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Through 2006, the teacher had broad latitude in choosing the content material of the course. In 1970, for instance, college students studied the differential geometry of Banach manifolds in the second semester of Math 55. In contrast, Math 25 was extra narrowly targeted, usually covering real analysis, along with the related theory of metric areas and linear maps. These topics usually culminated in the proof of the generalized Stokes theorem, though, time allowing, other related topics (e.g. class concept, de Rham cohomology) may also be coated.

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In her first semester, she enrolled in Math fifty five and Physics fifty five, essentially the most troublesome freshman math and physics lessons supplied. Demographics of students taking this course through the years have been used to study the causes of gender and race variations in STEM. Many of those that are capable of handle the workload and complete the course become professors in quantitative fields. Numbers of scholars dropping are due partially to the tendency of undergraduates to « shop round » for applicable programs initially of each semester.

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