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Math 55 is a two-semester freshman undergraduate mathematics course at Harvard University founded by Lynn Loomis and Shlomo Sternberg. The official titles of the course are Studies in Algebra and Group Theory (Math 55a)[1] and Studies in Real and Complex Analysis (Math 55b).[2] Previously, the official title was Honors Advanced Calculus and Linear Algebra.[3]

In the past, Harvard University's Department of Mathematics had described Math 55 as "probably the most difficult undergraduate math class in the country."[4] But Math 55 lecturer for 2022 Professor Denis Auroux clarified that "if you’re reasonably good at math, you love it, and you have lots of time to devote to it, then Math 55 is completely fine for you."[5]

Formerly, students would begin the year in Math 25 (which was created in 1983 as a lower-level Math 55) and, after three weeks of point-set topology and special topics (for instance, in 1994, p-adic analysis was taught by Wilfried Schmid), students would take a quiz. As of 2012, students may choose to enroll in either Math 25 or Math 55 but are advised to "shop" both courses and have five weeks to decide on one.[6]

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