Combinatorial optimization design for the identification and classification of mathematical knots**

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Through competition and game-based math content, Caribou Contests stimulates enthusiasm for math and inspires higher achievement in student learning. In the growing market of educational games, Caribou Contests is continually faced with the need to develop new and interesting interactive mathematical challenges to stay ahead of competitors and to grasp and hold on to the attention of children. To this end, Caribou Contests would like to develop a new, unique and interactive STEM educational module about knots, closed loops of string in three-dimensional space. Although several web pages on knots exist, a web site that allows one to work with knots interactively does not yet exist. This type of interactive format is ideally suited to reach out to young students to explore spatial concepts in knot theory in online course content and math competitions. ****The research project is to develop a computer search for knot identification, enabling the deformation of knots into each other and thus prove their equivalence when other methods cannot. There are two closely related computational challenges: first to find the "simplest" diagram representing a given knot, and second to identify whether two given knots are equivalent. Two search strategies, Genetic Algorithms and Simulated Annealing, will be applied to this research problem. Our approach is innovative because, if successful, it will provide a proof of knot identities and can be translated visually to online education materials to engage students. The resulting deformation sequences from this program are also useful for research purposes.****Results of the project will enable Caribou Contests to develop an application about knot theory to create questions for online contests and to sell as a mini-course in their e-shop, thereby opening the door to mathematics for students normally not interested in it, and further motivating students already fascinated by mathematics. ************************