Post by Admin on Jun 7, 2017 8:58:52 GMT
Gary
This may just be a personal thing, but in doing the exercises 16-22 I have found the notational inconsistencies between quite a lot of the text of chapter 7, especially sections IV through VIII, and these exercises to be quite confusing.
For the most part, in the text, $p$ is used to represent a value of $f$ in the $f$-plane of the mapping $z\mapsto f$, and the word $p$-point is used to denote a preimage of $p$ in the $z$-plane. This is particularly prominent in subsection 1 of section IV on pages 346-347.
However, in the exercises 16-22, $p$ is used as a point in the $z$-plane and particularly in exercise 19. This has the potential to cause confusion particularly as the exercise talks about the critical point $p$ of an analytic function and the modular surface above $p$ etc.
This exercise requires one to use the results and ideas in the subsection mentioned above, where $a$ is used as a root or critical point and $p$ is used as the value of $f$ at the critical point.
I find it quite difficult to envisage the $z$-plane, the mapping $z\mapsto f$ to the $f$-plane, the modular surface, points on the modular surface, etc. and this inconsistency in the notation just makes it worse.
Vasco
This may just be a personal thing, but in doing the exercises 16-22 I have found the notational inconsistencies between quite a lot of the text of chapter 7, especially sections IV through VIII, and these exercises to be quite confusing.
For the most part, in the text, $p$ is used to represent a value of $f$ in the $f$-plane of the mapping $z\mapsto f$, and the word $p$-point is used to denote a preimage of $p$ in the $z$-plane. This is particularly prominent in subsection 1 of section IV on pages 346-347.
However, in the exercises 16-22, $p$ is used as a point in the $z$-plane and particularly in exercise 19. This has the potential to cause confusion particularly as the exercise talks about the critical point $p$ of an analytic function and the modular surface above $p$ etc.
This exercise requires one to use the results and ideas in the subsection mentioned above, where $a$ is used as a root or critical point and $p$ is used as the value of $f$ at the critical point.
I find it quite difficult to envisage the $z$-plane, the mapping $z\mapsto f$ to the $f$-plane, the modular surface, points on the modular surface, etc. and this inconsistency in the notation just makes it worse.
Vasco
