R ) is the ring of n × n matrices over a ring R , M is an M n ( R )-module, and e i is the n × n matrix with 1 in the ( i , i ) -entry (and zeros elsewhere), then e i M is an ...
definition remarks rational equivalence Z ~ rat Z' if there is a cycle V on X × P 1 flat over P 1, such that [V ∩ X × {0}] − [V ∩ X × {∞}] = [Z] − [Z' ]. the finest adequate equivalence relation (Lemma 3.2.2.1 in Yves André's book [2]) "∩" denotes intersection in the cycle-theoretic sense (i.e. with multiplicities) and [.] denotes the cycle associated to a subscheme. see also ...
How To: Absurd Scientific Advice for Common Real-World Problems is a book by Randall Munroe in which the author provides absurd suggestions based in scientific fact on ways to solve some common and some absurd problems. [1] [2] [3] The book contains a range of possible real-world and absurd problems, each the focus of a single chapter. The book ...
In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues. On the other hand, in numerical algorithms for differential equations the concern is the growth of round-off errors and/or small fluctuations in initial data which might ...
Investigations was developed between 1990 and 1998. It was just one of a number of reform mathematics curricula initially funded by a National Science Foundation grant. The goals of the project raised opposition to the curriculum from critics (both parents and mathematics teachers) who objected to the emphasis on conceptual learning instead of instruction in more recognized specific methods ...