Why is calculus always the filtering agent in studies like computer science (the few that still teach it properly), physics and chemistry?What percentage of people can comprehensively learn calculus at the level of being able to solve all Spivak or East-European style textbook alternative to it?
technically discrete math is prereq for cs related fields, calc is on a higher on the causal chain, it is required for all stem fields
It's a fine combination of algebra and geometry. It is also often first introduction to proofs, together with linear algebra.
Basic calculus is easy for those who understand math and a struggle for those who do not.
>>16904205>What percentage of people can comprehensively learn calculus at the level of being able to solve all Spivak or East-European style textbook alternative to it?That goes beyond calculus, that's proof based elementary analysis, "honours calculus" maybe. Many physicists and engineers are formidable users and teachers of calculus, but they never studied proof based mathematics
what would you recommend for getting up to speed with proofs in order to tackle books like spivak or apostol? I took up to multivariate calculus in college and did very well but it wasn't proof based, they just taught us to do the calculations and we did them but I feel like I barely learned anything, and looking at these textbooks now it feels like I'm walking into a class that I'm missing a very important prerequisite for, even in working through the introductory section in apostol which is specifically for catching up.
>>16904737I recommend:>Journey into Mathematics: An Introduction to Proofs - Joseph J. RotmanWhen opening Apostol or Spivak, don't focus too much on the basics, try skipping the first chapters and focusing on the central concepts of limit, derivative, integral. Struggling with these will make your realize that the introductory chapters are the easy part, but dont let that discourage you. That being said, the part of the introductory chapters you must focus is inequalities (consequences of the order axioms). You must memorize things like the proof of the arithmetic-geometric inequality or the existence of sqrt2 from the supremum axiom, even if you dont understand them at first. Rotman, for example, teaches induction better than Spivak. But these introductory chapters are there for a reason so you'll get back to them eventually. On the other hand, you should look at two more recent books, Understanding Analysis by Abbott and Elementary Analysis by Ross. If what you want is the Apostol/Spivak level, other books like Tao's would be overkill.
>>16904958Thanks, I appreciate the recommendations. All of those books seem reasonably approachable considering how long it's been since I studied any math.
>>16904307>technically discrete math is prereq for cs related fieldsthat is indeed the case, but only because the analysis part is, on most courses, basically high school math with some of the most obvious per partes examples and some integrals you solve with preconfigured formulas. If you study say chemistry, you will endure a proof based calculus akin to the math students, that is levels more difficult than discrete math and analysis at cs combined >>16904737>what would you recommend for getting up to speed with proofs in order to tackle books like spivak or apostol?grit and youtube videos if you're stuck
