I think a nice and interesting topic that seems doable with basic calculus and linear algebra would be some kind of introduction in the theory of knots and surfaces. In particular, I have in mind the book "Knots and Surfaces. A guide to discovering mathematics" by Gilbert and Porter, Oxford Univ. Press, 1995. I think it would not be too sophisticated for you, it will introduce you to and get you thinking about various important objects in mathematics, and it may inspire you for your later studies. Have a look at it. If it turns out to be not that well doable for you, you could always take a second look at it in a year or so.
M.G.
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