The discussion revolves around the relationship between proof-based mathematics, specifically Real Analysis, and computational mathematics, particularly Calculus. Participants explore whether a strong understanding of Real Analysis makes Calculus problems trivial and whether knowledge of Real Analysis is necessary for formulating Calculus problems and exercises.
Participants express differing views on the necessity of Real Analysis for formulating Calculus problems, with some suggesting it is not required for basic exercises while others believe it can be beneficial for more complex problem design. The discussion remains unresolved regarding the extent to which Real Analysis impacts the understanding of Calculus.
There are varying assumptions about the definitions of "formulating" versus "solving" problems, and the discussion does not clarify the specific types of problems being referenced.
No. How would you prove that your computations are correct? Good courses about computation are more than cookbook classes.flamengo said:s it true that if you have a good understanding of proof based math courses( like Real Analysis), courses based in computations( like Calculus) become relatively trivial ?
No, I don't think so, not for the "drill" exercises in any case. However, the more you are "above" the subject, the better. Also, I could certainly think of more advanced calculus problems that require an understanding of real analysis for their proper design.flamengo said:Do I need to know Real Analysis to formulate Calculus problems and exercises ? Or, is a rigorous Calculus book enough for this finality ?