The problem I always had with math (when it came to integrals, anyway) was the whole 'dx' notation, where you apparently just had to "go with the flow" and understand what was being expressed. It ain't "d times x", it's this other thing that's syntactically similar to saying "ab" which means "a times b".
Someone on HN is going to hammer me. I just muddled through the ambiguity.
Then again, what I used to think was the real solution (an exensible grammar -- say, s-expressions -- which would remove the ambiguity) would result in really ugly-looking math.
[Don't get me started on denotational semantics. I tried, I really tried to understand the foundation of Standard ML through some DS-based books on the subject, but in the end I just got sick of yet another system of poorly defined heiroglyphics. Maybe I'm just allergic.]
One thing you learn in math/physics is all the different ways you can denote a derivative. It makes a lot more sense when you get into Lagrangian mechanics, ODEs/PDEs, QM, complex variables, your first analysis class, etc... classes where you learn why they denote operators and variables in certain ways because other ways don't make much sense given the context.
About that, one author of SICP build a new physics class based around functions for every physical operator, no more syntactic craze, just functions ( higher order though ). Check SICM on google.
This is exactly what I was going to reply when I saw the GP. SICM is a brilliant book I've only started that revolves around putting concrete understanding ahead of notation. Unlike most books of that type, this one is a seriously advanced math/physics work. At world class universities, upper division undergrads in Physics can study Lagrangian Mechanics in their third year if their calculus is good enough.
One note from the excellent introduction focused how to learn math (q.v.): "In his book on mathematical pedagogy [15], Hans Freudenthal argues that the reliance on ambiguous, unstated notational conventions in such expressions as f(x) and df(x)/dx makes mathematics, and especially introductory calcu- lus, extremely confusing for beginning students; and he enjoins mathematics educators to use more formal modern notation."
Someone on HN is going to hammer me. I just muddled through the ambiguity.
Then again, what I used to think was the real solution (an exensible grammar -- say, s-expressions -- which would remove the ambiguity) would result in really ugly-looking math.
[Don't get me started on denotational semantics. I tried, I really tried to understand the foundation of Standard ML through some DS-based books on the subject, but in the end I just got sick of yet another system of poorly defined heiroglyphics. Maybe I'm just allergic.]