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The Elementary and Secondary Education Act (ESEA) was passed by the 89th United States Congress and signed into law by President Lyndon B. Johnson on April 11, 1965. Part of Johnson's "War on Poverty", the act has been one of the most far-reaching laws affecting education passed by the United States Congress, and was reauthorized by the No Child Left Behind Act of 2001.
In mathematics, and more specifically in homological algebra, a resolution (or left resolution; dually a coresolution or right resolution [1]) is an exact sequence of modules (or, more generally, of objects of an abelian category) that is used to define invariants characterizing the structure of a specific module or object of this category.
The word mathematics comes from the Ancient Greek word máthēma (μάθημα), meaning ' something learned, knowledge, mathematics ', and the derived expression mathēmatikḗ tékhnē (μαθηματικὴ τέχνη), meaning ' mathematical science '. It entered the English language during the Late Middle English period through French and ...
However, many students take alternatives to the traditional pathways, including accelerated tracks. As of 2023, twenty-seven states require students to pass three math courses before graduation from high school (grades 9 to 12, for students typically aged 14 to 18), while seventeen states and the District of Columbia require four. [2]
[1] [2] [3] By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers ; more formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets [ 4 ] (finite sets or sets with ...
A 1‑tuple is called a single (or singleton), a 2‑tuple is called an ordered pair or couple, and a 3‑tuple is called a triple (or triplet). The number n can be any nonnegative integer . For example, a complex number can be represented as a 2‑tuple of reals, a quaternion can be represented as a 4‑tuple, an octonion can be represented as ...
P n 0, P n 1, P n 2, P n 3, ... For every integer n ≥ 0, there are infinitely many n-ary function symbols: f n 0, f n 1, f n 2, f n 3, ... When the arity of a predicate symbol or function symbol is clear from context, the superscript n is often omitted. In this traditional approach, there is only one language of first-order logic. [13]
In computer science, binary search, also known as half-interval search, [1] logarithmic search, [2] or binary chop, [3] is a search algorithm that finds the position of a target value within a sorted array. [4] [5] Binary search compares the target value to the middle element of the array. If they are not equal, the half in which the target ...