恒隆數學獎

4. 港大同學會書院 Reinforcement Learning on Geometric Construction Th i s pape r a ims to d i scuss the pr ocedur e o f app l y i ng reinforcement learning in geometric construction. The significant achievement of this paper includes a relatively general method of finding sufficient points for completing designated construction tasks, an algorithm suggesting the selection of necessary points in the process of construction, and two reinforcement learning models. The first learning model using greedy algorithms generates efficient construction results of four tasks specifically chosen from Euclidea. Moreover, the first model also generates a construction method of the regular heptadecagon. The second reinforcement learning model involves deep Q-learning. The framework and training demonstration are given, yet by all kinds of limitations, only an intermediate result is achieved. Eventually, the paper hopes to build connections between machine learning and the development of mathematics discovery. 5. 觀塘官立中學 On Polyadic Group and Ordinary Polyadic Equation The main aims of this paper are to give an insight on the binary algebraic structure called polyadic group (or n-ary group) and provide an initial study of an equation called polyadic equation, especially the ordinary polyadic equation (OPE). In this paper, we investigated n-ary group and related terms, for example: ternary group and the Hosszú-Gluskin theorem. Besides that, we established a classification of polyadic equations. After that, we studied ordinary polyadic equations in different forms.

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