Here is a class you can take right after real analysis, description from Harvard's website (I do not go to Harvard).
This is probably the most difficult undergraduate math class in the country; a variety of advanced topics in mathematics are covered, and problem sets ask students to prove many fundamental theorems of analysis and linear algebra. Class meets three hours per week, plus one hour of section, and problem sets can take anywhere from 24 to 60 hours to complete. This class is usually small and taught by a well-established and prominent member of the faculty whose teaching ability can vary from year to year. A thorough knowledge of multivariable calculus and linear algebra is almost absolutely required, and any other prior knowledge can only help. Students who benefit the most from this class have taken substantial amounts of advanced mathematics and are fairly fluent in the writing of proofs. Due to the necessity of working in groups and the extensive amount of time spent working together, students usually meet some of their best friends in this class. The difficulty of this class varies with the professor, but the class often contains former members of the International Math Olympiad teams, and in any event, it is designed for people with some years of university level mathematical experience. In order to challenge all students in the class, the professor can opt to make the class very, very difficult.
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