> And if you do learn it, do so with rigor so you actually learn it
This is not strictly necessary for everybody. The conceptual ideas are what are important; else you are merely doing "plug-and-chug" Maths without any understanding. You need to focus on rigor only based on your needs and at your own pace. Concepts come first Formalism comes second.
A good example; In the Principia Newton actually uses the phrase Quantity of Motion for what we define today as Momentum. The phrase is evocative and beautifully captures the main concept instead of the bland p = m x v definition which though correct and needed for calculations conveys no mental imagery.
In Mathematics one should always approach a concept/idea from multiple perspectives including (but not limited to) Imagination, Conceptual, Graphical, Symbolic, Relationship, Applications, Definition/Theorem/Proof.
Thank you for the book link! One major problem I always had with calculus was that we didn't focus nearly enough on applications of it, outside of some optimization problems, which I loved.
I originally went for engineering, and took cal I and II, then switched to cs and poof all of the math heavy stuff vanished (except maybe some LA for graphics)
People should have at the minimum a conceptual idea of Calculus. A good motivation is Everyday Calculus: Discovering the Hidden Math All around Us by Oscar E. Fernandez - https://press.princeton.edu/books/paperback/9780691175751/ev...
> And if you do learn it, do so with rigor so you actually learn it
This is not strictly necessary for everybody. The conceptual ideas are what are important; else you are merely doing "plug-and-chug" Maths without any understanding. You need to focus on rigor only based on your needs and at your own pace. Concepts come first Formalism comes second.
A good example; In the Principia Newton actually uses the phrase Quantity of Motion for what we define today as Momentum. The phrase is evocative and beautifully captures the main concept instead of the bland p = m x v definition which though correct and needed for calculations conveys no mental imagery.
In Mathematics one should always approach a concept/idea from multiple perspectives including (but not limited to) Imagination, Conceptual, Graphical, Symbolic, Relationship, Applications, Definition/Theorem/Proof.