Appreciation of real analysis/abstract algebra among science professors

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The discussion centers on the familiarity of professors in various scientific fields with advanced mathematical concepts such as real analysis, abstract algebra, and topology. In physics, a significant percentage of professors are expected to be well-versed in these areas, while in fields like biology, the consensus is that knowledge of such advanced mathematics is less common. Biologists typically engage with differential equations, particularly in areas like ecology where population dynamics are modeled. However, certain interdisciplinary fields like structural biology and biophysics do require a strong understanding of advanced mathematics, including concepts from quantum mechanics. The conversation highlights the variability in mathematical proficiency across different scientific disciplines, emphasizing that the specific requirements often depend on the subfield in question.
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What % of professors in, say, physics, would be familiar with real analysis/abstract algebra/topology? What about, say, the material in senior level CS courses?

How about professors in astrophysics, theoretical biology, earth/atmospheric sciences, and chemistry?
 
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I do not think biologists know real analysis or abstract algebra at all
 
I'm not an expert biologist, but I would think that the most difficult mathematics they have to be comfortable with is differential equations.
 
it really depends on what field of biology. ecology would probably need to differ eq as population dynamics are modeled by differ eqs.

although some areas of biology boarder physics or something. structural biology, for example, would involve plenty of quantum mechanics (the therefore the math needed). just look up biophysics. and a lot of protein modeling is basically theoretical physics/chemistry.
 

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