## Advances in Mathematics Research, Volume 3Mathematics has been behind many of humanity's most significant advances in fields as varied as genome sequencing, medical science, space exploration, and computer technology. But those breakthroughs were yesterday. Where will mathematicians lead us tomorrow and can we help to shape that destiny? This book assembles carefully selected articles highlighting and explaining cutting-edge research and scholarship in mathematics. |

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affine automorphisms affine charts affine fibration affine manifold affine map affine structure affine transformations affinely locally trivial algebra arrows associated asymptotics automobile base space block strongly nonsingular borel change of variable Chern class classify cocycle commutative compact and complete complete affine manifold composition series consider convergence convex cone deduce defined Delay Differential Equations denote element estimate exists a constant family of maps fibration flat bundle foliation full rank factorization function fundamental group gambling house gerbe given gluing GMRES GMRES method Gromov-Witten invariants GW-invariants hence holonomy implies integral invertible isomorphic Lemma linear holonomy locally trivial affine Lusin M,Vm mapping F Math Mathematics matrix mileage near-ring non-zero open set preconditioner Proposition rank reduction algorithm rank reduction operation representation restriction Schur complement solving Strang-type preconditioner Suppose symplectic theory total space trivial affine bundle typical fiber vector warranty period YTAX zero