If you want to get away from analysis, I've found that cryptography can be quite an engaging subject. If you have the right book, it can have the rigors of more

If you want to get away from analysis, I've found that cryptography can be quite an engaging subject. If you have the right book, it can have the rigors of more mathematical subjects, while being accessible without extensive background and having visible real-world applications. I unfortunately don't have much experience with books in this area, but I do like https://files.boazbarak.org/crypto/lnotes_book.pdf https://files.boazbarak.org/crypto/lnotes_book.pdf (plus it's free ;) ). [EDIT: Previously I recommended Calculus on Manifolds here also, but on further reflection and reading some of the other responses I think I both misremembered the difficulty level of the book and overestimated what early-undergrad level means]