By Thomas Koshy

Just like the exciting Fibonacci and Lucas numbers, Catalan numbers also are ubiquitous. "They have a similar pleasant propensity for shooting up suddenly, relatively in combinatorial problems," Martin Gardner wrote in * medical American*. "Indeed, the Catalan series is among the most often encountered series that continues to be vague adequate to reason mathematicians missing entry to *Sloane's instruction manual of Integer Sequences* to burn up inordinate quantities of strength re-discovering formulation that have been labored out lengthy ago," he continued.

As Gardner famous, many mathematicians may well be aware of the abc's of Catalan series, yet now not many are acquainted with the myriad in their unforeseen occurrences, purposes, and houses; they crop up in chess forums, computing device programming, or even educate tracks. This ebook provides a transparent and finished advent to at least one of the really interesting themes in arithmetic. Catalan numbers are named after the Belgian mathematician Eugene Charles Catalan (1814-1894), who "discovered" them in 1838, even though he used to be no longer the 1st individual to find them. the nice Swiss mathematician Leonhard Euler (1707-1763) "discovered" them round 1756, yet even prior to then and although his paintings used to be now not recognized to the skin international, chinese language mathematician Antu Ming (1692?-1763) first came across Catalan numbers approximately 1730.

Catalan numbers can be utilized through academics and professors to generate pleasure between scholars for exploration and highbrow interest and to sharpen a number of mathematical abilities and instruments, resembling trend acceptance, conjecturing, proof-techniques, and problem-solving recommendations. This ebook is not just meant for mathematicians yet for a far greater viewers, together with highschool scholars, math and technological know-how academics, computing device scientists, and people amateurs with a modicum of mathematical interest. a useful source ebook, it comprises an interesting array of functions to computing device technology, summary algebra, combinatorics, geometry, graph thought, chess, and international Series.