Computational economicsComputational Economics is an interdisciplinary research discipline that involves computer science, economics, and management science. This subject encompasses computational modeling of economic systems. Some of these areas are unique, while others established areas of economics by allowing robust data analytics and solutions of problems that would be arduous to research without computers and associated numerical methods.
Pólya conjectureIn number theory, the Pólya conjecture (or Pólya's conjecture) stated that "most" (i.e., 50% or more) of the natural numbers less than any given number have an odd number of prime factors. The conjecture was set forth by the Hungarian mathematician George Pólya in 1919, and proved false in 1958 by C. Brian Haselgrove. Though mathematicians typically refer to this statement as the Pólya conjecture, Pólya never actually conjectured that the statement was true; rather, he showed that the truth of the statement would imply the Riemann hypothesis.
Vertex arrangementIn geometry, a vertex arrangement is a set of points in space described by their relative positions. They can be described by their use in polytopes. For example, a square vertex arrangement is understood to mean four points in a plane, equal distance and angles from a center point. Two polytopes share the same vertex arrangement if they share the same 0-skeleton. A group of polytopes that shares a vertex arrangement is called an army. The same set of vertices can be connected by edges in different ways.
Beal conjectureThe Beal conjecture is the following conjecture in number theory: If where A, B, C, x, y, and z are positive integers with x, y, z ≥ 3, then A, B, and C have a common prime factor. Equivalently, The equation has no solutions in positive integers and pairwise coprime integers A, B, C if x, y, z ≥ 3. The conjecture was formulated in 1993 by Andrew Beal, a banker and amateur mathematician, while investigating generalizations of Fermat's Last Theorem. Since 1997, Beal has offered a monetary prize for a peer-reviewed proof of this conjecture or a counterexample.
Crossing number (graph theory)In graph theory, the crossing number cr(G) of a graph G is the lowest number of edge crossings of a plane drawing of the graph G. For instance, a graph is planar if and only if its crossing number is zero. Determining the crossing number continues to be of great importance in graph drawing, as user studies have shown that drawing graphs with few crossings makes it easier for people to understand the drawing.
IcosahedronIn geometry, an icosahedron (ˌaɪkɒsəˈhiːdrən,-kə-,-koʊ- or aɪˌkɒsəˈhiːdrən) is a polyhedron with 20 faces. The name comes . The plural can be either "icosahedra" (-drə) or "icosahedrons". There are infinitely many non-similar shapes of icosahedra, some of them being more symmetrical than others. The best known is the (convex, non-stellated) regular icosahedron—one of the Platonic solids—whose faces are 20 equilateral triangles. There are two objects, one convex and one nonconvex, that can both be called regular icosahedra.
