Math 55 is a two-semester freshman undergraduate mathematics course at Harvard University founded by Lynn Loomis and Shlomo Sternberg.
[10] Richard Stallman estimated that, in 1970, Math 55 covered almost four years worth of department coursework in two semesters, and thus, it drew only the most diligent of undergraduates.
[5] Even those who passed Advanced Placement Calculus and were veterans of the USA Mathematical Olympiad might feel that Math 55 was too much to handle.
[3] In short, Math 55 gives a survey of the entire undergraduate curriculum of mathematics in just two semesters and might even include graduate-level topics.
[12] Though Math 55 bore the official title "Honors Advanced Calculus and Linear Algebra," advanced topics in complex analysis, point-set topology, group theory, and differential geometry could be covered in depth at the discretion of the instructor, in addition to single and multivariable real analysis as well as abstract linear algebra.
[11] In contrast, Math 25 was more narrowly focused, usually covering real analysis, together with the relevant theory of metric spaces and (multi)linear maps.
[13] Although both courses presented calculus from a rigorous point of view and emphasized theory and proof writing, Math 55 was generally faster paced, more abstract, and demanded a higher level of mathematical sophistication.
Instructors for Math 55[15][16] and Math 25[13] have also selected Rudin's Principles of Mathematical Analysis,[17] Ahlfors' Complex Analysis,[18] Spivak's Calculus on Manifolds,[19] Axler's Linear Algebra Done Right,[20] Halmos's Finite-Dimensional Vector Spaces,[21] Munkres' Topology,[22] and Artin's Algebra[23] as textbooks or references.