If you majored in mathematics as an undergraduate, you should study mathematical analysis as a freshman. If your major is non-mathematics, and your freshman major is advanced mathematics, that is to say, mathematical analysis and advanced mathematics are the difference between professional and amateur. Mathematical analysis is much more theoretical than advanced mathematics, but the content only contains similar parts of advanced mathematics, without probability theory, linear algebra and so on. You can find a book on mathematical analysis and review it against your previous advanced mathematics book.