I recently looked at the syllabus of a course by my alma matar targeted at the same audience of ambitious first-year mathematics students with an emphasis on rigor. It is quite different from Hardy's book and the changes are, I think, for the better. Mostly, it introduces a lot more discrete mathematics, with a little bit of even graph theory and a little bit of enumerative combinatorics (generating functions and the like). In contrast this book is mostly focused on calculus and analysis, which are already separate courses. Freshman students should be exposed to a wider variety of topics in college-level mathematics and not just harder versions of what they already studied in high school.