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by qsort
2085 days ago
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> I feel that most math subjects are treated either as full-on “fluff” (e.g. calculus, all computing, no theory building) or full-on theory (real analysis) My background is computer science and I had a similar experience. Just a caveat: I'm not arguing that we should stop teaching theory, quite the contrary: most of the times we err on the side of the fluff. In particular, the fact that many reputable institutions are cutting formal logic, computability theory, etc. from their CS curriculums is an absolute disgrace. Intuition is hard to teach (easy to fall into the 'monads are burritos' trap) and it's something you have to work for yourself if you want to develop.
My point is just that lack of intuition/operative knowledge will lead to your theoretical knowledge of the field being less in-depth and generally less helpful to you. I honestly don't think it really matters what book you are studying as an introduction to a subject, as usually introductory courses are teaching well-established theory that everyone knows/agrees on.
If you have no prior knowledge, a decent starting point is this: https://www.amazon.com/gp/product/1981369198/
the author's website has similar content: https://www.statlect.com |
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Bioinformatics at my uni is just the typical CS minus some hardware stuff + molecular biology minus some chemistry stuff; in other words, I'm pretty close to CS, too. And I share your opinion — at least for me, I don't believe things until I see them proven.
> My point is just that lack of intuition/operative knowledge will lead to your theoretical knowledge of the field being less in-depth and generally less helpful to you.
In addition, building an intuition can help make the understanding come faster. To give you an example, I can stare at a proof for half a day and _then_ finally get it, but one clever diagram or a descriptive commentary can save me hours of pushing through the dense text — without cutting down on the rigour (as the proof is still there). Unfortunately, it seems that maths textbooks mostly come only with the former, or the latter, but not both.
> I honestly don't think it really matters what book you are studying as an introduction to a subject
I agree that it probably doesn't matter from the content POV (i.e. the basic definitions and theorems will be there), but it could matter if we take the intuition into account.
For example, in real analysis, there's baby Rudin, but there's also all sorts of books that include all (or most of) the content, but supply it with better commentary and/or illustrations to drive the point home quicker. And I'd day that's a pretty established field, too; probably more so than stats, in fact.