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Thurston's 24 questions [4] [5] 24-William Thurston: 1982 Smale's problems: 18: 14: Stephen Smale: 1998 Millennium Prize Problems: 7: 6 [6] Clay Mathematics Institute: 2000 Simon problems: 15 <12 [7] [8] Barry Simon: 2000 Unsolved Problems on Mathematics for the 21st Century [9] 22-Jair Minoro Abe, Shotaro Tanaka: 2001 DARPA's math challenges ...
For example, for 2 5 a + 1 there are 3 increases as 1 iterates to 2, 1, 2, 1, and finally to 2 so the result is 3 3 a + 2; for 2 2 a + 1 there is only 1 increase as 1 rises to 2 and falls to 1 so the result is 3a + 1. When b is 2 k − 1 then there will be k rises and the result will be 3 k a + 3 k − 1.
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More compact collections can be found in e.g. Brychkov, Marichev, Prudnikov's Tables of Indefinite Integrals, or as chapters in Zwillinger's CRC Standard Mathematical Tables and Formulae or Bronshtein and Semendyayev's Guide Book to Mathematics, Handbook of Mathematics or Users' Guide to Mathematics, and other mathematical handbooks.
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The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics, and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.
MAFELAP (MAthematics of Finite ELements and APplications) — international conference held at Brunel University; NAFEMS — not-for-profit organisation that sets and maintains standards in computer-aided engineering analysis; Multiphase topology optimisation — technique based on finite elements for determining optimal composition of a mixture
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). [1] [2] Alternative names are switching function, used especially in older computer science literature, [3] [4] and truth function (or logical function), used in logic.