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Concrete Mathematics: A Foundation for Computer Science, by Ronald Graham, Donald Knuth, and Oren Patashnik, first published in 1989, is a textbook that is widely used in computer-science departments as a substantive but light-hearted treatment of the analysis of algorithms.
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Informally, a field is a set, along with two operations defined on that set: an addition operation written as a + b, and a multiplication operation written as a ⋅ b, both of which behave similarly as they behave for rational numbers and real numbers, including the existence of an additive inverse −a for all elements a, and of a multiplicative inverse b −1 for every nonzero element b.
Form, Fit, and Function (also F3 or FFF) is a concept used in various industries, including manufacturing, engineering, and architecture, to describe aspects of a product's design, performance, and compliance to a specification.
The theory of finite fields, whose origins can be traced back to the works of Gauss and Galois, has played a part in various branches of mathematics.Due to the applicability of the concept in other topics of mathematics and sciences like computer science there has been a resurgence of interest in finite fields and this is partly due to important applications in coding theory and cryptography.
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules.
In mathematics, the composition operator takes two functions, and , and returns a new function ():= () = (()). Thus, the function g is applied after applying f to x . Reverse composition , sometimes denoted f ↦ g {\displaystyle f\mapsto g} , applies the operation in the opposite order, applying f {\displaystyle f} first and g {\displaystyle g ...
In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x , denoted ⌈ x ⌉ or ceil( x ) .