Learning dynamic programming through mathematical games

Abstract

Dynamic Programming (DP), which takes full advantage of the bottom-up method, is very significant in solving mathematical games because the solutions of mathematical games are probably to be developed efficiently by making good use of the Dynamic Programming, especially the problem size is enormous, and the problem tends to produce a vast array of the similar subproblems. This project explored the essential steps of developing the DP solution of mathematical problems. Moreover, these essential steps would be used to develop the DP solution of selected mathematical games from famous mathematical problems and Facebook Nemo Bot. Subsequently, the Dynamic Programming technique would be applied to a mathematical game called Algebra Game, which aims to solve the linear algebra equation by selecting the clues. Specifically, Dynamic Programming would be used to improve the efficiency of looking for the intersection or common subsequence between two subsequences named X-subsequence and Coefficient subsequence respectively in the process of generating steps to solve the algebra equation. In order to promote the importance of dynamic programming and the enjoyment of solving problems by using DP, Game-based learning is proposed to create a website that aims to display the Algebra Game and provide the tutorials which are about the DP technique in the Algebra Game and detailed steps to solve the algebra equation. And the website may attract the user to enjoy games and encourage them to understand the basic even more thorough knowledge of DP by providing the game.