Calculating the value of Ck ∈ {1, ∞} class of smoothness real-valued function's derivative in point of R+ in radius of convergence of its Taylor polynomial (or series), applying an analog of Newton's binomial theorem and q-difference operator. (P,q)-power difference introduced in section 5. Additionally, by means of Newton's interpolation formula, the discrete analog of Taylor series, interpolation using q-difference and p,q-power difference is shown.

General Game Playing (GGP) is the playing of a wide variety games you may have never seen before, by being told nothing but the rules of the game at run time. This sets it apart from traditional specific game players, like the famous chess player Deep Blue. Deep Blue can beat the world chess champion at chess however, it has absolutely no idea how to play checkers. It is designed for one particular game and cannot adapt to rule changes, and certainly cannot play entirely different games. The goal of this project is to create a program that will play a wide variety of 2d games given descriptions of their rules without the creator of the program having ever known of the games. This report will cover the design and implementation of this project, as well as the background research performed and reflections on the outcome of the project.

We describe what mimetic interpolation is and why it is critical for some pre- and post-processing tasks. A simple test case shows how using bilinear interpolation for a flux calculation introduces numerical errors that depend on the grid, the number of segments and the number of quadrature points. In contrast, mimetic interpolation will return the exact result regardless of the grid resolution and the number of segments.

Alex Pletzer and Wolfgang Hayek and Jorge Bornemann

A sample document with some code, useful packages, resources, and sample solution writeups to help Phillips Academy math students get started with Overleaf and LaTeX.