Publishing a thesis after graduation

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Hello /sci/entists

In May, I graduated with a BA in mathematics from a relatively well-regarded New York liberal arts college. Throughout my senior year I put together a thesis, and it's my single biggest achievement so far in life. It's about chess-derived games, how to win them, and the significance therein. The paper contains a handful of original results; nothing truly groundbreaking, but something to be proud of I think. A professor who read it told me it was the best-written thesis he had read in years, which made me very happy. The paper is hosted on the school's server, and it shows me where and when it has been downloaded, which has been fun to track (five continents are represented so far). Anyway, laypeople have suggested I try to publish the paper in some academic journal. How realistic is this? What steps would it entail, etc.? I still think about the thesis a lot, and I might continue with it and/or resolve some of the loose ends in the future.