I am a college student, struggling to decide whether or not to take pure maths electives on topics such as real analysis and measure theory. If I were to take them then I would definitely have to invest a lot of time into them in order to understand them and get better grades. However I am considering the opportunity cost for this, as I could have learned new skills such as deepening my programming skills. How important was this to you? Thanksss
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$\begingroup$ This is primarily an opinion based question and will likely be closed. My two cents though - it's not that relevant at all. Measure theory and real analysis comes up in the rigorous treatment of probability theory - while DS work may borrow from statistics and therefore, probability, I have yet to see any DS work that uses these ideas extensively. That being said, if you are interested in pursuing a PhD in something like stats/probability, then real analysis/measure theory is very strongly recommended. $\endgroup$– aranglolCommented Dec 12, 2021 at 4:37
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It’s probably one of the less important skills.
This isn’t to say that it would be worthless to take. Indeed, for someone pursuing a PhD in a data science field like statistics, I would expect some probability theory based on measure theory. If you plan to go that route, then you would be doing measure theory at some point.
However, so much of data science in industry is pretty unrelated to theoretical statistics or even statistics of any kind. Data science is more of a subfield of software engineering than statistics. Even when data science involves statistics, it tends to have more to do with the implementation of known methods than invention of new ones.
I know a lot of good, \$uccessful software engineers who definitely don’t know what measure theory is.
(Even if you do plan to get a PhD in statistics or mathematics, there is not much expectation of a background in measure theory. People will have bits and pieces of measure theory in undergrad, but that’s mostly a topic for graduate school. My recommendation, if you’re pursuing that path, is to take the elective classes that have the best teachers. If you can get a recommendation letter from a hotshot in their field, that has its advantages, too.)
