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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.
In algebraic geometry, flips and flops are codimension-2 surgery operations arising in the minimal model program, given by blowing up along a relative canonical ring.In dimension 3 flips are used to construct minimal models, and any two birationally equivalent minimal models are connected by a sequence of flops.
The books in this series, like the other Springer-Verlag mathematics series, are small yellow books of a standard size. The books in this series tend to be written at a more elementary level than the similar Graduate Texts in Mathematics series, although there is a fair amount of overlap between the two series in terms of material covered and ...
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 ...
A major rockslide prompted two highways to be shut down in Colorado over the weekend and witnesses captured the frightening moment on video. Highways 96 and 165 from Wetmore to Westcliffe in ...
In 1988, the method came to the attention to mathematical olympiad problems in the light of the first olympiad problem to use it in a solution that was proposed for the International Mathematics Olympiad and assumed to be the most difficult problem on the contest: [2] [3] Let a and b be positive integers such that ab + 1 divides a 2 + b 2.
The 2008 financial crisis didn’t happen overnight. Rather, it was the culmination of a series of factors. The details of what led to the financial crisis are detailed in the 2010 book “The Big ...