By George Boole

This Elibron Classics e-book is a facsimile reprint of a 1877 variation by way of Macmillan and Co., London.

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**Extra resources for A treatise on differential equations**

**Sample text**

Many applications that need to process and summarize large quantities of data fit this pattern. 4. Both map and reduce phases of this pattern can be executed in parallel. The attraction of MapReduce, implemented in a framework, is that the developer can build the mapper and reducer without any knowledge of how they are executed. Dense and sparse linear algebra computations are probably the two most common patterns. They are used by applications such as games, machine learning, image processing and high performance scientific computing.

Connection Machine: Art and Science Computers are becoming invisible as they become ubiquitous, either disappearing into devices or off in the cloud somewhere. Supercomputers tend to be physically impressive because of the space they occupy and the visible cables, cooling, and power infrastructure. It looked like a work of art, because in away it was. Produced by Thinking Machines between 1983 and 1994, it was the realization of Danny Hillis’s PhD research at MIT. The Connection Machine was a massively parallel SIMD computer.

In the map phase, (word, count) pairs are produced for each document. If we’re using a MapReduce framework then we just need to implement a mapper function to generate 〈word, count〉 pairs given a document and a reducer function to sum the values of a given word, as we’ll see in Chapter 4. The reduction phase is not as simple, since some coordination among tasks is needed, as described in the reduction algorithm pattern. A distributed approach is required if the documents are not stored in one place or if the number of documents is large enough to justify using a cluster of computers, which might be located in the cloud.