November 2014
Intermediate to advanced
326 pages
7h 46m
English
Content preview from From Mathematics to Generic ProgrammingBecome an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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6. Abstraction in Mathematics
Mathematicians do not study objects, but the relations between objects;to them it is a matter of indifference if these objects are replaced by others,provided that the relations do not change. Matter does notengage their attention, they are interested in form alone.Poincaré, Science and Hypothesis
The history of mathematics is filled with discoveries of new abstractions: finding ways to solve a more general problem. For example, we saw in Chapter 5 how Euler generalized Fermat’s Little Theorem so it would work with composite numbers as well as primes. Eventually, mathematicians realized that they could generalize beyond numbers, and derive results about abstract entities called algebraic structures—collections of ...
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.