It's true that a standard undergraduate curriculum in mathematics will contain a lot of analysis (including calculus), a lot of ODEs/PDEs and some algebra. But

It's true that a standard undergraduate curriculum in mathematics will contain a lot of analysis (including calculus), a lot of ODEs/PDEs and some algebra. But if I wanted to get someone interested in math I would also point them towards some of the more fun (and less known stuff), such as combinatorics, probability, topology, differential geometry and number theory. Some of these are also much more applicable today than, say, complex analysis.