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Category theory is a branch of mathematics that seeks to generalize all of mathematics in terms of categories, independent of what their objects and arrows represent. Virtually every branch of modern mathematics can be described in terms of categories, and doing so often reveals deep insights and similarities between seemingly different areas ...
The apparent plural form in English goes back to the Latin neuter plural mathematica , based on the Greek plural ta mathēmatiká (τὰ μαθηματικά) and means roughly "all things mathematical", although it is plausible that English borrowed only the adjective mathematic(al) and formed the noun mathematics anew, after the pattern of ...
Additional Mathematics is a qualification in mathematics, commonly taken by students in high-school (or GCSE exam takers in the United Kingdom). It features a range of problems set out in a different format and wider content to the standard Mathematics at the same level.
Nevertheless, his views—however informal—are a valuable contribution to the philosophy and anthropology of mathematics. [2] His views anticipate, in some respects, the more detailed account of the cognitive basis of mathematics given by George Lakoff and Rafael E. Núñez in their Where Mathematics Comes From.
An m × n matrix: the m rows are horizontal and the n columns are vertical. Each element of a matrix is often denoted by a variable with two subscripts.For example, a 2,1 represents the element at the second row and first column of the matrix.
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. [1] The set X is called the domain of the function [2] and the set Y is called the codomain of the function. [3] Functions were originally the idealization of how a varying quantity depends on another quantity.
For example, taking the prime n = 2 results in the above-mentioned field F 2. For n = 4 and more generally, for any composite number (i.e., any number n which can be expressed as a product n = r ⋅ s of two strictly smaller natural numbers), Z / n Z is not a field: the product of two non-zero elements is zero since r ⋅ s = 0 in Z / n Z ...
In mathematics, two functions have a contact of order k if, at a point P, they have the same value and their first k derivatives are equal. This is an equivalence relation, whose equivalence classes are generally called jets. The point of osculation is also called the double cusp.