Experimental mathematics in action
With the continued advance of computing power and accessibility, the view that “real mathematicians don't compute” no longer has any traction for a newer generation of mathematicians. The goal in this book is to present a coherent variety of accessible examples of modern mathematics where intelligent computing plays a significant role and in so doing to highlight some of the key algorithms and to teach some of the key experimental approaches. This book is an excellent choice for researchers [in mathematics] interested in exploring new avenues.
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Algorithms for Experimental Mathematics I
Algorithms for Experimental Mathematics II
Exploration and Discovery in Inverse Scattering
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algebraic algorithm AMM Problem approximation arctan arithmetic Borwein boundary calculate Cantor function Catalan's constant chaos game Chapter closed form coefficients colons columns conjecture constant continued fraction continuous convergence corresponding defined definite integrals denotes density differentiable digits discussed domain dyadic rationals Euler Euler-Mascheroni constant evaluation example experimental mathematics factor field pattern formula functional equations Gamma function given Helmholtz equation Hence Herglotz wave high-precision Hint identity implementation incident field inequality infinite integer relation inverse iterated function system iteration linear log2 Maple math Mathematica mathematicians methods Note obtain parameters polynomial precision prime numbers probability proof prove PSLQ PSLQ algorithm Quadratic Sieve random rational recursion roots rows satisfies scattering test response Schauder scheme Section sequence shown in Figure smooth numbers solons solution summation symbolic tanh-sinh quadrature theorem tion Weierstrass function zero zeta function