I agree. Math is extremely subtle. And despite its nature as the most exacting and rigorous of sciences, the notation used in mathematics is anything but. Each author uses their own conventions. Abuse of notation runs rampant.
Sometimes the difference between theta and phi is more than just alpha conversion... some authors use certain variable names to communicate important properties that must be satisfied in the premise of theorems -- but without making those premises explicit.
A derivative is a 'special form' in calculus when it is so cleanly expressed as a higher-order function. And indefinite integrals introduce a mysterious constant, C, when really, what you're talking about is a multivalued-function!
I think math is pretty much the coolest subject one could study, but in many of the books I've read, the difficulty in understanding is evenly divided between the concepts and the author himself.
Sometimes the difference between theta and phi is more than just alpha conversion... some authors use certain variable names to communicate important properties that must be satisfied in the premise of theorems -- but without making those premises explicit.
A derivative is a 'special form' in calculus when it is so cleanly expressed as a higher-order function. And indefinite integrals introduce a mysterious constant, C, when really, what you're talking about is a multivalued-function!
I think math is pretty much the coolest subject one could study, but in many of the books I've read, the difficulty in understanding is evenly divided between the concepts and the author himself.